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 A n American National Standard
IEEE Recommended Practice for
Industrial and Commercial
Power Systems Analysis

Published by
The Institute of Electrical and Electronics Engineers, Inc

Distributed in cooperation with

Wiley-Interscience, a division of John Wiley & Sons, Inc

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 AN SI/IEEE
Std 399-1980

A n American National Standard

IEEE Recommended Practice for
Industrial and Commercial
Power Systems Analysis

Sponsor
Power System Technologies Committee
of the
IEEE Industry Applications Society

Approved December 20,1979

IEEE Standards Board

Approved June 28,1982

American National Standards Institute

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 Approved December 20,1979
IEEE Standards Board

Joseph L. Koepfinger, Chairman Irvin N. Howell,Jr, Vice Chairman

Ivan G. Easton, Secretary
G. Y. R. Allen Harold S . Goldberg J. E. May
William E. Andrus Richard J. Gowen Donald T. Michael*
C. N. Berglund H. Mark Grove R. L. F’ritchard
Edward Chellotti Loering M. Johnson F. Rosa
Edward J. Cohen Irving Kolodny Ralph M. Showers
Warren H. Cook W. R. Kruesi J. W.Skooglund
R. 0. Duncan Leon Levy W. E. Vannah
Jay Forster B. W. Whittington
*Member emeritus

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 IEEE Standards documents are developed within the Technical Com-
mittees of the IEEE Societies and the Standards Coordinating Commit-
tees of the IEEE Standards Board. Members of the committees serve
voluntarily and without compensation. They are not necessarily mem-
bers of the Institute. The standards developed within IEEE represent
a consensus of the broad expertise on the subject within the Institute
as well as those activities outside of IEEE which have expressed an in-
terest in participating in the development of the standard.
Use of an IEEE Standard is wholly voluntary. The existence of an
IEEE Standard does not imply that there are no other ways to pro-
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to change brought about through developments in the state of the art
and comments received from users of the standard. Every IEEE Stan-
dard is subjected to review at least once every five years for revision or
reaffirmation. When a document is more than five years old, and has
not been reaffirmed, it is reasonable to conclude that its contents,
although still of some value, do not wholly reflect the present state of
the art. Users are cautioned t o check to determine that they have the
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Comments for revision of IEEE Standards are welcome from any
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 Foreword
(This Foreword is not a part of IEEE Std 399-1980, IEEE Recommended Practice for Industrial
and Commercial Power Systems Analysis.)

This Recommended Practice is the product of about ten years of effort by a work-
ing group of the Power System Technologies Committee of IEEE Industry Applica-
tions Society. It is intended as a practical, general treatise on the theoretical basis of
power system analysis, and as a reference work on the analytical techniques most
commonly applied to electric power systems in industrial plants and commercial
buildings.
IEEE Recommended Practice for Industrial And Commercial Power System
Analysis, the IEEE Brown Book, joins the series of Color Books sponsored by the
Power System Technologies Committee of IEEE Industry Applications Society. It is
both complementary and supplementary to the other color books, extending the
coverage of some topics which they introduce as well as discussing some entirely
new material.
Comments, corrections, and suggestions for the next revision of the Brown Book
are welcome and should be submitted to the
IEEE Standards Board
345 East 47th Street
New York, New York 10017.
At the time it recommended these practices, the working group of the Power Sys-
tem Technologies Committee had the following members and contributors :

Richard H. McFadden, Chairman

R. Gene Baggs A. Dewitt Patton

Graydon M. Bauer H. Paul Rouleau
Kao Chen David D. Shipp
Lonnie E. Crawford David H. Smith
Leon C. Glahn James F. Smith
M. Shan Griffith J. R. Smith
William R. Haack George A. Terry
John Lockhart George W. W alsh
Russell 0. Ohlson A. Jack Williams, J r
Myron Zucker

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 Industrial and Commercial
Power Systems Analysis
1st Edition

Working Group Members and Contributors

Richard H. McFadden, Working Group Chairman

Chapter 1 - Introduction: Kao Chen

Chapter 2 - Applications of Power System Analysis: Leon Glahn
Chapter 3 - Analytical Procedures: M. Shan Griffith
Chapter 4 - System Modeling: Paul Rouleau
Chapter 5 - Load Flow Studies: J. R. Smith
Chapter 6 - Short Circuit Studies: David H. Smith
Chapter 7 - Stability Studies: Richard H. McFadden
Chapter 8 - Motor Starting Studies: A. J. Williams, Jr and M. Shan Griffith
Chapter 9 - Harmonic Studies: David Shipp
Chapter 10 - Switching Transients Studies: George Walsh
Chapter 11 - Reliability Studies: A. D. Patton
Chapter 12 - Grounding Mat Studies: L. E. Crawford and M. Shan Griffith
Chapter 13 - Computer Services: John Lockhart

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 Contents
SECTION PAGE

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.1 General Discussion ......................................... 21
1.2 History of Power System Studies .............................. 21
1.3 Applying Power System Analysis Techniques t o Industrial
and Commercial Power Systems ............................. 22
1.4 Purposes of this Recommended Practice ........................ 22
1.4.1 WhyaStudy ........................................ 22
1.4.2 How t o Prepare for a Power System Study . . . . . . . . . . . . . . . . . 22
1.4.3 The Most Important System Studies ...................... 23
1.5 Standard References ........................................ 23
2 . Applications of Power System Analysis ............................. 24
2.1 Introduction .............................................. 24
2.2 Load Flow Studies ......................................... 25
2.3 Fault and Short-circuit Studies ............................... 25
2.4 Stability Studies ........................................... 25
2.5 Motor Starting Studies ...................................... 26
2.6 System Transients Studies ................................... 26
2.7 Reliability Analysis ........................................ 26
2.8 Power Generation Planning .................................. 26
3. Analytical Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 The Fundamentals .......................................... 29
3.2.1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.3 The Thevenin Equivalent Circuit ......................... 32
3.2.4 The Sinusoidal Forcing Function ........................ 34
3.2.5 Phasor Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.6 The Fourier Representation ............................ 37
3.2.7 The Single-phase Equivalent Circuit ...................... 37
3.2.8 The Symmetrical Component Analysis .................... 39
3.2.9 The Per Unit Method .................................. 42
3.3 References and Bibliography ................................. 43

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 SECTION PAGE

4 . System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 Review of Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.1 Passive Elements ................................... 45
4.3.2 Active Elements ................................... 46
4.4 Power Network Solution ................................... 49
4.5 ImpedanceDiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6 Extent of the Model ....................................... 55
4.6.1 General .......................................... 55
4.6.2 Utility Supplied Systems ............................. 55
4.6.3 Isolated Systems ................................... 55
4.6.4 Swing Bus ........................................ 56
4.7 Models of Branch Elements ................................. 56
4.7.1 Lines ............................................ 56
4.7.1.1 Long Lines ................................ 58
4.7.1.2 Medium Lines .............................. 58
4.7.1.3 Short Lines ................................ 59
4.7.2 Cables ............................................ 59
4.7.3 Determination of Constants .......................... 60
4.7.3.1 Resistance ................................. 60
4.7.3.2 Inductive Reactance ......................... 61
4.7.3.3 Shunt Capacitive Reactance . . . . . . . . . . . . . . . . . . . 62
4.7.4 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7.5 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.7.6 Transformers ...................................... 63
4.7.6.1 Two-Winding Transformers .................... 63
4.7.6.2 Transformer Taps ........................... 64
4.7.6.3 Three-Winding Transformers . . . . . . . . . . . . . . . . . . . 65
4.7.6.4 Phase-Shifting Transformers . . . . . . . . . . . . . . . . . . . 66
4.7.6.5 Other Transformer Models .................... 66
4.8 Power System Data Development ............................. 66
4.8.1 Per Unit Representations ............................. 66
4.8.2 Applications Example ............................... 68
4.9 Models of Bus Elements .................................... 72
4.9.1 Loads in General ................................... 72
4.9.2 Induction Motors .................................. 75
4.9.2.1 Constant kVA Model ......................... 77
4.9.2.2 Models for Short-circuit Studies . . . . . . . . . . . . . . . . 78
4.9.2.3 Constant Impedance Model .................... 79
4.9.3 Synchronous Machines .............................. 79
4.9.3.1 Steady State Models ......................... 79
4.9.3.1.1 Generators ........................ 79
4.9.3.1.2 Synchronous Condenser . . . . . . . . . . . . . . 80
4.9.3.1.3 Synchronous Motors . . . . . . . . . . . . . . . . 80

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 SECTION PAGE
4.9.3.2 Short-circuit Models ......................... 80
4.9.3.3 Stability Models ............................ 84
4.9.3.3.1 Classical Model ..................... 84
4.9.3.3.2 The H Constant .................... 84
4.9.3.3.3 Stability Model Variations . . . . . . . . . . . . 85
4.9.3.4 Exciter Models ............................. 85
4.9.3.5 Prime Movers and Governor Models . . . . . . . . . . . . . 88
4.10 Miscellaneous Bus Elements Models ........................... 88
4.10.1 Lighting and Electric Heating ......................... 88
4.10.2 Electric Furnaces ................................... 88
4.10.3 ShuqCapacitors ................................... 89
4.10.4 Shunt Reactors .................................... 89
4.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 . Load Flow Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.1 Introduction ............................................. 91
5.2 System Representation ..................................... 92
5.3 System Data Organization .................................. 94
5.4 Load Flow Study Example .................................. 94
5.4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4.2 Input Requirements ................................. 94
5.4.3 Special Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.5 Input Card Preparation ..................................... 101
5.6 Load Flow Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.7 Load Flow Analysis ....................................... 105
5.8 Load Flow Output Presentation .............................. 106
5.9 Load Flow Analysis ....................................... 106
5.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6. Short-circuit Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Short-circuit Study Procedure ................................ 109
6.2.1 Preparing a One-Line Diagram ........................... 109
6.2.2 Determining Depth and Accuracy of a Study . . . . . . . . . . . . . . 110
6.2.3 Calculating Impedance Values ........................... 110
6.2.4 Developing an Impedance Diagram ....................... 111
6.2.5 Converting Impedances to a Common Base . . . . . . . . . . . . . . . . . 111
6.2.6 Interpretation and Application of the Study . . . . . . . . . . . . . . . . 111
6.3 Use of the Computer ....................................... 112
6.4 Short-circuit Study Example ................................. 113
6.5 Digital Computer Program Output Records ...................... 119
6.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7 . Transient Stability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 Stability Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2.1 Definition of Stability ................................. 125

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 SECTION PAGE
7.2.2 Steady-State Stability ................................. 125
7.2.3 Transient Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.2.4 Two-Machine Systems ................................. 128
7.2.5 Multimachine Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3 Problems Caused by Instability ............................... 128
7.4 System Disturbances that can Cause Instability . . . . . . . . . . . . . . . . . . . 129
7.5 Solutions t o Stability Problems ............................... 129
7.5.1 System Design ....................................... 129
7.5.2 Design and Selection of Rotating Equipment . . . . . . . . . . . . . . . 130
7.5.3 System Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.5.4 Voltage Regulator and Exciter Characteristics . . . . . . . . . . . . . . . 130
7.6 Transient Stability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.6.1 History ............................................ 130
7.6.2 How Stability Programs Work ........................... 131
7.6.3 Simulation of the System .............................. 131
7.6.4 Simulation of Disturbances ............................. 132
7.6.5 Data Requirements for Stability Studies . . . . . . . . . . . . . . . . . . . 132
7.6.6 Stability Program Output .............................. 133
7.6.7 Interpreting Results-Swing Curves ....................... 134
7.7 Stability Studies on a Typical System .......................... 134
7.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8 . Motor Starting Studies .......................................... 140
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.2 Need for Motor Starting Studies ............................... 140
8.2.1 Problems Revealed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.2.2 Voltage Dips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.2.3 Weak Source Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2.4 Special Torque Requirements ........................... 141
8.3 Recommendations ......................................... 142
8.3.1 Voltage Dips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.3.2 Analyzing Starting Requirements ........................ 144
8.4 Types of Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.4.1 The Voltage Drop Snapshot ............................ 144
8.4.2 The Detailed Voltage Profile ............................ 144
8.4.3 The Motor Torque and Acceleration Time Analysis . . . . . . . . . . 144
8.4.4 Adaptations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.5 Data Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.5.1 Basic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.5.2 Simplifying Assumptions ............................... 146
8.6 Solution Procedures and Examples ............................. 146
8.6.1 The Mathematical Relationships ......................... 147
8.6.2 Other Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.6.3 The Simple Voltage Drop Determination . . . . . . . . . . . . . . . . . . 153
8.6.4 Time-Dependent Bus Voltages ........................... 156
8.6.5 The Speed-Torque and Motor Accelerating Time Analysis . . . . . 159

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 SECTION PAGE

8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

8.8 References ................................................ 162
9 . Harmonic Analysis Studies ....................................... 164
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
9.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
9.3 General Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9.3.1 What are Harmonics? .................................. 165
9.3.2 Resonance .......................................... 166
9.4 Modeling ................................................ 167
9.5 Solutions t o Harmonic Problems .............................. 169
9.6 When is a Harmonic Study Required? .......................... 175
9.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
1 0. Switching Transient Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.2 Basic Concept of Switching Transients ........................ 177
10.3 Control of Switching Transients ............................. 178
10.4 Methods of Analysis ...................................... 178
10.5 Analysis Aids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
10.6 Data Required for a Switching Transient Study . . . . . . . . . . . . . . . . . 180
10.7 Switching Transient Problem Areas .......................... 181
10.8 Switching Transient Study Objectives ........................ 182
10.9 Switching Transient Study via Transient Network Analyzer (TNA) . . 182
10.9.1 Model Components ............................... 183
10.9.2 Model Scale Factors .............................. 184
10.9.3 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
10.9.4 Study Procedures ................................ 185
10.9.5 Example of TNA Study Case Documentation . . . . . . . . . . . 185
10.10 Field Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
10.10.1 Signal Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
10.10.2 Signal Circuits, Terminations, and Grounding . . . . . . . . . . . 188
10.10.3 Transient Measurement/Monitoring Instrumentation . . . . . 189
10.10.4 Objectives of Field Measurements .................... 190
11 Reliability Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
191
11.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.3 System Reliability Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
11.4 Data Needed for System Reliability Evaluations . . . . . . . . . . . . . . . . . 193
11.5 Method for System Reliability Evaluation ...................... 193
11.5.1 Service Interruption Definition ........................ 194
11.5.2 Failure Modes and Effects Analysis ..................... 194
115.3 Computation of Quantitative Reliability Indexes . . . . . . . . . . 195
11.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
1 2. Grounding Mat Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

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 SECTION PAGE
12.2 The Human Factor ........................................ 197
12.3 The Physical Circuit ....................................... 200
12.3.1 Ground Resistivity ................................. 200
12.3.2 Fault Current-Magnitude and Duration . . . . . . . . . . . . . . . . . 201
12.3.3 Fault Current-The Role of Grid Resistance . . . . . . . . . . . . . . . 202
12.3.4 GridGeometry .................................... 203
12.4 The Computer in Action ................................... 206
12.5 Input Data Requirements ................................... 208
12.6 Typical Computer Output .................................. 214
12.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
12.8 References .............................................. 214
13. Computer Services ............................................. 217
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
13.2 Computer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
13.2.1 In-House Systems .................................. 217
13.2.2 Commercial Computing Services ....................... 218
13.3 Types of Computing Service ................................. 218
13.4 Use of Computing Services .................................. 219
13.5 Availability of Computing Services ............................ 220
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

FIGURES
Fig 1 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Fig 2 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Fig 3 The Thevenin Equivalent ..................................... 31
Fig 4 Current Flow of a Thevenin Equivalent Representation . . . . . . . . . . . . . 33
Fig 5 Fault Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Fig 6 The Sinusoidal Forcing Function .............................. 35
Fig 7 The Phasor Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Fig 8 The Fourier Representation .................................. 36
Fig 9 (a) Three-phase Diagram. (b) Single-phase Equivalent.
and (c) One-Line Diagram .................................... 38
Fig 1 0 (a) Three-phase Diagram. (b) Single-phase Equivalent.
and (c) One-Line Diagram .................................... 39
Fig 11 The Symmetrical Component Analysis .......................... 40
Fig 1 2 (a) Classical Ohmic Representation. (b) Per Unit Representation . . . . . . 43
Fig 13 Squirrel Cage Induction Motor Model ........................... 47
Fig 1 4 Section of a Typical Industrial Plant Impedance Diagram . . . . . . . . . . . . 48
Fig 15 Single Line Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Fig 1 6 ImpedanceDi agram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Fig 1 7 Flow Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Fig 18 Suggested Format Raw Data Diagram ........................... 54
Fig 1 9 Equivalent Circuit of Short Conductor .......................... 56

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 FIGURE PAGE
Fig 20 (a) Line with Distributed Constants. (b) Long Line
Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Fig 21 Medium Line Equivalent Circuits. (a) Nominal n (b) Nominal T . . . . . . . 59
Fig 22 Short Line Equivalent Circuit ................................. 59
Fig 23 Two-Winding Transformer Equivalent Circuits .................... 63
Fig 24 Two-Winding Transformer Approximate Equivalent Circuits . . . . . . . . . 64
Fig 25 Three-Winding Transformer Approximate Equivalent Circuits.
(a) Simplified-Delta. (b) Simplified-Wye ....................... 65
Fig 26 Impedance and Flow Diagrams. (a) Impedance Diagram.
(b) Flow Diagram .......................................... 67
Fig 27 Impedance Diagram Raw Data ................................ 69
Fig 28 Impedance Diagram Per Unit data .............................. 73
Fig 29 Effect of Voltage Variations for Three Types of Loads . . . . . . . . . . . . . . 74
Fig 30 Induction Motor Equivalent Circuit ............................ 75
Fig 31 Induction Motor Torque Versus Speed .......................... 76
Fig 32 Induction Motor Current Versus Speed .......................... 76
Fig 33 Induction Motor Power Factor Versus Speed ..................... 77
Fig 34 Effect of Votlage Variations on Typical Induction Motor
Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Fig 35 Model of Induction Motor for Short-circuit Study . . . . . . . . . . . . . . . . . 78
Fig 36 V--C urves. Synchronous Motor. 2000 hp. 4000 V. 180 rlmin.
0.8 Lead Power Factor ...................................... 81
Fig 37 Models of Synchronous Machines for Short-circuit Studies . . . . . . . . . . 83
Fig 38 General Model for AC Machines in Short-circuit Studies . . . . . . . . . . . . 84
Fig 39 Saturation Curves .......................................... 86
Fig 40 IEEE Type 1 Excitation System ............................... 86
Fig 41 Lagcircuit ............................................... 87
Fig 42 Leadcircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Fig 43 Generators Connected t o their Bus ............................. 93
Fig 44 Connection of Buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Fig 45 Auxiliary Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Fig 46 One-Line Connection Diagram ................................ 95
Fig 47 ImpedanceDiagram ......................................... 96
Fig 48 InputDataSheet F o r m 1 .................................... 97
Fig 49 Input Data Sheet Form 2 .................................... 99
Fig 50 Input Data Sheet Form 3 .................................... 100
Fig 51 Printed Computer Output .................................... 103
Fig 52 Printed Computer Output .................................... 104
Fig 53 Typical Industrial Plant Electric System ......................... 107
Fig 54 One-Line Diagram of Industrial System for Short-circuit
Study Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Fig 55 Impedance Diagram for Short-circuit Study Example . . . . . . . . . . . . . . . 117
Fig 56 Data Taken from the Impedance Diagram and Arranged for Program
Input Data Paper Tape Medium Voltage Interrupting Calculation . . . . . . 120
Fig 57 Program Listing of Input Data from Data Tape .................... 121

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 FIGURE PAGE
Fig 58 Sample Computer Output Listing of Remote Bus Voltages and
Short-circuit Contributions t o the Faulted Bus. Medium Voltage
Interrupting Case Short-circuit Study ........................... 122
Fig 59 Computer Output Giving Fault Levels in MVA for the Four Faulted
Buses. Medium Voltage Interrupting Case Short-circuit Study . . . . . . . . 123
Fig 60 Simplified Two-Machine Power System .......................... 125
Fig 6 1 Torque Versus Rotor Angle Relationship for Synchronous
Machines in Steady State ..................................... 127
Fig 62 Computer Printout of Swing Curves for Case I Fault on
System in Fig 6 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Fig 63 Single-Line Diagram of System whose Swing Curves Appear in
Figs62and64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Fig 64 Computer Printout of Swing Curves for Case I1 Fault on System
ShowninFig63 ........................................... 137
Fig 65 Single-Line Diagram of a Typical Large Industrial Power System
with On-Site Generation ..................................... 138
Fig 66 Typical Generator Terminal Voltage Characteristics for Various
Exciter Regulator Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Fig 67 Typical Wound Rotor Motor Speed-Torque Characteristics . . . . . . . . . . . 143
Fig 68 Typical Motor and Load Speed-Torque Characteristics . . . . . . . . . . . . . . 145
Fig 69 Simplified Equivalent Circuit for a Motor on Starting . . . . . . . . . . . . . . . 146
Fig 70 Simplified Impedance Diagram ................................ 147
Fig 71 Typical One-Line Diagram .................................... 148
Fig 72 Impedance Diagram for System in Fig 71 ........................ 149
Fig 73 Revised Impedance Diagram Showing Transient Reactance
ofGenerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig 74 Simplified Representation of Generator Exciter/Regulator System . . . . . 151
Fig 75 Load Flow Computer Output - Steady State ..................... 154
Fig 76 Load Flow Computer Output - Voltage Dip on Motor Starting . . . . . . . 155
Fig 77 Simplified System Model for Generator Representation
During Motor Starting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Fig 78 Typical Output - Generator Motor Starting Program . . . . . . . . . . . . . . . 157
Fig 79 Typical Output . Generator Motor Starting Program . . . . . . . . . . . . . . . 157
Fig 80 Typical Output . Plot of Generator Voltage Dip . . . . . . . . . . . . . . . . . . 158
Fig 81 Typical Output . Plot of Motor Voltage Dip ..................... 158
Fig 82 Simplified Representation of Typical Regulator/Exciter
Models for Use in Computer Programs .......................... 159
Fig 83 Simplified System Model for Accelerating Time and
Speed-Torque Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Fig 84 Typical Motor Speed-Current Characteristic ...................... 160
Fig 85 Typical Output . Motor Speed-Torque and Accelerating
TimeProgram ............................................. 161
Fig 86 6.Phase, 6-Pulse Rectifier .................................... 165
Fig 87 6.Phase, 6-Pulse Rectifier .................................... 165
Fig 88 SeriesCircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

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 FIGURE PAGE

Fig 89 Impedance Versus Frequency ................................. 166

Fig 90 Parallelcircuit ............................................. 167
Fig 91 Impedance Versus Frequency ................................. 167
Fig 92 Typical Thyristor Drive Characteristics .......................... 168
Fig 93 No 1 Scheme for Adequate Filtering ............................ 170
Fig 94 No 2 Scheme for Adequate Filtering ............................ 170
Fig 95 No 3 Scheme for Adequate Filtering ............................ 170
Fig 96 6-Phase Rectifier Transformers ................................ 171
Fig 97 24-Phase System ........................................... 171
Fig 98 Partial One-Line Diagram .................................... 172
Fig 99 Example of TNA Case Sheet from an Actual
Switching Transient Study ................................... 186
Fig 100 Oscillogram 12-10-2 as Described in TNA
Case Sheet of Fig 99 ........................................ 187
Fig 101 TouchPotenti al ............................................ 199
Fig 102 Step Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
Fig 103 Physical Model Used in Calculating Voltage at
Point a Due t o a Single Conductor ............................. 205
Fig 104 Experimental Grids Showing Various (Mesh) Arrangements . . . . . . . . . . 207
Fig 105 Typical Ground Mat Design Showing All Pertinent
Soil and System Data ....................................... 209
Fig 106 Typical Ground Mat Design Showing Meshes with Hazardous
Potentials as Identified by Computer Analysis .................... 210
Fig 107 Typical Ground Mat Design, First Refinement Showing
Meshes with Hazardous Touch Potentials ........................ 211
Fig 108 Typical Ground Mat Design, Final Refinement with no
Hazardous Touch Potentials .................................. 212
Fig 109 Typical Ground Mat Layout Showing Possible Locations of
Critical Step and Touch Potentials Near Grid Corners . . . . . . . . . . . . . . . 213
Fig 110 Sample Output Report, Computer Calculated Ground
Gridpotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

TABLES

Table 1 Defining Equation References for Conductance.

Susceptance. Impedance and Admittance ....................... 46
Table 2 Four Expressions for Power Quantities ......................... 47
Table 3 Fundamental Equations for Translation and Rotation . . . . . . . . . . . . . . 49
Table 4 Comparison of Overhead Lines and Cable Constants . . . . . . . . . . . . . . . 60
Table 5 ConductorData ........................................... 60
Table 6 System Base Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Table 7 CableData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Table 8 Basic Impedance Values Required for Three-phase
Short-circuit Studies ....................................... 111

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 TABLE PAGE

Table 9 Assumed Values for Motors when Exact Impedances

arenotKnown ............................................ 115
Table 10 Modification Factors for Momentary and Interrupting
Duty Calculations ......................................... 115
Table 11 Sample Summary of Results for Example Short-circuit Study . . . . . . . 124
Table 12 Auto-Transformer-Line Starting Current ........................ 152
Table 13 Average Values for Accelerating Torque Over Time
Interval Defined by a Speed Change ........................... 160
Table 14 First Computer Solution: Without Filters ....................... 173
Table 15 Second Computer Solution: With Filters ........................ 174
Table 16 Frequency and Expected Duration Expressions for
Interruptions Associated with Forced Outages Only . . . . . . . . . . . . . . . 195
Table 17 Representative Values of Soil Resistivities ....................... 201
Table 18 Decrement Factor for Use in Calculating Electrical Shock
Effect of Asymmetrical ac Currents ............................ 201

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 1. Introduction

1.1 General Discussion. IEEE Std 399- ments the other IEEE color book
1980, IEEE Recommended Practice for standards, and emphasizes up-to-date
Industrial and Commerical Power System techniques in system studies which are
Analysis, commonly known as the IEEE most applicable t o industrial and com-
Brown Book, is published by the Institute mercial power systems. Today, such tech-
of Electrical and Electronics Engineers niques are mostly computer oriented.
(IEEE) as a reference source for plant 1.2 History of Power System Studies.
electrical engineers in making power sys- The planning, design, and operation of a
tem studies. The IEEE Brown Book can power system require continual and
also be helpful in preparing system comprehensive analyses t o evaluate cur-
modeling and data acquisition for an rent system performance and t o ascertain
outside engineering consultant t o per- the effectiveness of alternative plans for
form necessary engineering studies prior system expansion.
t o designing a new system or expanding The computational work t o determine
an existing power system. Such informa- power flows and voltage levels resulting
tion will help ensure high standards of from a single operating condition for
power system reliability and maximize even a small network is all but insur-
the utilization of capital investment. mountable if performed by manual
The IEEE Brown Book has been pre- methods. The need for computational
pared on a voluntary basis by engineers aids led t o the design of a special purpose
and designers functioning as the Power analog computer (AC Network Analyzer)
System Analysis Working Group within as early as 1929. It provided the ability
the IEEE, under the Industrial Power t o determine load flows and system
Systems Department of The Industry voltage during normal and emergency
Applications Society. This recommended conditions and to study the transient
practice is not intended as a replacement behavior of the system resulting from
for the many excellent texts available in fault conditions and switching opera-
this field. The IEEE Brown Book comple- tions.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

The earliest application of digital com- technology now enable engineers t o

puters to power system problems dates communicate with the computer and
back to the late 1940s. Most of the early change or modify the system t o meet
applications were limited in scope, how- whatever design criteria may arise.
ever, because of the small capacity of the
punched card calculators in use during 1.4 Purposes of this Recommended Prac-
that period. The large scale digital com- tice
puters became available in the middle 1.4.1 Why a Study. As is stated in
1950s. The initial success of the load Section 2, the planning, design, and
flow program led t o the development of operation of industrial or commercial
programs for short circuit and transient power systems require several studies t o
stability calculations. assist in the evaluation of the initial and
Today, the digital computer is an in- future system performance, reliability,
dispensable tool in power system plan- safety, and ability to grow with produc-
ning where it is necessary to predict tion or operating requirements. The
future growth and simulate day-to-day studies most likely needed are load-flow
operations over periods of 20 years or studies, short-circuit studies, stability
more. studies, and motor-starting studies. A
brief summary of such studies and what
1.3 Applying Power System Analysis each can accomplish are given in Section
Techniques t o Industrial and Commercial 2 t o help a plant engineer determine
Power Systems. As computer technology overall system needs before he proceeds
has advanced, so has the complexity of with specific planning and engineering
industrial and commercial power systems. design.
These power systems have grown in re- Additional studies of transients, reli-
cent decades with capacities far exceeding ability, grounding, and harmonics may
that of a small electric utility system. also be required. The plant engineer in
Today, plant or building management charge of system design must decide
personnel are highly concerned with which studies are needed t o ensure that
system interruptions and their effect on the system will operate safely, economi-
overall operation. Therefore, they de- cally, and efficiently over the expected
mand assurances of maximum return on life of the system.
capital investment for any sizable expan- 1.4.2 How t o Prepare for a Power Sys-
sion. The complexity of modem indus- tem Study. For a plant engineer t o solve
trial and commercial power systems has a power system analysis problem, he
made manual performance of power sys- must be thoroughly familiar with valid
tem studies difficult and time consuming, electrical engineering fundamentals, such
if not impossible. However, through the as the Thevenin equivalent circuit, the
use of digital computers these studies phasor representation, the Fourier series,
can be made with relative ease. Answers symmetrical components, etc. He can
t o many perplexing questions regarding then analyze the problem and prepare
impact of expansion on the system, necessary equivalent circuits and basic
short circuit capacity, stability, load system data before proceeding with a
distribution, etc, can be intelligently computer program. Failure t o use a valid
obtained. analytical procedure to establish a sound
The recent advances in computer basic approach to the problem could

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 IEEE
INTRODUCTION Std 399-1980

lead t o disastrous consequences in both lowing sections represent the most needed
the design and operation of a system. studies for the design or operation of an
Section 3 offers an excellent review of industrial or commercial power system :
the most essential fundamentals in a Section 5 , Load Flow; Section 6, Short
system study. Circuit; Section 7, Stability; Section 8,
To set up a computer program for sys- Motor Starting; Section 9, Harmonics;
tem analysis, certain basic data must be Section 10,Switching Transients; Section
gathered with accuracy and proper pre- 11, Reliability; and Section 12,Ground
sentation. System modeling is a must Mat. Each of the above sections contains
technique. The extent of system repre- a sample study which includes a com-
sentation, choosing the swing and in- puter input data file and a computer
finite bus, restrictions in terms of nodes print-out for that specific study. The
(buses) and branches (lines and trans- purpose of each study and what can be
formers), balanced three-phase network achieved by it are briefly explained.
and a single-phase equivalent network, After studying these sections, a plant
single line diagram, impedance diagram, engineer should be better equipped in
etc, are all important inputs t o a mean- preparing necessary data and criteria for
ingful system study. a specific computer study if the necessity
Section 4 deals with system modeling arises. The study can be performed in-
and data requirements t o illustrate how house or by an outside consultant. There
these basic inputs for a study can be is a growing number of consulting firms
prbperly prepared or organized. that specialize in system studies with
Once the basic preparations are com- reasonable costs if the plant engineer can
pleted, the next step is t o look for an supply the necessary system data with a
actual computer program, whether it be fair degree of correctness and accuracy.
in-house or a commercial computing
service. Today, many types of comput- 1.5 Standard References. The following
ing services are available, such as batch, standards were used as references in the
time-sharing, and consulting services. A preparation of this standard :
plant engineer must select the most ANSI/IEEE Std 142-1972,IEEE Recom-
suitable configuration for his needs. mended Practice for Grounding of Indus-
Section 13 discusses the basic compu- trial and Commercial Power Systems
tation methods, various types of compu-
IEEE Std 141-1976, IEEE Recommended
ter systems and their requirements, and
Practice for Electric Power Distribution
the availability of commerical computing
for Industrial Plants
services and their capabilities. Section 13
gives a plant engineer the basic knowledge IEEE Std 241-1974, IEEE Recommended
and direction of approach whenever he is Practice for Electric Power Systems in
called upon t o perform a power system Commercial Buildings
study with the aid of a computer pro- IEEE Std 242-1975,IEEE Recommended
gram. Practice for Protection and Coordination
1.4.3 The Most Important System of Industrial and Commercial Power
Studies. For the plant engineer, the fol- Systems

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

2. Applications of
Power System Analysis

2.1 Introduction. The planning, design duction of time-sharing techniques, have

and operation of industrial power systems helped t o reduce computing costs. Time-
require several studies to evaluate the sharing terminals can be installed in any
current system performance, reliability, office. Some are portable and can be car-
safety, and ability t o grow with produc- ried t o the industrial site. By means of a
tion requirements. Plant management is telephone line, the terminal can be con-
concerned with system outages, their nected t o a large computer system located
effect on production, and in maximizing many miles away. By way of the terminal,
utilization of capital investment. Man- the engineer has access t o the computer
agement requests justifications before and the power system analysis programs
decisions are made regarding the addi- stored in its memory. The user does not
tion of equipment in the system and have t o be familiar with computer pro-
its impact on future system operation. gramming or languages. Program manuals
The complexity of modern industrial describe t o the engineer, in a simple,
power systems makes such studies diffi- logical way, how to feed information
cult, tedious and time consuming t o per- into the computer, what kind of input
form manually. By using digital com- formats t o use, the output options and
puters, however, these computational how t o store his master file for further
tasks have been extremely simplified. system studies, changes and modifi-
cations. The cost of running these
Modern Digital Computers. The modern programs and the speedy way in which
digital computer offers power system the results are obtained is very surpris-
engineers a powerful tool t o perform ing. In fact, the engineer can converse
more effective studies of any industrial with the computer t o change or modify
power system. Computers help engineers the system t o meet whatever design
design optimum power systems at mini- criteria are imposed. Power system
mum cost, regardless of system complex- studies given below can be performed
ity. Recent advances in computer tech- digitally using the time-sharing computer
nology, and in particular, the intro- access method.

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 IEEE
APPLICATIONS OF POWER SYSTEM ANALYSIS Std 399-1980

2.2 Load Flow Studies. Load flow studies breakers are called upon t o open the line
determine the voltage, current, power, on both sides of the fault. Both these
and power factor or reactive power at currents differ widely from the current
various points in a power system under that would flow under steady-state con-
existing or contemplated conditions of ditions if the fault were not isolated
normal and emergency operation. Load from the rest of the system by the opera-
flow studies are essential in planning the tion of circuit breakers. The proper
system. They are used to determine the selection of circuit breakers and switch-
best operating procedure for the system, gear depends on two factors, the current
especially in the event of a loss of one or flowing immediately after the fault
more generating units or transmission occurs and the current that the breaker
lines. They offer valuable information must interrupt. Short-circuit calculations
regarding system losses, data for equip- consist of determining these currents for
ment specifications, overall system capa- various types of faults at various loca-
bility and limitations, proper settings of tions in the system. The data obtained
transformers in the system, and optimiza- from fault calculations also determine
tion of circuit usage in the system. Load the settings of relays which control the
flow studies can be used t o study an in- circuit breakers.
dustrial power system under suddenly Digital computers are used effectively
applied loads (impact loads). Impact in the calculation of the three-phase
load studies are essential in determining short-circuit levels at various points in
whether this type of load can be im- the system, and in determining the
posed on an existing system design. Any momentary and interrupting ratings of
changes needed in system design t o en- circuit breakers. Line-to-ground faults
sure the successful operation of the over- and double-line short circuits can also be
all system are also determined. Load digitally analyzed. In this aspect, the
flow studies also determine the most method of symmetrical components used
suitable location of capacitors in the in the computer model represents the
system for power factor improvement. system sequence networks and enables
Because of the complexity of load flow the calculation of unsymmetrical faults
calculations, digital computers are used in the system. Without digital computers,
extensively in such studies. Digital com- such calculations are tedious and time
puter models have been developed to consuming.
study practically any industrial power
system under any loading condition and 2.4 Stability Studies. In industrial power
to provide the initial system data (initial systems, the current which flows in an ac
system power flows, voltages at various generator or synchronous motor depends
system nodes, and initial machines’ elec- on :
trical angles) for transient stability (1)The magnitude of its generated, or
studies. internal voltage
(2) The phase angle OI its internal volt-
2.3 Fault and Short-circuit Studies. The age with respect t o the phase angle of
current which flows in different parts of the internal voltage of every other
an industrial power system immediately machine in the system
after a fault differs from that flowing a (3) The characteristics of the network
few cycles later, just before circuit and loads

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

The problem of stability is maintaining 2.6 System Transients Studies. Industrial

the synchronous operation of generators power systems that include arc furnaces
and motors in the system. and capacitor banks, resonance and
Stability studies are usually complex, switching transients can impose serious
but by using digital computers, such problems. By using modern digital
studies can be performed effectively at a analysis techniques, all such problems
relatively reasonable cost. Depending on can be detected early in the design stage.
the program used, the synchronous gen- These computer programs are also used
erators are simulated t o include voltage in investigating the effect of adding
regulators, excitation systems and gover- capacitor banks t o an existing system,
nor response. Motors are represented by the switching surges in a system, system
their dynamic characteristics and system response t o lightning surges, lightning ar-
disturbances are simulated digitally. restor applications, ferro-resonance prob-
Through analysis, a thorough under- lems and system transient recovery
standing of the power system perform- voltage.
ance under various system disturbances 2.7 Reliability Analysis. When comparing
can be determined. various industrial power system design
2.5 Motor Starting Studies. Starting large alternatives, system reliability and cost
synchronous or induction motors in an are essential factors in selecting optimum
industrial power system can be a prob- design. Using probability and statistical
lem. It is preferable t o start these motors analysis techniques, the system reliability
across the line, if possible. This can cause can be studied in depth with digital sim-
severe voltage dips in the system how- ulation techniques.
ever, and, in certain circumstances, the Interruptions. Reliability is expressed
motor may not be able t o break away as the frequency of interruptions and
from standstill or might stall during expected number of hours of interrup-
acceleration. tion during one year of system operation.
By using digital computer techniques, Momentary and sustained system inter-
all such problems can be predicted in ruptions, component failures and outage
advance before the installation of the rates are used in available digital com-
motor in the system. If a starting device puter reliability programs to compute
is needed, its characteristics and rating overall system reliability indexes at any
are determined by this computer motor node in the system, and t o investigate
their sensitivity to parameter changes.
start-up simulation technique.
With these results, management can
Available computer programs simulate
select the optimum power system design
the dynamic characteristics of the motor
and justify the decision when requested.
digitally. From these programs, the
motor’s voltage, current, speed, torque, 2.8 Power Generation Planning. In plan-
and acceleration time can be computed as ning industrial power systems, manage-
well as system voltage dips and currents ment is faced with certain difficult
at various time intervals from motor start- questions. One problem is the decision
ing t o full load speed. If a reactor or of whether t o build a local power plant
other starting device is required for motor or t o purchase the required power from
starting, the speed at which switching a neighboring utility system. In case of
should occur can be determined. local generation expansion, the unit type,

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 IEEE
APPLICATIONS OF POWER SYSTEM ANALYSIS Std 399-1980

size, and time of availability in the sys- fossil unit), the fuel costs, operation and
tem is another problem. By using modern maintenance costs and capacity factors
digital computer analysis techniques, a are computed. Demand charges on
thorough investigation of all such prob- purchased power plus other operating
lems can be achieved. parameters are calculated t o arrive at a
Digitally Simulated Loads. The indus- comparative cost for the cases under
trial load is simulated digitally. For investigation. The digital analysis model
specific unit outage rates, the loss of proceeds to use present worth mathe-
load probability associated with having matics t o plant investment costs to deter-
insufficient generation to meet the load mine the present worth costs. Yearly and
is calculated. Whether power is purchased total plant life fixed charges on invest-
or generated locally, load carrying capa- ment, plus other fixed costs associated
bility of the system for various specified with the type of generation, are com-
and tolerable loss of load probabilities in puted to find a final plant cost for
the system is then computed. The eco- comparison purposes. Management can
nomics of both generation systems are now justify not only local generation or
then investigated. Depending on the type purchased power schemes, but also the
of units used in local generation (for type of units t o be used in system
example, diesel driven, gas turbine or expansion.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

3. Analytical Procedures

3.1 Introduction. With the development which exist during various power system
of the digital computer and advanced network events and operating conditions.
computer programming techniques, pow- Secondly, these basic analytical solution
er system problems of the most complex methods will be demonstrated where not
types can be rigorously analyzed. Pre- otherwise self-evident. Finally, critical
viously solutions were usually only ap- restraints that must be respected t o avoid
proximate and errors were introduced by serious error in app1yin.g analytical solu-
many simplifying assumptions necessary tion methods will be discussed.
to permit classical longhand calculating Whether a power system analysis prob-
procedures. For progress t o be realized lem is t o be solved directly or by a com-
in using the computer for power system puter program, proper application of
analysis work, it has been necessary for sound analytical solution methods is
the specialist involved in the creation of essential for three reasons. First, accu-
power system analysis computer pro- racy of the solution t o each individual
grams t o understand thoroughly the problem being considered will be directly
application of basic analytical solution affected. Second, and perhaps the most
methods that apply. It is also important important because of the significant
for those concerned with assembling expense involved, accuracy of the solu-
and preparing data for input t o a power tion determines the validity and effective-
system analysis computer program and ness of any remedial measures suggested.
those interpreting and applying results Finally, extension of erroneous resuIts t o
generated by such a program t o under- related problems or t o what appears t o
stand the application of analytical solu- be a trivial modification of the original
tion methods. problem, possibly in combination with
This section attempts, first, t o identify other misapplied or misunderstood tech-
and document the basic analytical solu- niques, can lead t o a compounding of
tion methods that are valid for determin- initial error and a progression of incor-
ing the voltage and current relationships rect conclusions.

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

The most common causes of errors in (8) The Symmetrical Component Anal-
circuit analysis work are : ysis
(1)Failure to use a valid analytical (9) The Per Unit Method
procedure because the analyst is unaware Rigorous treatment of these analytical
of its existence or applicability, or both techniques is available in several circuit
(2)Careless or improper use of cook- analysis tests [I]', [21, 131, [41, [SI, [GI,
book methods that have neither a factual and is beyond the scope of this discus-
basis, nor support in the technical litera- sion. In the following sections, however,
ture, nor a valid place in electrical engi- a brief qualitative explanation of each
neering discipline principle is presented, along with a re-
(3) Improper use of a valid solution view of major benefits and restraints
method due t o application beyond lim- associated with the use of each principle.
iting boundary restraints or in combina- 3.2.1 Linearity. Probably the simplest
tion with an inaccurate simplifying concept of all, linearity is also one of the
assumption most important because of its influence
Many situations occur in industrial and on the other principles. Linearity is best
commercial power systems that illustrate understood by examination of Fig 1.
some or all of these common causes of
error, as well as the resulting evils. Any Fig 1
problem investigated as a part of the Linearity

*
general types of power-system analysis
studies covered in other sections of this i ( t ) =RESPONSE FUNCTION

recommended practice and described as

follows would qualify.
(1)Short circuit studies CIRCUIT
ELEMENT
(2)Load analysis studies E XCI TATlON
SOURCE
(3) Load flow studies
(4) Stability studies
(5) Motor starting studies
(6) Harmonic studies
(7) Reliability studies
(8) Grounding mat studies
I C- NON-LINEAR

/
(9) Switching transient studies I/ RESP/ONSE

3.2 The Fundamentals. The following MAGNITUDE A-LINEAR

IOF
i ( t RESPONSE
)l RESPONSE
identify the more important analytical
solution methods that are either available .--
-- /
B - NON-LINEAR
RESPONSE
as or are the basis for valid techniques in :,/

Y
solving power system network circuit MAGNITUDE OF
problems. SOURCE EXCITATION
(1)Linearity Ic(t)l
(2)Superposition
(3)The Thevenin Equivalent Circuit
(4) The Sinusoidal Forcing Function
(5) The Phasor Representation
(6) The Fourier Representation 'Numbers in brackets correspond t o those in
(7) The Single-phase Equivalent Circuit the References at the end of each section.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

The simplified network represented by impedance circuit will yield a current

the single-impedance element 2 in Fig that is linear with voltage). This restraint
l ( a ) is linear for the chosen excitation must be recognized in addition t o the
and response functions, if a plot of previously mentioned limitations of con-
response magnitude (current) versus stant source excitation frequency for ac
source excitation magnitude (voltage) is circuits and constant circuit element
a straight line. impedances for ac or dc circuits. Excita-
This is the situation shown for case A tion sources, if not independent, must be
(solid line) in Fig l ( b ) . When linearity linearly dependent. This restraint forces
exists, the plot applies either t o steady a source to behave just as would a linear
state value of the excitation and response response (which, by definition, is also
functions or t o the instantaneous value linearly dependent).
of the functions at a specific time. 3.2.2 Superposition. This very powerful
When linear dc circuits are involved, principle is a direct consequence of
the current doubles if the voltage is linearity and can be stated as follows:
doubled. The same holds for linear ac In any linear network containing several
circuits if the frequency of the driving dc or fixed frequency ac excitation
voltage is held constant. In a similar sources (that is, voltages), the total
manner, it is possible t o predict the response (that is, current) can be calcu-
response of a constant impedance lated by algebraically adding all the indi-
circuit (that is, constant R , L, and C vidual responses caused by each indepen-
elements) t o any magnitude of dc source dent source acting alone (that is, voltage
excitation or fixed frequency sinusoidal sources shorted; current sources opened).
excitation based on the known response An example which illustrates this
at any other level of excitation. For the principle is shown in Fig 2. The equation
chosen excitation function of voltage written is for the sum of the currents
and the chosen response function of from each individual source VI and V,.
current, both dotted curves B and C are Although Fig 2 also illustrates a way this
examples of the response characteristic principle might actually be used, more
of a nonlinear element. often its main application is in support
With the circuit element represented of other calculating methods. The only
by any of the response curves shown in restraint associated with superposition is
Fig 1 (including the linear element that the network should be linear. All
depicted by curve A) the circuit will, in limitations associated with linearity
general, become nonlinear for a different apply.
response function, for example, power. The nonapplicability of superposition
If, for example, the element was a con- is why all but the very simplest nonlinear
stant resistance (which would have a circuits are almost impossible t o analyze
linear voltage-current relationship), the using hand calculations. Although most
power dissipated would increase by a real circuit elements are nonlinear to
factor of 4 if voltage were doubled some extent, they can often be accurately
( P = I*R). represented by a linear approximation.
An important limitation of linearity, Solutions t o network problems involving
therefore, is that it applies only t o re- such elements can be readily obtained.
sponses that are linear for the circuit Problems involving complex networks
conditions described (that is, a constant having substantially nonlinear elements

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 IEEE
SYSTEM MODELING Std 399-1980

=lo.2.1,:. 2.1
5 6 5 6
'L

Fig 2
Superposition

Voc=l - 3 + 5

-10-5.3+5
- 6
15

= 7.5 v

3.3
ZE0 = 3+3 = s=2 a
9 3

qzy-p
1
I, = 7.5 ' 3
6+5

15
=-.- 2
7.5v 2 12+3

TH E V E N IN EQUIVALENT REPRESENTATION

(b)

Fig 3
The Thevenin Equivalent

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

can practically be solved only through for the source voltage and branch imped-
the use of certain simplification proce- ances would be substantially different
dures, or through adjustment of calcu- from those used in this case. (The circuit
lated results t o correct for nonlinearity. property of linearity would, incidentally,
Both of these approaches can potentially allow them t o be scaled up or down.)
lead t o significant inaccuracy. Tiresome The network shown in Fig 3(a), with the
iterative calculations performed in an 6 C? resistance shorted and the other
instant by the digital computer make resistances visualized as reactances, might
accurate solutions possible when an well serve as an oversimplified repre-
equation can be written mathematically sentation of a power system about t o
to describe the nonlinear circuit elements. experience a bolted fault with the
3.2.3 The Thevenin Equivalent Circuit. closing of the switch.
This powerful circuit analysis tool is The VI branch of the circuit would
based on the fact that any active linear correspond t o the utility supply while
network, however complex, can be the V, branch might represent a large
represented by a single voltage source motor running unloaded, immediately
equal t o the open-circuit voltage across adjacent t o the fault bus, and highly
any two terminals of interest, in series idealized so as t o have no rotor flux leak-
with the equivalent impedance of the age. For such a model, the 5 V source
network viewed from the same two corresponds t o the pre-fault, air-gap
terminals with all sources in the network voltage behind a stator leakage (sub-
inactivated (that is, voltage sources transient) reactance of 3 C? [7]. In a
shorted and current sources opened). more realistic situation where rotor leak-
Validity of this representation requires age is evident, a model that accurately
only that the network be linear. Exis- describes the V, branch in detail before
tence of linearity is a necessary restraint. and after switch closing is much more
Application of the Thevenin equivalent difficult t o develop, because the air-gap
circuit can be appreciated by referring t o voltage decreases (exponentially) with
the simple circuit of Fig 2 and develop- time and varies (linearly) with the steady-
ing the Thevenin equivalent for the net- state &s magnitude of the motor stator
work with the switch in the open position current following application of the fault.
as illustrated in Fig 3. After connecting The problem of accounting for motor
the 6 C2 load t o the Thevenin equivalent internal behavior is avoided altogether
network by closing the switch, the solu- by use of a Thevenin equivalent. This
tion for IL is the same as before, 1 A. permits the V, branch t o be represented
Use of the simple Thevenin equivalent by the apparent motor reactance (or,
shown for the entire left side of the net- more generally, impedance) effective at
work makes it easy t o examine circuit the time following switch closure. In
response as the load impedance value is shunt with the equivalent impedance for
varied. the remainder of the network, the
The Thevenin equivalent circuit solu- Thevenin equivalent impedance for the
tion method is equally valid for complex motor (at any point in time of interest)
impedance circuits. It is the type of rep- is simply connected in series with the
resentation shown in Fig 3 that is the pre-fault open-circuit voltage t o obtain
basis for making per unit short-circuit the corresponding current response t o
calculations, although the actual values switch closing.

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

1
I", = (1 *6-5) -
3

= -1- -
5
2 6

= _ -2= - 13 A (INTO BRANCH)

Fig 4
Current Flow of a Thevenin
Equivalent Representation

The current response obtained in each rent flowing in the V2 branch prior t o
branch of a network using a Thevenin closing the switch ( 5 / 6 A from inspection
equivalent circuit solution represents the of the circuit in Fig 3A) from the current
change of current in that branch. The Ivz = l/2 A, calculated t o be flowing in
actual current that flows is the vector the Thevenin equivalent for this V,
sum of currents before and after the branch.
particular switching event being con- In the branch of the circuit defined by
sidered. See Fig 4. the switch itself, the change of current
In Fig 4A the current flowing in the V, due t o closing is normally the response
branch circuit is shown to be 1/3 A. A of interest. This means the solution t o
more detailed representation of the the Thevenin equivalent is sufficient. The
Thevenin equivalent circuit previously resultant current in the other branches,
examined in Fig 3 is shown in Fig 4B. however, cannot be determined by the
Here, the solution for the same current solution t o the Thevenin equivalent net-
Iv2 is determined by subtracting the cur- work alone.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

3sl

Fig 5
Fault Flow

In the case where the V, branch repre- 3.2.4 The Sinusoidal Forcing Function.
sents a motor switched onto a bolted It is a most fortunate truth in nature
fault, the motor contribution is the that the excitation sources (that is, driv-
locked-rotor current minus the pre-fault ing voltage) for electrical networks, in
current as illustrated in Fig 5 and not general, have a sinusoidal character and
just the locked-rotor current as it is so can be represented by a sine wave plot
often carelessly described. As a rule, of the type illustrated in Fig 6. There are
this effect is never as significant as the two important consequences of this cir-
example suggests, even when the motor cumstance. First, although the response,
is loaded prior t o the fault; the load cur- that is, current, for a complex R, L, C
rent is much smaller than the locked- network represents the solution to at
rotor current and almost 90' out of least one second-order differential equa-
phase with it. tion, the result will also be a sinusoid of
A Norton equivalent which consists of the same frequency as the excitation and
a current source in parallel with a (dif- different only in magnitude and phase
ferent) equivalent impedance can alter- angle. The relative character of the cur-
nately be developed for the Thevenin rent with respect t o the voltage for
equivalent circuit. This representation is simple R, L,and C circuits is also shown
not generally as useful in power system in Fig 6.
analysis work. The second important concept is that

34

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

Fig 6
The Sinusoidal Forcing Function

when the sine wave shape of current is 3.2.5 Phasor Representation. Phasor
forced t o flow in a general impedance representation allows any sinusoidal
network of R, L, and C elements, the forcing function t o be represented as a
voltage drop across each element will phasor in a complex coordinate system
always exhibit a sinusoidal shape of the as shown in Fig 7. As indicated, the ex-
same frequency as the source. The sinu- pression for the phasor representation of
soidal character of all the circuit re- a sinusoid can assume any of the follow-
sponses makes the application of the ing shorthand forms:
superposition technique to a network Exponential: E ejs
with multiple sources surprisingly man- Rectangular: E cos 8 + jE sin 8
ageable. The necessary manipulation of Polar: E LQ
the sinusoidal terms is easily accom- For most calculations, it is more con-
plished using the laws of vector algebra, venient t o work in the frequency domain
which evolve from the next technique t o where any angular velocity associated
be reviewed. with the phasor is ignored, which is equiv-
The only restraint associated with the alent t o assuming the coordinate system
use of the sinusoidal forcing function rotates at a constant angular velocity of W .
concept is that the circuit must be com- The impedances of the network can
prised of linear elements, that is, R, L, likewise be represented as phasors using
and C are constant as current or voltage the vectorial relationships shown. As
varies. illustrated, the circuit responses, that is,

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

IMAGINARY

1
Z=R +j W L - j -=
WC
R +j X
x, =WL

1
xc=

IZI = +m
X
@ = tan-'-
R

R = resistance
XL = inductive reactance
Xc = capacitive reactance
Z = impedance

Fig 7
The Phasor Representation

V ( t )= V, + V, COS w,t + V, cos 2w,r + . . .

+ V, sin w,t + V, sin 2w,t + . . .

Fig 8
The Fourier Representation

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

current, can be obtained through the conditions that must be satisfied to use
simple vector algebraic manipulation of a Fourier representation. The only
the quantities involved. The need for restraints of practical interest t o the
solving complex differential equations power systems analyst are that the origi-
to determine the circuit responses is nal driving function must be periodic
completely eliminated. (repeating) and the network must remain
The restraints that apply are: linear.
(1)The sources must all be sinusoidal 3.2.7 The Single-phase Equivalent Cir-
(2) The frequency must remain con- cuit. The single-phase equivalent circuit
stant is a powerful tool for simplifying the
(3) The circuit R, L and C elements analysis of balanced three-phase circuits,
must remain constant (that is, linearity yet its restraints are probably most often
must exist) disregarded. Its application is best under-
3.2.6 The Fourier Representation. This stood by examining a three-phase dia-
powerful tool allows any nonsinusoidal gram of a simple system and its single-
periodic forcing function, of the type phase equivalent, as shown in Fig 9.
plotted in Fig 8, t o be represented as the Also illustrated is the popular one-line
sum of a dc component and a series diagram representation commonly used
(infinitely long, if necessary) of ac sinu- t o describe the same three-phase system
soidal forcing functions. The ac com- on engineering drawings.
ponents have frequencies that are an If a three-phase system has a perfectly
integral harmonic of the periodic func- balanced symmetrical source excitation
tion (fundamental) frequency. The gen- (voltage) and load, as well as equal series
eral mathematical form of the so-called and shunt system and line impedances
Fourier series is also shown in Fig 8. connected t o all three phases (see Fig
The importance of the Fourier repre- 9(a)), imagine a conductor (shown dot-
sentation is immediately apparent. The ted) carrying no current connected be-
response to the original driving function tween the effective neutrals of the load
can be determined by first solving for and the source. Under these conditions,
the response t o each Fourier series com- the system can be accurately described
ponent forcing function and summing by either Fig 9(b) or Fig 9(c).
all the individual solutions t o find the The single-phase equivalent circuit is
total superposition. Since each compo- particularly useful since the solution to
nent response solution is readily ob- the classical loop equations is much
tained, the most difficult part of the easier t o obtain than for the more
problem becomes the determination of complicated three-phase network. To
the component forcing function. The determine the complete solution, it is
individual harmonic voltages can be only necessary t o realize that the other
obtained, occasionally in combination two phases will have responses that are
with numerical integration approximat- shifted by 120" and 240" but are other-
ing techniques through several well- wise identical t o the reference phase.
established mathematical procedures. Anything that upsets the balance of
Detailed discussion of their use is better the network renders the model invalid. A
reserved for the many excellent texts subtle way this might occur is illustrated
[2], [3] that treat the subject. in Fig 10. If the switching devices oper-
There are several abstract mathematical ate independently in each of the three

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

EL-N 6 LINE TO
:EPJDTRAL

LOAD

Fig 9
(a) Three-phase Diagram, (b) Single-phase
Equivalent, and (c) One-Line Diagram

poles, and for some reason the device in ing device operates in reqonse to a fault
phase A becomes opened, the balance or conditon in the same phas-., as depicted
symmetry of the circuit is destroyed. at location X, the system sources would
Neither the single-phase equivalent nor continue to supply fault current from
the one-line diagram representation is the other unopened phases through the
valid. Even though the single-phase and impedance of the load. The throttling
the one-line diagram representations effect of the normally substantial load
would imply that the load has been dis- impedance, possibly in combination with
connected, it continues t o be energized additional arc impedance, can reduce the
by single-phase power. This can cause level of the current t o a point where de-
serious damage to motors and result in tection may not occur in phases (b) and
unacceptable operation of certain load (c). Needless t o say, substantial damage
apparatus. can result before the fault finally burns
More importantly, if only one switch- enough t o involve the other phases

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

0
EL-N 'L
# FAULT L I N E TO
NEUTRAL LOAD

LOAD
EL-N
d FAULT
(c)

Fig 10
(a) Three-phase Diagram, (b) Single-phase
Equivalent, and ( c ) One-Line Diagram

directly and accomplish complete inter- method. The symmetrical component

ruption. Meanwhile, both of the single- analysis allows the response t o any
line representations fail t o recognize the unbalanced condition in a three-phase
problem, and in fact, suggest that the power system to be investigated and
condition has been safely disconnected. correctly synthesized by the sum of the
Therefore, the restraints of this calculat- responses t o as many as three separate
ing aid are : balanced system conditions. The appli-
(1)Symmetry of the electrical system, cation of an unbalanced set of voltage
including all switching devices, and bal- phasors, such as displayed in Fig 11,t o a
ance of the applied load balanced downstream system and load
(2) Any of the other previously de- is the sum of the responses of the bal-
scribed restraints which apply t o the anced components which vectorially add
analytical technique being used in com- t o form the original unbalanced set.
bination with the single-phase equivalent Similar conclusions apply when the
3.2.8 The Symmetrical Component voltages are balanced, but the connected
Analysis. This approach comes t o the phase impedances or loads, or both, and
analyst's rescue when he is confronted therefore, the line currents are unbal-
with an unbalance, the most common anced. Here, the unbalanced current
circuit condition which invalidates the phasors are the sum of up t o three bal-
single-phase equivalent circuit solution anced sets that flow through the balanced

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

1 ' 1 BALANCED
LOAD

I
I
I
I
I
I

t A

P H AS OR RELATIONS H I P RESOLUTION INTO

OF LOAD VOLTAGE SEQUENCE COMPONENTS

B'*c'

POSITIVE NEGATIVE ZERO

SEQUENCE SEQUENCE SEQUENCE

Fig 11
The Symmetrical Component Analysis

system impedances on either or both A=xo + + Az

sides of the unbalance producing voltage B=A, a2xl aA2-
+ +
drops that satisfy the needs of the applied -
voltages and the boundary conditions at c = KO+ + a'&
the point of unbalance.
The positive (l), negative (2), and zero
The mathematical expression for three
(0) sequence vector components of any
unbalanced phasors (see Fig 11) as a
phase always have the angular relation-
function of the balanced phasor com-
ship with respect to one another as
ponents is as follows:
described in the vector diagram of Fig 11.

40

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

These are assigned a counter-clockwise The three impedance networks (positive,

direction of rotation in the time domain negative, and zero sequence) are symbol-
as illustrated. In the space domain, the ically represented in short-hand fashion
negative sequence phasors will produce by an empty block diagram for the phase
exactly the same results as a set of equal most definitive of the condition being
magnitude phasors that are displaced studied up to the unbalance or other
from one another by 120" and that rotate point of interest. Here, the final inter-
clockwise with time. connections of the networks are shown
Although the proof that a set of N un- which satisfy the necessary boundary
balanced vectors can be completely rep- conditions describing the system at the
resented by N sets of balanced vectors is point of concern. The analyst can fill
seldom presented in the texts dealing the block diagrams with the proper
with the subject of symmetrical compon- sources and impedances, including loads,
in each sequence network and solve the
ents, it is true. First, it is postulated that
it might be possible t o describe - - three single-phase loop equations. This, then,
arbitrary but defined vectors, A , B yand produces the three sequence responses,
by the expressions (previously provided) that is, current or voltage, which add
involving only the three unknowns To, vectorially to produce the resultant
xl , and 2;. Then the terms are rearranged phase responses. Similarly, the other
t o solve for these unknowns as follows: phase responses can be obtained by ad-
ding vectorially the individual sequence
Xo = 1/3 (X+B+ E) solutions shifted by the appropriate
AL; = 1/3 (X+ aB + .'E) multiple of 120'.
One curious and often confounding
K2= 1/3 (X+ a 2 E+ ai?) feature of this solution procedure is that
the phase in the system which usually
Here are three independent equations
for three unknowns (xo,xl
and T2),
provides the best, and sometimes the
only, approach t o the solution for an
which are all that are required to uniquely unbalance is the one least actively in-
and completely describe To, TI, and Z2 volved in the event. The unbalance illus-
and, therefore, substantiate their exis-
trated in Fig 11 is one such example
tence. The corresponding B and C phase where the solution is obtained through
components are, then, defined by the an analysis of the non conducting phase
vector relationship shown in Fig 11. A. A double line-to-ground fault is
The merit of the symmetrical compon- another, where examination of the open
ent analysis is that a relatively compli- phase gives the most direct access t o the
cated, and often unwieldy problem, can network solution.
be solved by simply vectorially summing The symmetrical component analysis
the solution to no more than three always involves the use of superposition
balanced network problems. Several ref- as well as most of the other procedures
erence texts [7], [l], [5] provide con- previously discussed. The restraints which
venient tables showing the network apply t o these other procedures, there-
interconnections that must be used t o fore, must also govern the use of the sym-
solve for the responses t o many com- metrical component analysis. In addition,
monly encountered system unbalances, due t o mutual phase winding coupling
as well as certain balanced conditions. and other effects, the impedance dis-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

played by electrical machines will be dif- (1)Three-phase Network

ferent when excited by the different kVAbase
sequence sources. Hence, the per phase Ibase =
impedance of the negative and zero
6kVbase
kV2base
sequence networks will, in general, be zbase = ~ ' 1000
different from the positive, Currents kVAbase
flowing in the zero sequence network, kVAbase = 6 kVbase Ibase
being in phase, do not add to zero as do
both the positive and negative sequence
currents and are, therefore, influenced ( 2 ) Single-phase Network
by impedance in this additional circuit kVAbase

path. When harmonic excitation sources

Ibase = -
kVbase
are present (requiring the use of the kV2base
Fourier representation) special care must Zbase = -
kVAbase
' 1000
be exercised in treating the sequence
kVAbase = kVbase Ibase
networks. Starting with the fundamental,
the harmonic term progressively shifts
from the positive to the negative t o the The equivalent open-circuit driving
zero sequence networks, and then the voltage ahead of the entire network can
process repeats. then conveniently and properly be ex-
3.2.9 The Per Unit Method. This meth- pressed as 1.0 per unit (or 100%)if the
od of calculation and its close companion, base kV is selected to match the operating
the percentage method, are well docu- voltage. The method is simply illustrated
mented in [4],[5] and [6] and are gen- and compared t o the conventional ohmic
erally well known. As a result, they will calculation method for a single phase
only be mentioned in passing here. network in Fig 1 2 where the equivalent
Fundamentally, the per unit method circuit impedances as viewed from the
and the percentage method amount to a primary and secondary sides at the trans-
short-hand calculating procedure where former' are identified as 2, and Z,,
all equivalent system and circuit imped- respectively.
ances are converted to a common kVA Before combining impedances it is
base. This permits the ready combination essential that the corresponding per unit,
of circuit elements in a network where or percentage, ratings have been expressed
different system voltages are present on a common kVA base and that they
without the need t o convert impedances are connected t o a system having a line-
each time responses are to be determined to-line voltage equal to the kV base to
at a different voltage level. which the per unit, or percentage, rating
Associated with each impedance ele- is referenced. Since the per unit method
ment and its kVA base is a line-to-line of calculation is based on the existence
kV base (usually the nominal line voltage of linearity and is always used in com-
at which the element is connected t o the bination with one or more of the other
system), along with the resulting base principles, it is necessary to observe all
impedance, and base current related by of the associated restraints discussed
the following expressions: earlier as they apply.

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 IEEE
ANALYTICAL PROCEDURES Std 399-1980

w --A&
m
It 1o:I I2 Z, = 20 . (A) * + 0.8= 1 .O R

1000
/ =-= 10A
'. 100

1000 v 1,- 1~~0~(&)+lO=lOOA

d
I I I: I
- I2 z, = 0.8 + (1/10)2. 1000 = 400 per ()"it
5ooo

ZEQ = 100 + 400 = 500 per unit

1 .O per unit volts
1.0 PU ZI = zz = 500 per unit
= 0.002 per unit

5MVA

l2base = 5MVA = 5 0 0 0 0 A

Z2 = ( 5 0 000) (0.002) = 100 A

Fig 12
(a) Classical Ohmic Representation,
(h) Per Unit Representation

3.3 References and Bibliography Power Systems Handbook, New York:

[l] WAGNER, C. F., and EVANS, R. D. McGraw-Hill, 1955, chap 2.
Symmetrical Components , New York : [6] WEEDY, B. M. Electric Power Sys-
McGraw-Hill, 1933. tems, New York: John Wiley and Sons,
[2] HOYT, Jr, W. H., and KEMMERLY, Inc, 1972, chap 2.
J. E. Engineering Circuit Analysis, New [71 Electrical Transmission and Distribu-
York: McGraw-Hill, 1962. tion Reference Book, East Pittsburgh, Pa:
Westinghouse Electric Corporation, 1964,
[3] CLOSE, C. M. The Analysis of Linear chaps 2 and 6.
Circuits, New York: Harcourt, Brace and [8] FITZGERALD, A. E., and KINGS-
World, Inc, 1966. LEY, Jr, CHARLES. Electric Machinery,
[4] STEVENSON, Jr, W. D. Elements New York: McGraw-Hill, 1961.
o f Power System Analysis, New York: [9] PUCHSTEIN, A. F., and LLOYD,
McGraw-Hill, 1962. T. C. Alternating Current Machines, New
[5] BEEMAN, DONALD. Industrial York: John Wiley and Sons, Inc, 1947.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

4. System Modeling

4.1 Introdi ction. This ection addresses Derivations nd proofs of mathemat-

the following questions: ical expressions will not be given. Ref-
(1)How can each component or each erences should be used for such purpose.
group of components of an industrial or However, several fundamental relation-
commercial power system be represented ships of electrical and mechanical quanti-
so that an analysis of the system perfor- ties will be mentioned in the text. This
mance can be made should save the reader the time needed
(2) Which of the several possible repre- to locate them in text books or hand-
sentations, or models, of the given com- books. It should also help refresh the
ponents will best describe the system to memories of those who have not been
meet the objectives of a given study exposed to power studies or academic
(3) What mathematical expressions will activities for a long time.
describe the characteristics of each system The material is intended to be as basic
element so that it can be quantified and and simple as permitted by the subject.
programmed for computer input The emphasis is to correlate real life
There are an infinite number of possible systems with the abstraction of mathe-
power system configurations and a large matics in order t o communicate with the
variety of study types. Consequently computer properly.
standards cannot be established to dic-
tate specific models for all specific cir- 4.2 Modeling. Scale modeling of power
cumstances? This text will therefore systems as a means of analyzing their
serve as a guide to help the reader make performance is impractical. However,
judicious trade-offs in selecting models scale models of certain mechanical com-
for his study. ponents of power systems are used t o
evaluate their characteristics. This is
'An exception t o this statement are the applica- often the case with hydraulic sections of
tion standards for circuit breakers where models
for sources of short circuit current are specified. hydroelectric plants such as turbine
See 4.9.2.2 and 4.10.3. runners, spiral cases, gates, draft tubes,

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 IEEE
SYSTEM MODELING Std 399-1980

etc. Nonetheless, much expertise is re- usefulness are written in general non-
quired to establish scaling and normaliza- specific terms. This exposes the analyst
tion factors, t o construct the model, to to a choice of program features and
gather meaningful data by measurement alternatives that require decisions t o be
and t o interpret and extrapolate the made every step of the way. Finally the
results. programs are often structured to handle
A step in the direction of abstraction is extensive power systems (3000 bus pro-
the approach used in ac and dc analyzer grams are not uncommon). This aspect
boards for the study of power systems. suggests that the analyst should consider
Here the power system elements are to what extent his system will be modeled
modeled by modules of equivalent char- to avoid, on the one hand, an expensive
acteristics but physically much smaller. overkill and on the other an incomplete
Most modules do not bear visual resem- problem statement that ensures question-
blance t o the components they repre- able answers.
sent. A 200 mi transmission line module
may look like a few potentiometers,
4.3 Review of Basics. Power network
inductances and capacitors. The modules elements may be classified in two cate-
are adjustable so the system variables can gories, passive elements and active ele-
be modeled easily. These modules can be ments.
interconnected, each adjusted t o satisfy 4.3.1 Passive Elements. The passive
the conditions of the power system being elements comprise such components
studied, and the required measurements as transmission lines, transformers, reac-
made and interpreted. Once the board is tors, and capacitors. They will, in gen-
configured for a base case, the effect eral, be regarded as linear. They will be
of one variable on the overall system modeled by one or more of the follow-
can be readily analyzed simply by ing electrical quantities:
adjusting the affected module. Most
analyzing boards have been abandoned Name Symbol -
Unit
today in favor of the more economical resistance R ohm
digital method using computers. inductance L henry
Digital computers can be programmed capacitance C farad
t o solve quickly and at relatively low cost
a large number of simultaneous equa- The voltage across and the current
tions and can handle the algebra of large through the element will be governed by
matrices. This makes them particularly these relationships :
well suited for applications in power . v
system analysis. An immense variety of U = Ri 1 = -
(Eq 1)
R
programs have been written t o study an
ever increasing number of problems in
the electrical field. These programs are U = L -di i = '/,dt (Eq2)
dt L
usually set up to receive the problem
information in the form of numbers
rather than analog settings. This then
forces the power system analyst t o where the lowercase letters represent
model the system quantitatively. The the instantaneous values of voltage and
programs, designed to maximize their current.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

In dc circuits under steady state condi- R, X and 2 quantities for the series (line)
tions these equations will reduce to: elements and the G , B and Y quantities
for the shunt (line t o neutral) elements.
Note also that 2 and Y are complex
quantities that can be expressed in the
di rectangular form above or the polar form
V = 0 (since - = 0) 2 = IZI le or Y = I YI D. Most computer
dt
programs accept the 2 and Y values in
du the rectangular form.
I = 0 (since dt
-= 0) (Eq 4) A final remark concerns the sign ahead
of the reactances and susceptances. The
In ac circuits with sinusoidal wave four diagrams of Fig 13 are self explana-
shapes, the equations become : tory. The wise analyst will verify the
program instructions to make sure that
V = RI I = -V the computer will interpret the input
R data properly.
V = jX,Z 4.3.2 Active Elements. The active ele-
ments of a power system comprise such
components as motors, generators, syn-
where
chronous condensers, other loads like
x,= 27rfL furnaces, adjustable speed drives, etc. The
= inductive reactance (Eq 5) active elements will be regarded as non-
linear, although some of the components
V = -jXJ
may behave linearly under certain cir-
where cumstances.
1 One or more of the parameters of a
model of an active element will vary as
a function of time, phase angle, fre-
= capacitive reactance (Eq 6, quency, speed, etc.
The capital letters for voltages and cur- The four expressions for power quanti-
rents represent their rms values, f is the ties given in Table 2 can be used t o model
frequency in hertz, a n d j the 90" operator non linear elements. Given any'two of
(= n). Inverting and combining these the four values, the remaining two can
elements in series or parallel will define be defined. Power can also be expressed
the set of quantities of Table 1. in polar form: S = IS1 le which yields
It should be noted here that it is these relationships: PF = cos 8, P = S cos
customary in ac power circuits t o use the 8 and Q = S sin 8.
Table 1
Equation References for Conductance, Susceptance,
Impedance and Admittance
Name Symbol Unit Defining Esuation
conductance G S (mho) 1 lR
inductive susceptance B S (mho) 1l X
capacitive susceptance B S (mho) 1l X
impe danc e Z S (ohm) ( R+ i X )
admittance Y S (mho) (G + j B )

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 IEEE
SYSTEM MODELING Std 399-1980

8 2 = R + jx,

Y G + jBc

Fig 13
Squirrel Cage Induction Motor Model

Table 2
Four Expressions for Power Quantities
Name Symbol Unit Exmession
complex power S VA S =P+jQ
active power P w P =dL?-zp
reactive power Q var Q = d m
power factor PF per unit PF =e
S

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Note that the signs of P or Q may be 1=111 & = I , +j$ = I ( c o s 8 + j s i n 8 )

positive or negative. By convention, the V=IVI & = V x + j & = V ( c o s 8 + j s i n 8 )
positive sign of Q is used for inductive
loads, that is, the current will lag the where the x axis of the coordinate system
voltage applied t o a load that consumes is taken as the reference shown in Fig 14.
vars. In this sense it is said that capacitors So far we have reviewed most of the
generate vars (current leads the voltage) quantities used in the type of studies that
and that squirrel cage induction motors require network solutions at a single
absorb vars. instant: a snapshot of the network in
By convention also, the sign of P is equilibrium. This instant shows the
positive for a load that consumes energy system in a steady state or during a tran-
or a source that generates energy. Thus a sient, at an instant for which all network
load with a negative sign for P could be parameters are known, say ?hcycle after
used t o represent a generator, and vice a short circuit has occurred.
versa. Some studies, of which motor starting
Some of the power system components and transient stability are examples, re-
can best be expressed in terms of current quire that a complete period of time be
or voltage. For instance, an infinite bus covered to assess the effects of a disturb-
may be specified by a voltage source of ance on system performance. This re-
constant magnitude and angle, and a quirement for a certain period of time t o
particular load may be described as a be considered introduces the need for
constant current element. The current mechanical quantities.
and voltage quantities may be complex The fundamental quantities of mechan-
numbers, in which case they have t o be ics are space, matter and time. Length
described in terms of a reference vector measures space and mass measures
that may be a voltage or current quan- matter. Other mechanical quantities are
tity. This introduces the phase angle derived from these three. Some of the
concept: derived quantities officially recognized

Fig 14
Section of a Typical
Industrial Plant Impedance Diagram

JX
+
(REFERENCE A X I S )

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 IEEE
SYSTEM MODELING Std 399-1980

Table 3
Fundamental Equations for
Translation and Rotation

Name Symbol Unit Defining Equation

Fundamental
length 1 meter (m)
mass m kilogram (kg)
time t second (s)
Translation
velocity U m/s " = -dl
dt
acceleration a m/s2 d 21
a = ?
dt
force F newton ( N ) F = ma
work W joule (J) W = JFdl
power P watt ( W ) p = -dw
dt
momentum M' N/s M' = mu
Rotation
radius r m
circular arc s m
moment of inertia I kg-m2 I = Jr2dm
angle e radian (rad) e = E
angular velocity w rad/s
dt
angular acceleration ff rad/s2 d2e
f f = -

dt2
torque T N-m T = rF
work W J W = STde
power P W P = To
angular momentum M J slrad M = Io

for electrical engineering work have been It also requires that a reference voltage
tabulated in Table 3, with the MKS and angle be specified for one bus.
system of units and the defining equa- Consider for instance Fig 1 5 which
tions. shows a small section of the typical plant
electrical system of Section 5, Load
4.4 Power Network Solution. Before Flow. Assume that the voltages at buses
dealing with the detailed models of power 2, 4 and 24 (also called A, B and C , to
system components, it is important t o simplify notations) and the impedances
review what constitutes the solution of a of T2 and line 8 are known. They are
network. summarized on Fig 16 and listed as
It can be said that a network is resolved follows :
if all the bus voltages and the relative
phase angles between these voltages are V, = V, = 69.00 kV /o"
known. This of course requires that the V4 = VB = 13.60 kV /-1.6"
impedance between the buses be known. V2, = V, = 13.51 kV 1-1.82"

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

A 15 M V A
69 - 13.8 k V
8 OIo 2

A
3
\L
1200A

500 MVA
SG2

3 c A W G 310

500 M V A
SG3

Fig 15
Single Line Diagram

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 IEEE
SYSTEM MODELING Std 399-1980

69.00

Z = 3. I 7 4 t j 2 5 . 3 9 SZ

Z = 0.12 7 0 + j 1.016 4

1 3 . 6 0 /-I 6 "

Z = 0 I 9 1 3 8 t jO.12119 SZ

1 3 . 5 7 /-1.82O

(.>
Fig 16
Impedance Diagram

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

ZAB = 1.0 + $3.0 (5%) on = - 6 V B IAB(at 13.8 kV)

1 5 MVA base = -(613.60 1-1.6")
(0.01 + j0.08) -
15
-
6g2
=
(243.7 121.33")
- 5741 119.73'
kVA
3.174 + j 25.39 !2 (at 69 kV) = P+jQ
13A2 = -5403 - j1938
(0.01 + j0.08) -
15
The transformer losses can now be
0.1270 + j1.016 s2 (at 13.8kV)
found by adding the power from A t o B
ZBc = 0.19138 + j0.12119
and that from B t o A:
The current from bus A to bus B can
be found by: Sh,,, = SAB+ &A
= (5425 + j2118)
+ (-5403 - j1938)
= 22+j180

The losses are 22 kW and 180 kvar

between buses A and B. Figure 17 sum-
/(3.174+j25.39) 6
marizes these results.
= lo3 [69.00+ j0 - (67.97 This example illustrates that once the
- j1.90)]/(25.59 182.87") 6 bus voltages are known, the remaining
= lo3 (1.03 + j 1.90)
calculations are straightforward.
/( 25.59 182.87")fi The real problem of analyzing even a
= lo3 (2.16161.54) '
modest size system is the determination
l(25.59 1 8 2 . 8 7 ' ) G
-
= 103 2.16
at the bus voltages. The loads are known
but mostly non linear and complicated
/ 2 5 . 5 9 d % 161.54 - 82.87' further by the fact that the reference
= 48.73 1-21.33" A (at 69 kV)
voltage is often many buses away from
The power flow from bus A t o bus B is: the loads. In order t o find the bus volt-
ages, one has t o resort to a cut-and-try
SA, = 6VA (the caret
&B method. The computer is an effective
on f means conjugate) (Eq 8) tool for this method since it can com-
= - 69 /o") (48.73 /+21.33")
(fi plete the set of calculations shown above
much faster than if done by hand.
= 5823 121.33' kVA
-
- P~~+ j QAB 4.5 Impedance Diagram. Several things
= 5425 + j2118 remain to be said about Figs 1 5 , 1 6 , and
17.
The current IABon the 13.5 kV side is
(1)Obviously all three diagrams show
that at the 69 kV side multiplied by the
a single-phase equivalent of the three-
transformation ratio:
phase system. The conditions for this
equivalence t o be true were covered in
L B = 48.73 1-21.33' .-69
13.8 Section 3.
= 243.7 1-21.33" (at 13.8 kV) (2) The impedance diagram of Fig 1 6
is the correct way t o represent graphic-
Next find the power flow from bus B ally resistances and reactances. However,
to bus A : it is felt that drawing the graphical sym-

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 IEEE
SYSTEM MODELING Std 399-1980

I S = 5 4 2 5 t j2118 ( k V A )

S,= 22+ jl80 ( k V A )

T
I= 243.7/-21.3' (A)

t S = - 5 4 0 3 - j 1938 ( k V A )

13.60 / - I . S 0

13.57 1-1.82' I
(c>
Fig 17
Flow Diagram

bok of resistances, inductances and cap- fectly well. Along this line, the graphical
acitances is superfluous since the expres- representation described by Fig 18 is
sions for impedances alongside a straight suggested as a method for bridging the
line do describe the line elements per- gap between the single line diagram and

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

-D
L I N E OR CABLE LINE IMPEDANCE I N Q

/
NUMBER

0.04 t JO.ll0 ( Z )

0 00 + j0.02 (Y)

\
L I N E ADMlTTANCE
IN S ( m h o )

LOAD
RATED k V

I LSYNCHRONOUS
MOTOR DATA
CONSTANT kVA .

Fig 18
Suggested Format
Raw Data Diagram

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 IEEE
SYSTEM MODELING Std 399-1980

the computer input document. A skele- to 6000 buses. It is also probable that
ton drawing of the power system show- the engineer’s time t o prepare the data
ing buses, lines, generators, and loads, will cost more than the computer time.
each with its assigned numbers, can be A rough guideline would be: when in
duplicated for multiple use as impedance doubt, model the more extensive system.
diagrams and as a flow diagram. It should Of course, there are penalties in doing so:
be noted that these diagrams are working (1)More data preparation time required
tools and as such do not require stan- (2) Increased possibilities of input error
dardization. However, the analyst should (3) More output data generated
adopt a method suitable for keeping track (4) Significant results become a smaller
of masses of data, for even small system section of the output
studies require and generate a large
amount of information. The objectives of the study should
(3) In power systems analysis the term always be kept in focus. This will help in
bus does not always have the meaning eliminating useless work.
understood by a plant electrician, for 4.6.2 Utility Supplied Systems. A large
instance. The analyst calls bus any point number of industrial and commercial
of the system where voltages are calcu- establishments are supplied by stiff
lated. The term is interchangeable with utility systems. Stiffness is a relative
node. Fictitious buses may be introduced function of the size of the plant load and
on the network to obtain voltage solu- local generation. If the external power
tions at certain points of interest. An system or utility is large compared with
example of this may be a 150 mi trans- that of the plant, disturbances within the
mission line broken down in 5 sections plant do not affect the voltage at the
of 30 miles (that is, a bus introduced point of connection. In such a case the
every l/5 of the length) in order t o avoid utility system is said t o be an infinite
the complicated but exact model of the system. The connection point will be
long line. an infinite bus.
(4)In the same vein, the term line is This concept can be extended within
often given the more general meaning of the plant electrical distribution system
branch, that is, any element between two when studies are concerned with small
areas electrically remote from the utility
nodes. For example, the transformer
supply. Conversely sections of utility
data will be entered on a computer input
systems may require modeling in cases
document called line data.
where this stiffness does not exist. It is,
4.6 Extent of the Model therefore, important that a sound know-
4.6.1 General. No rigid rules can be ledge of the utility supply systems be
established on how much of a power acquired before going ahead full bore
system should be modeled for a given with studies.
study. The system analyst has to exercise 4.6.3 Isolated Systems. The question
judgment and develop a feel for this as of whether an isolated system should be
he gains experience. modeled in full or in part is easier t o
The capability of available computer determine. These are usually relatively
programs will not likely be the limiting small and as such could be represented
factor in industrial and commercial fully for most kinds of studies. The extra
power system applications. There are effort of gathering a set of data for the
load flow programs that can handle up entire system, even though a smaller sec-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

tion would suffice, will not be lost since 4.7 Models of Branch Elements
the additional data will be used in some 4.7.1 Lines. Four parameters affect the
future study. The nature of an isolated performance of a line connecting a source
system is such that a modification or a t o a load: series resistance, series induc-
disturbance is more apt t o be felt through- tance, shunt capacitance, and shunt con-
out the system. ductance. A short length of conductor
4.6.4 Swing Bus. The requirement that can be modeled as in Fig 19. A line can
a reference voltage and angle be specified be considered as many short lengths of
at one bus for a network solution t o be conductors placed in series t o yield the
possible (see 4.4) introduces the concept model of Fig 20(a). The individual lengths
of swing or slack bus. of conductor could be made shorter thus
For the network t o be in equilibrium increasing the number of lengths for a
at any instant the total generation must given length of line. Continuing this pro-
equal the total load plus the total losses. cess t o the limit defines the model called
Since the line losses are not specified as line with distributed constants. This
an input, at least one bus of the network model has been reduced t o the equivalent
has t o be capable of adjusting the gen- circuit shown in Fig 20(b), where the
erated power for the equilibrium t o be series arm is defined by
achieved.
This bus is called the swing or slack
bus. It is usually the bus assigned the
fixed voltage and reference angle. It is
and the shunt branches by:
usually a generator bus in the case of iso-
lated systems, or the infinite bus behind y’ Y tanh (yQ/2)
the source impedance for a utility sup-
plied system.
z-- 21 (CoshyQ-1)
($/a)
The system analyst should always - _
specify the swing bus. It should be that 2, sinh yQ (Eq 10)
bus in the system that maintains the TWO figures of merit appear in these
closest voltage regulation. equations:

Fig 19
Equivalent Circuit of Short Conductor

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 IEEE
SYSTEM MODELING Std 399-1980

Fig 20
(a) Line with Distributed Constants
(b) Long Line Equivalent Circuit

2, = m,defined as the g = shunt conductance t o neutral in

characteristic or surge siemens (mho) per unit of length
impedance of the line (Eq 11) b = shunt capacitive susceptance in
siemens (mho) per unit of length
y = 6,
defined as the
X = 2 71 f L
propagation constant (Eq 12)
Y = '/i 71 fC
Both Zc and y are complex numbers. L = conductor total inductance in
The propagation constant y can be henry per unit of length
expressed in the rectangular form: C = conductor shunt capacitance in
y=a+jO farads per unit of length
z = r + jx = series impedance in ohms
per unit of length
This defines : (Eq 13)
Y = g + j b = shunt admittance t o neu-
a = attenuation constant tral in siemens (mhos) per unit of
= phase constant (in radians) length
z = zl = total series impedance of line
The other variables are: in ohms
Y = yl = total shunt admittance of
1 = total length of line line t o neutral in siemens (mhos)
r = conductor effective resistance in per unit of length.
ohms per unit of length sinh , cosh, tanh = hyperbolic functions
x = conductor series inductive reac-
tance in ohms per unit of length These functions of complex numbers

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

can be evaluated by using the following Mvar = 3 (kV)’ * B’ (Eq 1 9 )

relationships :
The program will internally assign half
sinh (yQ) = sinh (d+jpQ) of that value t o the bus at each end of
= sinh (aQ)cos(pa) (Eq 1 4 ) the line.
+ j cosh (a1)sin (01) The value of G’/2 can be modified to:
cosh ($2) = cosh (a1)cos (On)
+ sinh (aQ)sin ( 0 9 ) (Eq 15)
MW = 3 (kV)2 . G‘A
(Eq 20)
sinh X
tanhX = -
cosh X (Eq 16) and input as a constant impedance bus
eo‘!i - e-LYY load.
sinh (an) = The voltage (kV) is the line-to-line
2
eay + e=‘ voltage corresponding to the base voltage
cosh ( a Q )= (Eq 18) used in the program input document.
2 4.7.1.2 Medium Lines. In the range
The surge impedance Zc is approxi- of 50 to 150 mi approximately, little
mately 400 f2 for single circuit power accuracy is lost by simplifying Eqs 9 and
lines. The distributed constants model is 10 t o
valid for short or long lines at power or
communication frequencies. 2’ = z
4.7.1.1 Long Lines. Power frequency _Y’ -- -Y
overhead lines in excess of 150 mi could 2 2
be represented by the distributed con-
stants model reduced to an equivalent a sinh yQ
Thus neglecting the products ___ and
as shown in Fig 20(b). YQ
The shunt conductance g may be ne- tanh (yQl2)
yields the model of Fig 21(a),
glected since the dielectric is air (a good (YW)
dielectric) and the conductor spacing is called the nominal 7~ circuit. In this
large. However, if the corona losses are model the shunt branches are purely
important, they may be represented as a capacitive (no inductance).
value for g. Computer programs will The nominal a circuit can be thought
readily accept the data for 2’ expressed of as being formed by the process de-
in the rectangular form, that is, the scribed at the beginning of 4.7.1, with
equivalent series resistance R’ and the the exception that the unit length of
equivalent series inductive reactance X’. conductor is made longer (instead of
It should be noted that even though g is shorter), and the circuit made symmet-
neglected (g = 0), a non zero value of G’ rical (bilaterally). This results in the con-
will appear in the equivalent circuit of stants being lumped by an approximation
Fig 20B. The values of G72 and B‘/2 process. The nominal T circuit is formed
(in siemens) may have t o be modified t o the same way, with the difference that
MW or Mvar t o suit the program input all the shunt constants are lumped into
requirements. (The computer treats one as compared with the a circuit where
them as constant impedance loads.) If series constants are lumped into a single
the computer requires a line charging one.
Mvar the value B’ and not B ’ / 2 )must be Use of the nominal T model is not
used t o calculate: popular since it requires addition of a

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 IEEE
SYSTEM MODELING Std 399-1980

Q y

Fig 21
Medium Line Equivalent Circuits
(a) Nominal 71 (b) Nominal T

fictitious bus in the middle of the line. medium line model, the nominal n,
Entering data into the program, for the should be used for cables in the order of
nominal n circuit follows the same one mile in length (approximately '/40 of
requirements as for the long line model. 50 mi). The shorter the cable run the
4.7.1.3 Short Lines. For overhead better the accuracy when using this
lines shorter than 50 mi, neglecting the model. However, the computer program
shunt capacitance in the models presented used may have a limitation as t o how
earlier will not greatly affect the results small a quantity it will accept.
of load flow, short-circuit or stability It is doubtful that any medium voltage
calculations. This yields the model of system will have feeder lengths requiring

-
Fig 22. representation of the capacitive reac-
4.7.2 Cables. The overhead line models tance.
are equally applicable to cables. While
the resistances are substantially the same, Fig 22
the relative values of reactances are Short Line Equivalent Circuit
vastly different. Table 4 compares two
cases, one at 69 kV, the other at 13.8 kV.
The cable inductive reactance is about
1/4 that of the line, but the capacitive
reactance is 30 t o 40 times that of the
line.
This comparison suggests that the 0 0

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Table 4
Comparison of Overhead Lines and Cable Constants
Values in /mile for 500 kcmil Cu Conductors
69 kV 13.8 kV
Overhead L i n e * Cable** Overhead Linet Cable?
Resistance 0.134 0.134 0.134 0.134
Inductive reactance 0.695 0.176 0.613 0.146
Capacitive reactance 0.162 x l o 6 0.005 X l o 6 0.142 X l o 6 0.003 X l o 6
*Open-wire equilateral conductor spacing of 8 ft
**Three-conductor oil-filled paper-insulated cable rated 69 kV
*Open-wire equilateral conductor spacing of 4 f t
+Three-conductor oil-filled paper-insulated cable rated 1 5 kV

Table 5
Conductor Data

Material % Conductivity Application

Copper
soft 100 cable construction
soft, tinned 93.15 t o 97.3 cable construction
hard, shape 98.4 bus bar
hard, round 97.0 overhead line conductors
Aluminum 61.0 cables, bars, tubes

Aluminum alloys
5005-H19 53.5 overhead line conductors
6201-T81 52.5 overhead line conductors
Galvanized steel
Siemens-Martin 12.0
high strength 10.5
extra high strength 9.4

4.7.3 Determination of Constants. Elec- (1)Material

trical conductor characteristics are avail- (2)Size
able from numerous sources and need (3) Shape
not be repeated here. A few general (4) Temperature
comments are in order. (5) Frequency
4.7.3.1 Resistance. The effective (6) Environment
resistance of the conductors should be Copper and aluminum are the most used
used. The effective resistance takes into conductor materials for lines and cables.
account the conductor: Soft annealed chemically pure copper

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 IEEE
SYSTEM MODELING Std 399-1980

has 100% conductivity (IACS standards). ductors or metallic masses in its proximity
This is equivalent t o 875.2 52 for a one thus generating voltages in those parts.
mile long round wire weighing one pound These voltages may cause currents t o flow
at 20 "C. All other materials can have through closed circuits and thus cause
their conductivities expressed as a per- 12R losses other than those of the con-
centage of the standard, a few of which ductor itself. These losses can be repre-
are listed in Table 5. sented as an additional component of
The conductor resistance will vary resistance in series with the conductor
with temperature according t o the fol- resistance. The reader should consult [ 11
lowing formula: and [ 21 for information on this subject.
4.7.3.2 Inductive Reactance. The in-
R, = R,[l + a(t2- t, )] ductive reactance of a circuit has two
R, = resistance at temperature t, components: that due t o its own circuit
R, = resistance at temperature tl (self) and that due t o other circuits in its
a temperature coefficient per de-
= vicinity (mutual). The inductance of a
gree at temperature t, . conductor also has two components: that
At 20 'C, the coefficient a per degree caused by the current in itself and that
Celsius is: caused by the currents in other conduc-
Copper: 0.00393 tors of the same circuit. Finally the in-
Aluminum: 0.00403 ductance of a conductor due t o ,its own
Galvanized steel: current is divided in two parts: the first
SM: 0.0039 part considers the flux internal t o the
HS: 0.0035 conductor; the second part, the flux
EHS: 0.0032 external t o the conductor. This last divi-
It is not possible t o predict the exact sion has been modified t o simplify tables
operating conductor temperature if the of conductor characteristics. Tables list
conductor current is not known. The the conductor inductive reactance & at
analyst has the choice of either estimat- one foot spacing even if the actual spac-
ing the conductor temperature or assum- ing is larger or smaller than one foot.
ing the worst case, which, in some studies, A second table, valid for any type or
might be the maximum allowable temper- size of conductor, lists spacing factors
ature of the cable. Other studies might X, which, added t o the one foot reac-
require that the minimum conductor tance will give the correct total reactance
temperature be used for the worst case. for the given circuit conductor spacing.
The ac resistance of conductors is The spacing factor table is calculated
higher than the dc resistance due t o skin from the equation:
effects. The effect is more pronounced
as the conductor cross section or the xd = 4.657 f log GMD
operating frequency increases. Conductor =52/(conductor * mile) (Eq 22)
data tables usually include ac resistances where
at power frequencies. The skin effect is a
GMD = geometric mean distance of the
major factor in the design of high current
(several thousand amperes) ac bus sys- conductors
For three conductors spaced d, , d,, d3
tems, such as for electric furnaces.
The flux established by alternating cur-
rent in a conductor may link other con- GMD = d d , d, * d,.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Note that in Eq 22 a GMD smaller than 4.7.4 Reactors. Reactors are used as
1yields a negative spacing factor. branch elements in the following applica-
Cables in steel conduit exhibit higher tions:
reactances than in free air. The calcula- (1) To limit current during fault condi-
tions are too complex t o develop by tions
hand, hence, the curves presented in (2) To buffer cyclic voltage fluctuations
Section 4 of [ l ] and Section .691 of caused by repetitive loads (in conjunction
[21] should be used for estimating with condensers)
purposes. Tables are also available in (3) To limit motor starting currents
Chapter 1 of [17]. They are modeled as impedances consist-
4.7.3.3 Shunt Capacitive Reactance. ing of an inductive reactance in series
The determination of the capacitive reac- with a resistance expressed as R + jX.
tance follows the same pattern as the in- Manufacturers' design or test data should
ductive reactance. Conductor tables give be obtained for existing applications.
the value of reactance X' at one-foot The resistance section of this model
spacing. A spacing factor X ' is added t o can usually be neglected in motor start-
X' t o yield the total capacitive reactance ing studies since it is small with respect
of the conductor, Spacing factor tables t o the reactance and the power factor of
are calculated from: the motor is low during starting.
4.7.5 Capacitors. Series capacitors are
sometimes used on transmission and
= -
!2/(conductor mile) (Eq 23) distribution lines t o compensate for the
inductive reactance drop or t o improve
The capacitive reactance of shielded the system stability by increasing the
cables is determined from: amount of power that can be transmit-
ted on tie lines. They are represented by

xc =
, 1.79 G * l o 6 a negative reactance of the form 0 -JX,
f ' k in series with the line impedance.
= CL/(phase * mile) (Eq 24) For capacitors specified in microfarads
per phase, the reactance may be expressed
where in the general form:
G = geometric factor
k = dielectric constant of cable insula- x = -lo6 = !2/(per phase) (Eq 26)
2 7r fc
tion
f = frequency When specified in kilovars per phase
(Qc), the capacitor voltage rating (Vc)
2r must also be known t o calculate:
G = 2.303 log (Eq 2 5 )

where X = -
Qc
"C
- lo3 = !2/(per phase) (Eq 27)
r = inside diameter of shield
d = outside diameter of conductor It should be noted that the series capa-
Typical values of k are 6.0 for rubber, citor voltage rating is a function of the
5.0 for varnished cambric, 2.6 for poly- amount of compensation of the design
ethylene, and 3.7 for paper. and will generally be a fraction of the

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 IEEE
SYSTEM MODELING Std 399-1980

system line-to-neutral voltage. The appli- It can be demonstrated that Fig 23(a)
cation of series capacitors should always is equivalent t o Fig 23(b). In the latter
be accompanied by thorough studies, the secondary resistance and reactance
since it is easy t o create destructive over- has been reflected to the primary side of
voltage and ferro-resonance conditions. the ideal transformer by multiplication
4.7.6 Transformers with the inverse of the square of the
4.7.6.1 Two-Winding Transformers. turns ratio N.A close approximation of
The equivalent circuit of a transformer is this circuit is possible by moving the
shown in Fig 23(a). The rectangle repre- shunt branch and combining the primary
sents an ideal voltage transformation and secondary impedances as shown on
ratio ns/np = N, where n, and np are the Fig 24(a). Another simplification con-
number of turns of the primary and sists in eliminating the shunt branch al-
secondary windings respectively. & and together t o yield Fig 24(b). In many
R, are the effective resistances of the types of studies, the resistance RT,being
windings X,, and X,, their leakage reac- small with respect t o X,, is also neglec-
tances. Go, the shunt conductance, ted thus reducing the model of the trans-
models the iron losses that remain con- former to a single series reactance.
stant when the transformer is energized Transformer nameplate specifies the
at rated voltage and &, the shunt in- impedance 2, and the transformation
ductive susceptance, is equivalent t o the ratio. An assumption may be made that
quadrature magnetizing current at no X , E &. and the single series reactance
load. model used.

Fig 23
Two-Winding Transformer
Equivalent Circuits

63
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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Fig 24
Two-Winding Transformer
Approximate Equivalent Circuits

Use of Fig 24(b) model requires that an 4.7.6.2 Transformer Taps. Thus far,
estimate of R be made from typical data only single ratio transformers have been
[l],and a value for XTcalculated from dealt with. In real life, transformers have
taps, normally on the high voltage wind-
XT = 4
2
- ings, t o provide a voltage ratio best suited
t o the power system. The taps may be
Transformer test data will usually be changeable automatically under load
sufficient t o calculate all the parameters (LTC transformer) or fixed (manually
for the circuits of Figs 23(a), 23(b) and changed in de-energized condition).
24(a). When maximum accuracy is needed The resistance and leakage reactance of
the effective resistance R, should include the tapped windings are slightly different
the winding resistances corrected for the at different taps. This may be ignored if
operating temperature and another series the correct values are not known. On the
resistance to account for stray losses other hand, transformer test data may
[2], [3]. The model of Fig 23 necessi- specify values for the taps, in which case
tates the creation of a fictitious bus for these values should be used. The main
entry of the shunt admittance data in effect of changing taps is the change of
the program. voltage ratio and therefore the change of

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 IEEE
SYSTEM MODELING Std 399-1980

Fig 25
Three-Winding Transformer Approximate Equivalent Circuits
(a) Simplified-Delta (b) Simplified-Wye

voltage base for which the impedance bus is required, the computer program
diagram should be prepared. This will be will, upon request, automatically adjust
described in more detail in 4.8. the taps and modify the system imped-
The analyst should pay particular atten- ances as necessary for the new turns
tion to the specific requirements of pro- ratio.
grams for specifying taps. For instance 4.7.6.3 Three-winding Transformers.
the tap value 1.05 per unit (105%),inter- The circuits of Figs 23 and 24 apply to
preted as an additional 5% to the voltage any two windings of the three-winding
ratio, yields opposite results if applied t o transformers.
the opposite sides of the transformer. The three possible combinations, put
Once the data is input for a given con- together using Fig 24(b) as basic model,
dition and a certain voltage on a specified form a delta as shown on Fig 25(a), where

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

the new subscript T denotes the tertiary has the same magnitude but that the angle
winding. Elimination of the ideal trans- is shifted back another 2" by the wind-
former symbols is made possible by cal- ing arrangement within the transformer,
ling the voltages at nodes A, B and C, and that the rest of the information on
1.0 per unit and remembering that those Fig 17 is the same as before. The new
nodes have base voltage values E,, E, and impedance diagram will appear as shown
Et respectively. Assuming that the 3- in Fig 26(a).
phase system is balanced, the fictitious Now resolve as before with V, = 13.60
neutral will be common to all three /-1.6" -2.0". The results are shown in
voltage levels and can be eliminated t o Fig 26B. Note that the phase shift of a
simplify the diagram. mere 2" has caused the real power from
The loop formed by the delta (A) cir- A t o B to jump from 5425 t o 22 803 kW,
cuit can also be eliminated. This requires but the reactive power decreased from
making a delta-wye transformation. The 2118 t o 1605 kvar.
end result shown in Fig 25(b) is a format This example illustrates the main pur-
acceptable to computer programs. The pose of phase-shifting transformers to
new node D at the center of the Y control the flow of real power between
creates a fictitious bus that cannot be two buses.
identified physically but that is necessary These transformers usually have load
t o identify the impedance values to the tap changing mechanisms that will vary
computer. the phase angle between primary and
secondary automatically or manually.
The relationships for reduction from Thus computer programs will be set up
A t o Yare: to vary the amount of angle shift (plus
or minus), within limits specified in the
z'= 1 input, t o achieve the desired amount and
p (ZPS + ZPt - 9 Zst) (Eq 28)
1 the direction of real power flow.
The data required by computer pro-
2,' =
1 zs,+ z,
%(2 - Z,,) (Eq 29) grams will generally include the follow-
NI ing:
(1) Center (0"shift) position impedance
z = lh(Z,t +
1
91 zs, - 2,s) (Eq 30)
(2) Positive limit position impedance
(3) Negative limit position impedance
(4)Angle shift interval between taps
The relationship as a function of the Y (5) Number of taps
values is: Program subroutines allow the computer
to automatically estimate the value of
z,,= 2,: + 2,' (Eq 31) the impedances at the intermediate taps.
4.7.6.5 Other Transformer Models.
qt = 2,: +z; (Eq 32) The foregoing discussion has been in-
tended to give the reader a running start
Z,, = N ; (2;+ 2,') (Eq 33) on the subject of transformer modeling.
It is far from being complete.
4.7.6.4 Phase-Shifting Transformers.
Consider again the example of 4.4. As- 4.8 Power System Data Development
sume this time that the voltage at bus B 4.8.1 Per Unit Representations. Net-

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 IEEE
SYSTEM MODELING Std 399-1980

3.174 + J 25.3951 S = II 803 + 11605 ( k V A )

1 = 99 67 1-7 75' ( A )

13.60- 13.60 1-360

Fig 26
Impedance and Flow Diagrams
(a) Impedance Diagram (b) Flow Diagram
work calculations can be made with are then derived for each of the voltage
impedances, voltages and currents ex- levels in the system.
pressed either in actual ohms, volts or In power system studies, the base volt-
amperes or in the dimensionless per unit age is usually selected as the nominal
method. While both representations will system voltage at one point of the system
yield identical results, the per unit such as the voltage rating of a generator
method is generally preferred as it will or the nominal voltage at the delivery
do the job much more conveniently point of the utility supply. The base
especially if the system being studied has kVA is similarly taken as the kVA rating
several different voltage levels. Also, the of one of the predominant pieces of sys-
impedances of electric apparatus are usu- tem equipment such as a generator or a
ally given in per unit or percent by transformer, but usual practice is to
manufacturers. choose a convenient round number such
The per unit value of any quantity is as 10 000 for the base kVA. The latter
its ratio to the chosen base quantity of selection has some advantage of com-
the same dimensions, expressed as a monality when several studies are made,
dimensionless number. For example, if while the former choice means that at
base voltage is taken as 4.16 kV, voltages least one significant component will not
of 3740 V, 4160 V, and 4330 V will be have t o be converted t o a new base.
0.9, 1.00, and 1.04, respectively, when The basic relationships for the electrical
expressed in per unit on the given base per unit quantities are as follows:
voltage. The chosen base voltage, 4.16
kV, is referred t o as base voltage, 100% actual volts
voltage or unit voltage. Per unit volts = (Eq 34)
base volts
There are four base quantities in the
per unit system: base kVA, base volts, actual amperes
Per unit amperes =
base ohms, and base amperes. They are base amperes
so related that the selection of any two
of them determines the base values of
the remaining two. It is a common prac-
actual ohms
tice t o assign study base values t o kVA Per unit ohms = (Eq 36)
and voltage. Base amperes and base ohms base ohms

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

For three-phase systems, the nominal expressed in terms of their own kVA and
line-to-line system voltages are normally voltage ratings which differ from the
used as the base voltages. The base kVA base values of a circuit, it is necessary to
is assigned the three-phase kVA value. refer these values to the system base
The derived values of the remaining two values. This may also happen when ma-
quantities are: chines rated at one voltage may actually
be used in a circuit at a different voltage.
base kVA In such cases, the per unit impedance of
Base amperes = (Eq 37)
fibase kV the device must be changed to either a
new base kVA or new base voltage, or
(base kV)’ both, by the equation:
Base ohms = (Eq 38)
base MVA
Per unit 2, = per unit 2,
It is convenient in practice t o convert (base kV,)’ base kVA2
directly from ohms to per unit ohms (base kV2)2base kVA,
without first determining base ohms
according to the following expression: (Eq 40)
Per unit ohms =
-
ohms base MVA where subscripts 1 and 2 referto the old
(base kV)’ and new base conditions, respectively.
(Eq 39) 4.8.2 Applications Example. A sec-
tion of the power system described in
For a three-phase system, the imped- 4.5 has been repeated in Fig 27 as an
illustration of the per unit system. The
ance is in ohms t o neutral and the base
transformer ratios were changed slightly
kVA is the three-phase value.
to improve this example. The steps in
Where two or more systems with dif-
reducing the data to per unit are as
ferent voltage levels are interconnected
follows:
through transformers, the kVA base is
(1)Select base power: S = 10 000 kVA
common for all systems, but the base
(2) Determine base voltages
voltage of each system is forced by the
(a) Select bus 2 nominal voltage of
turns ratio of the transformer connect-
69 kV as base
ing the systems, starting from the one
(b) Calculate base voltages at other
point for which the base voltage has been
system levels
declared. Base ohms and base amperes 13.8
will thus be correspondingly different BUS4: kV = 69.0 -
66
for systems of different voltage levels.
= 14.427 kV
Once the system quantities are expres-
2.4
sed as per unit values, the various sys- BUS36: kV = 14.427 * 13.2
tems with different voltage levels can be
treated as a single system and the neces- = 2.623 kV
sary variables can be solved. Only when 0.48
BUS37: kV = 14.427 -
13.2
reconverting the per unit values t o actual
voltage and current values is it necessary = 0.525 kV
t o recall that different base voltages
exist throughout the system.
When impedance values of devices are

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 IEEE
SYSTEM MODELING Std 399-1980

T2 66.0 - 13.8
N 1.0+j8.0

510' 2865'
I - 3 ~ I - 3 ~
400 MCM 310

-@
GI
L
485'
13.2 k V 13.8 k V I-3C
I O 000 h p 8 . 5 MW AWG N O 4
0.8 POWER 0.8POWER
FACTOR FACTOR
9800 kVA x; = 0.20
x i = 0.28 -Q
T I4
2.5 a M I 0
TI3 13.2 - 2 . 4 13.2 -0.48
0.8+ j5.75 0.8tJ 5.75

Fig 27
Impedance Diagram Raw Data

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

(3) Calculate base impedances using (d) 0.48 kV system:

Eq 38 1 0 000
(a) 69 kV system: I= m
692 103
z= - = 11 000 A
(5) Summarize the base data in Table 6
10 000
= 476.1 C2 (6) Convert transformer impedances to
(b) 13.8 kV system: per unit using Eq 40
14.4272 * l o 3 (a) T2:
z= 10 000 1 . 0 + j 8 . 0 .-.-
662 1 0
= 20.82 C2
z= 100 6g2 15
(c) 2.4 kV system:
= 0.006 10 + j0.048 80
2.6232 * lo3
z= 10 000
or
+ j8.0 .-.-
13.€i2
= 0.688 C2
(d) 0.48 kV system:
z=1.0100 14.4272
10
15
0.52!j2 l o 3
z= 10 000
= 0.006 1 0 + j0.048 80
(b) T13:
= 0.02756 C2
0.8 + j5.75 .-.-13.22 10
(4) Calculate base currents using Eq 37 z= 100 14.4272 2.5
(a) 69 kV system:
10 000 = 0.026 79 + j0.19254
z=m or
83.67 A
=
j5.75 .-.-
(b) 13.8 kV system : z=0.8 +100 2.42
2.6232
10
2.5
10 000
Z =4 = 0.026 79 + j0.192 55
3 * 14.427
= 400.2 A (c) T14:
(c) 2.4 kV system:
10 000
z= 0.8 +j5.75
100
.-.-
13.22 10
14.4272 1
I=J3.Z.s23 = 0.066 97 + j0.481 35
= 2201 A or

Table 6
System Base Values
(Base Power 1 0 000 kVA)
Bus Base kV Base 2 Base I
2 69.00 476.1 83.67
4 14.427 20.82 400.2
8 14.427 20.82 400.2
24 14.427 20.82 400.2
31 14.427 20.82 400.2
32 14.427 20.82 400.2
36 2.623 0.688 2201.0
37 0.525 0.027 56 11 000.0

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 IEEE
SYSTEM MODELING Std 399-1980

Table 7
Cable Data
Length r ( a/1000’) x1 ( n / 1 0 0 0 ’ ) Conductor Outside Insulation Thickness
Line (ft) Conductor Size (ft) ( ft) Diameter (inches) (inches)
7 510 400MCM 0.0297 0.0370 0.728 0.175
8 2865 310 0.0668 0.0423 0.470 0.185
18 340 4 0.2992 0.0516 0.232 0.220
19 485 4 0.2992 0.0516 0.232 0.220

z=
0.8 + j5.75 .-.-
0.48* 10 (d) Line 18:
-
Xc = 4683 5280/2865
100 0.525* 1
= 8630 S2
= 0.066 87 + j0.480 65 -
R = 0.2992 340/1000
= 0.101 73 S2
(7) Calculate line impedance in ohms
(a) Lines 7, 8, 18 and 1 9 are 3/c, -
X , = 0.0516 340/1000
= 0.017 54 S2
copper cables, paper insulated,
shielded conductors; dielectric
Xc = (neglect due t o
constant: 3.7. See Table 7. short length)

(e) Line 19:

(b) Line 7: R = 0.2992 * 485/1000
R = 0.0297 * 510/1000 = 0.145 11 S2
= 0.015 1 5 S2 X , = 0.0516 485/1000
X , = 0.0370 * 510/1000 = 0.025 03 S2
= 0.018 87 S2 X c = (neglect due t o
X c = (neglect due t o short short length)
length)
(8) Calculate line impedances in per
(c) Line 8:
R = 0.0668 2865/1000 - unit with Eq 36
(a) Line 7:
= 0.191 38 S2
5 + j0.018 87
X , = 0.0423 * 2865/1000 z=0.015 1 20.82
= 0.121 1 9 S2
= 0.000 728
+ jO.000 906 per unit
From equations 24 and 25
1.79 lo6 - (b) Line 8:
xc = 60 3.7 -
2.303 log
z= 0.191 38 + j0.121 19
(0.470 + 2 0.185) 20.82
0.470 = 0.009 192
= 4683 S2/mi + j0.005 821 per unit

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

y=--zc - - 20.82 can represent the three load types by

-jXc -j8630 making h = 0 for constant power, h = 1
= 0 + j0.002 413 per unit for constant current and h = 2 for con-
(c) Line 18: stant impedance loads. Si is the initial
0.101 73 + j0.017 54 power at V,, the initial voltage, S the
Z= power at voltage V.
20.82
= 0.004 886 A more general expression can be
+ jO.000 842 per unit formulated by expanding Eq 41 for the
(d) Line 19: real and reactive power:
0.145 11+ j0.025 03
Z=
20.82
= 0.006 97
+ jO.001 202 per unit
(9) Calculate Xi of two synchronous The subscript has the same meaning as
machines in per unit with Eq 40 above. The exponents kl and k , could be
(a) Synchronous motor on bus 8 different and nonintegers.
A load or group of loads could also be
XA = j0.28 -13.2' 10000
-
14.4272 9800
~ - expressed in a more restrictive way by:
= j0.2392 I- -l

. , Generator G1
(b)
X: = j0.20 ___
13.8'
-
10 000

ID I):('
14.4272 8500/0.8
= j0.1722 Qi (Eq 43)
L J

The per unit data and the base voltages

again to reflect voltage dependency. In
have been transferred t o the impedance
this case A , B, C and D, E , F represent
diagram of Fig 28, in readiness for the
fractions of P and Q respectively. The
preparation of computer input document
sums A + B + C and D + E + F must
and as a record of the basic information
equal 1.
for the study.
In stability studies, frequency, like
4.9 Models of Bus Elements voltage, may become an important fac-
tor in the modeling of loads. Linear
4.9.1 Loads in General. Power system
frequency dependance would take the
loads may be classified by one or a com-
form
bination of the following types, to ac-
count for their voltag8 dependence:
Constant power S P + jQ = (1 + G A f ) S + j(1 + HAf)Qi
Constant impedance Z (Eq 44)
Constant current I
where G and H a r e the fractions of and
Figure 29 shows their respective power/ Qi, respectively, being affected by the
voltage relationships. A single expression : frequency deviation f from the steady
state frequency.

=):( k):(
The problem of assigning correct values
to the constants (h, , k 2 , A through H ) is

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 IEEE
SYSTEM MODELING Std 399-1980

0.0061

T2
N

14.427 ( k V b )

0.000 73 0.00919
+ j O . 0 0 0 91 +j0.00582 (Z)

0.00
+j0.002 41 ( Y )

.@ -
M 0.004 89 0.006 97
+ j 0.000 84 t j0.0012
j0.2392 j0.1722

-Q --@
0.026 79 0.066 97
.IO.I92 55 +j0.481 35
U. hl a U
TI3 t14

Fig 28
Impedance Diagram Fer Unit Data

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

1.4 - /
IM PEDANCE
1.3 .-

1.2 '-
-c,
1.1 -
3
a
1.0 -
W
Q

a
;
W
0.9 - POWER

0.8 -- Pi (INITIAL) = 1.0 per u n i t

vi (INITIAL) = 1.0 Per unit
0.7 .-

I I I 1 I I I I I
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
VOLTAGE ( P E R U N I T )

Fig 29
Effect of Voltage Variations for Three Types of Loads

very difficult when studying utility type tems are relatively modest in size. More-
systems, because the nature of the load over bus loads are often arranged in such
is not known accurately. Additionally, a way that grouping by type is easy to
the tasks of simulating the load in all its do, thus facilitating the preparation of
details would require a computer pro- computer input data and offering the
gram of such size and cost that the effort possibility of combining large sections of
would be prohibitive [4], [ 5 ] , [6], [ 7 ] . the system to reduce the overall size of
Industrial and commerical power sys- the study sections.

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 IEEE
SYSTEM MODELING Std 399-1980

RI x2

Fig 30
Induction Motor-Equivalent Circuit

4.9.2 Induction Motors. The induction where V is the line-to-neutral voltage.

motor single phase equivalent circuit is In some cases the equivalent circuit
shown in Fig 30 [ 21 , [ 31 , [ 81 . The solu- constants will be known along with the
tion of this circuit for values of slip s at a input or output power. The analytical
given input voltage and frequency will solution consists of finding the correct
yield, amongst other performance char- value of slip that will match the specified
acteristics, three sets of curves, torque, power. A cut-and-try method may be
current and power factor, typified in used here, but this will prove t o be a
Figs 31, 32,33. tedious process if resolved by hand
If the three curves are known, the because of the repeated reduction of the
shaft output power can be calculated for complex network for each trial of slip
any speed using the slip and torque with value. Computers excel at cut-and-try
the equation: methods, and for this reason programs
will generally be written t o accept this
kind of input. The equivalent circuit
model finds its major applications in
motor starting and stability studies. At
least one computer load flow program
where has been written t o accept motor equiva-
r = torque in lb-ft lent circuit data.
Po= output power in watts The curves of Figs 31, 32, 33 are used
N,= synchronous speed in r/min also in motor starting studies. The com-
Input power can also be calculated puter input data will consist of sets of
using the current and power factor curves values of torque, current and power
for the desired voltage. factor taken at different intervals of slip
along these curves. The mechanical load
S = 3VI (COS 8 + j sin 8 ) (Eq 46) characteristics in the form of a torque-
speed curve (in the same format as for
8 = arccos PF (Eq 47) the motor) will normally be required as
well by the program. The motor and

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

PERCENTOFSYNCHRONOUSSPEED

Fig 31
Induction Motor Torque Versus Speed

25 50 75 IO0
PERCENT OF SYNCHRONOUS SPEED

Fig 32
Induction Motor Current Versus Speed

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 IEEE
SYSTEM MODELING Std 399-1980

I I I I I
25 50 75 100
PERCENT OF SYNCHRONOUS SPEED

Fig 33
Induction Motor Power Factor Versus Speed

load moments of inertia will comple-

ment the description of the mechanical
system. Q (kvar) = P tan 0 (Eq 50)
The equivalent circuit constants can be Both the efficiency and power factor are
calculated from motor test data or ob- functions of motor voltage and percent
tained from the manufacturer (calculated
load. An example is shown in Fig 34.
or test values). References [2], [3] and Consequently if the objectives of the
[9] describe the methods used for the study warrant, it may be necessary t o
calculations from test data.
estimate the voltage in order to deter-
4.9.2.1 Constant kVA Model. It may
mine appropriate values for 7) and PF.
be appropriate in some study t o repre-
Manufacturers publish motor characteris-
sent a motor as a constant kVA load:
tics (current, efficiency, power factor) at
various loadings for a wide spectrum of
S = P + jQ = constant motor sizes and types.
This model is generally applicable t o
This requires that the shaft horsepower load flow studies or other studies where
(BHP), nameplate voltage, motor effi- the effect of model simplification is of
ciency 7,and power factor be known or secondary importance.
estimated and substituted in the follow- It should be emphasized that the reac-
ing equations : tive power Q is positive for an induction
motor, even if the motor is operating in
BHP
P (kW) = 746 * 17 the generating mode, that is, negative
slip.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

I50

140

I30

120
z
a
I
0 ll0
+
z
W
g 100
w
a

90

ao / \
P F AT 7 5 %
LOAD

I 1 I
90 I00 110 I20
PERCENT VOLTAGE CHANGE

Fig 34
Effect of Voltage Variations on
Typical Induction Motor Characteristics

4.9.2.2 Models for Short-circuit rapidly, there being no source of current

Studies. In this area of power system to maintain it. Thus, the time constant
analysis standards specify the model t o will be in the order of a few cycles only.
be used for motors-to account for their
contribution to short-circuit currents
[9], [lo]. The model is invariably a Fig 35
voltage source in series with an imped- Model of Induction Motor
ance as in Fig 35. for Short-circuit Study
The voltage source is justified by the
fact that at the very instant of a short
circuit, the flux that exists at the air gap
cannot change instantly. The energy that
this flux represents has to dissipate itself
in the form of current through resistance.
This current flows in the electrical cir-
cuits linked by that flux, and is limited
by the inductance of these circuits. The
stator winding, being linked by that flux
and having inductance, will therefore act
as a limited source of current t o the net-
work connected to it. The flux will decay

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 IEEE
SYSTEM MODELING Std 399-1980

The value of impedance in series with 4.9.3 Synchronous Machines. Synchro-

the voltage source is nearly the same nous machine models vary tremendously
value as the impedance which limits the whether a study considers steady state or
locked rotor current when voltage is transient conditions. In this section the
applied to the motor at rest. Accordingly, text will include both the simpler model
the impedance in Fig 35 can be calcu- for steady state conditions, and the more
lated from: complicated ones for transient condi-
tions.

4.9.3.1 Steady State Models

4.9.3.1.1 Generators. Once a power
where V is the motor nameplate line system has settled down after a change
of any kind, generator output voltages
voltage and ILR is the motor locked rotor
will have been automatically brought
current.
back to the desired output values by the
The resistance R is usually small rela-
voltage regulator. The prime mover
tive to the reactance x.
Moreover short-
governor will also have taken a steady
circuit currents have a low power factor.
position to maintain the generator speed,
These two factors justify neglecting R in
consistent with the rest of the system,
short circuit studies, where only the cur-
and to supply the amount of power
rent magnitude is required.
programmed by its setting.
When the short circuit study objective
is to check circuit breaker capabilities, it The generator output voltage will be a
is necessary t o consider different condi- function of the field current. Its output
tions such as first cycle duty, momentary power will be a function of the mechani-
duty, interrupting duty, and breaker cal power applied to its shaft which will
speed, in order to determine an appro- also be a function of the rotor angle that
priate value of motor series impedance the field poles maintain relative t o the
that will account for the decay in current revolving magnetic field in the stator.
Thus in a load flow study for steady
it contributes t o the fault. This is spelled
state conditions, the generator can be
out in [22] and [23] and takes the form
modeled as a constant voltage source and
of impedance multiplying factors that
a scheduled amount of kW. The system
vary as a function of time from the mo-
operating conditions may demand that a
ment the fault occurred. The rationale
generator voltage output be adjusted
for neglecting small motors’ contributions
automatically so that it supplies an
is based on their remoteness, electrically,
amount of reactive power such that a
from the power circuit breakers and their
bus, somewhere on the system, maintains
very short time constants.
a specified voltage. In this situation, the
4.9.2.3 Constant Impedance Model. analyst specifies a range of reactive power
It is sometimes desirable t o determine the
(kvar) within which he is happy t o oper-
system voltages at the instant a motor at
ate the machine. The generator voltage
rest is energized. The appropriate model
will be adjusted by the program.
is the equivalent circuit given earlier with
the slip s equal to 1.This circuit is a con- Other possibilities are:
stant impedance. It is generally simplified (1)Specify a voltage and let the kW
t o a single impedance to ground and cal- and kvar fall where they may. At least
calculated from Eq 51. one bus of the system called the swing

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

bus will have t o be specified for the spe- a particular motor. The reactive power is
cific voltage. calculated as follows:
(2) Specify fixed kW and kvar and let (1)Draw a vertical line for the fixed
the voltage fall where it may. excitation current
The last alternative suggests that a gen- (2) Read the armature current I, at the
erator may be considered analytically as intersection of the load line representing
a negative constant power load. Many the motor running load, and the I line
computer programs will accept negative (3) Estimate the motor terminal voltage
power signs. Thus negative kW input t o (line t o line)
the bus load data would model a gen- (4)Calculate the reactive power
erator.
4.9.3.1.2 Synchronous Condenser. kvar = d 3 ( VI)2- kW2
One difference between this machine
and a generator is that the condenser will Alternately, if the power factor curves
be a fixed load with very small kW value are shown on the graph, replace above
t o represent its losses. Otherwise, it will steps 3 and 4 with:
generally be equipped with a voltage reg- (3) Read the power factor at the inter-
ulator similar t o a generator and have its section of the load line and I line
reactive power output, specified within (4)Calculate the reactive power
certain limits, adjusted by the computer
program t o maintain a specified voltage kvar = kW tan 8 (Eq 53)
at its own terminals or elsewhere in the
system.
4.9.3.1.3 Synchronous Motors. The
synchronous motors may or may not be 4.9.3.2 Short Circuit Models. The
equipped with regulators t o control the current contributed t o a fault by a syn-
excitation. Those equipped with regu- chronous machine varies with time, from
lators may control voltage, power factor, a high initial value t o a moderate final
reactive power or even current, at their steady state value. Equations 55, 56 and
terminals or elsewhere. The real power in 57 depict this variation of current as a
kW will be a function of the load driven function of time for a short circuit at the
by the motor, and will not be adjustable terminals of a machine operating initially
for the given set of conditions under at no-load.
study.
The analyst may, therefore, resort t o
modeling the motors as negative generat-
ors with reactive power limits, if a volt-
age or current control device is supplied.
In the case of power factor or reactive
power regulators, the specified kW will
define a value of kvar using Eqs 52
through 54. E a ,.t/Td
For motors with fixed excitation and a hc =
X”
given fixed load, vee-curves must be used
t o calculate the equivalent reactive
power. Figure 36 shows the V curve for IT =di?Xg

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 IEEE
SYSTEM MODELING Std 399-1980

30C 0.80 LEAD

RATED 0.90 LAG
+
1
,

250

200

a
w
z
-
1

100

50

RATED

0
0 25 50 75 100 I25
FIELD A

Fig 36
Vee-Curves: Synchronous Motor, 2000 hp,
4000 V, 180 r/min, 0.8 Lead Power Factor

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

The total current Z is made up of two

components:
(1)A power frequency ac component
I,,, the rms value of which decreases At time t = 00
with time t , in accordance with Eq 55.
This component is called the symmetrical
current.
(2) A dc component zdc, which de-
creases with time in accordance with
Eq 56.
The initial magnitude of zdc is a function
of the angle (Y of the voltage wave at Since TA is much larger than
a time t' smaller than and larger than
c,
there is
which the short circuit occurred. It is the
amount of offset of the current wave. It T:, that will make e-nT: approximately
is proportional t o the rate of change of equal t o 1 and e - Q 6 approximately
voltage a t the instant of short-circuit. The equal to 0. In this case, the original
offset is maximum at (Y = 0, because the equations reduce to :
rate of change of voltage is maximum
when the voltage is 0. The offset is 0 at E
1' = -
(Y = 90" because the rate of change is x:
zero at the positive or negative peak
voltage values.
In the above equations:
E = the open circuit voltage
xd, x,& X: = the direct-axis synchro- Should there be an impedance ZL=R, +
nous, transient, and sub- jX between the machine terminal (still at
transient reactances, re- no load) and the point of fault, Eqs 58,
spectively 62 and 61 will become:
T,,Ti,Ti1= the armature and the
direct-axis transient and 11 E
subtransient short-circuit = RL + j(XL + Xy)
time constants, respec-
tively E
For typical values of reactances and = RL + j(XL + XA)
time constants, and with the maximum
offset condition (cos (Y = 1)the equations
will reduce to:
At time t = 0 (under subtransient con-
ditions) The armature Time constant T, will be
shortened appreciably by addition of
resistance R, in the external circuit. So
Eq 6 3 will become:

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 IEEE
SYSTEM MODELING Std 399-1980

The offset current will decay more work at times t = 0 or t = t', or both,
rapidly the farther away (electrically) using the models of Fig 37. Network
the machine is from the point of fault. solutions at t = CY are meaningless since
The voltage E , in all the above equa- the machine field excitation has likely
tions, is equal t o the terminal voltage V,, been changed at that time.
since it was assumed that the machine Depending on the study objectives, the
was carrying no load before the short effect of the offset current may or
circuit. If the machine is carrying a may not be important. In power circuit
current IL before the short circuit, the breaker applications, however, it is a
voltage E will be different in each equa- very important consideration. To obviate
tion, to satisfy prefault conditions. For the difficulties in resolving Eq 63, the
the case of a generator the voltage in breaker standards specify multipliers for
Eqs 58,62 and 61 will be: the X y and XA current components.
These are a function of machine type
E" = V, + IL X l and of the time from the inception of
the short circuit. Figure 22 of [ l o ] lists
those multipliers, gives examples of their
use and expands on this important aspect
of short circuit studies.
The models of Figs 37 and 38 are also
respectively. These voltages have been applicable t o synchronous motors and
called, voltage behind subtransient reac- synchronous condensers, the difference
tance (E"), voltage behind transient reac- being that the E", E' and E voltages are
tance ( E ' ) , and voltage behind synchro- calculated with :
nous reactance ( E ) . It is not practical, in
short circuit studies, t o calculate the sys-
tem currents for the entire period -from
the time of fault t o the time that the
current reaches a steady state value. The
normal procedure is t o resolve the net-

Fig 37
Models of Synchronous Machines for Short-Circuit Studies

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

4.9.3.3 Stability Models. In stability be indicated under the above assump-

studies it is necessary t o resolve the elec- tions, the system may in fact be stable!
trical networks at a series of intervals Thus there is a need t o account for the
starting from the time of inception of a neglected factors in certain circum-
disturbance and for as long as necessary stances. Which factors should be con-
t o establish a trend in the system per- sidered under which circumstances? This
formance. This may cover a period question will remain unanswered in this
shorter than 1 s for transient stability or text. The various models, in increasing
several seconds for dynamic stability degree of sophistication, will be pre-
studies. sented with simple explanations, if
4.9.3.3.1 Classical Model. The clas- possible, or without explanations in
sical model for transient stability study which case references will be given for
consists of a simple constant voltage the reader t o consult.
source behind a constant transient reac- 4.9.3.3.2 The H Constant. Stability
tance as in Fig 37(b). This model neglects studies are concerned with relative speed
the following factors by assuming that: variations of rotating masses. The kinetic
(1)The shaft mechanical power remains energy of a rotating mass, using units of
constant Table 3, is:
(2) Field flux linkages remain constant
(3) Damping is non-existent
(4)The constant voltage and reactance
are not affected by speed variations The rotating mass associated with a
(5)'The rotor mechanical angle coin- generator includes the rotor, shaft, coup-
cides with the phase angle of the internal ling, turbine and exciter, if the rotating
voltage type is used. Since this mass is designed
A system found stable under these as- to rotate at a fixed (synchronous) speed,
sumptions will likely be stable if any or the stored energy, at synchronous speed,
all of the above factors are taken into con- of' a given machine is used as a constant.
sideration. However, should instability This constant is usually normalized by
defining a quantity H that expresses the
stored energy per unit of machine rated
Fig 38
power. If kinetic energy is in megajoules
General Model for AC Machines in
and the rated power S in megavolt-
Short-circuit Studies
amperes the H constant will be:

FE H = -KE
=- J
S VA

Since 1 joule is equal t o 1 watt-second,

the H constant is sometimes stated in
j x . MF
equivalent kilowatt-second per kVA

MF =
L
multiplier specified
units.
To calculate the H constant use:

H = 0.231
( w R ~(r/minl2
) 10-~ -
(Eq 75)
in A N S I / I E E E C37.010-1979 MVA

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 IEEE
SYSTEM MODELING Std 399-1980

where WR2 is the moment of inertia in those of the first improved model will
pounds-feet squared and r/min is the increase the accuracy in the case of a
speed in revolutions per minute. The H generator with solid iron rotor. But, as
constant values will fall within the nar- before, the damping effect will have
row range of approximately 1 t o 15, been mostly neglected. The solid iron
irrespective of the size of the machines. rotor will be fully represented by all
4.9.3.3.3 Stability Model Varia- direct- and quadrature-axis, synchronous,
tions. In the discussion of 4.9.3.2, only transient and subtransient reactances and
the direct-axis parameters were consid- associated time constants.
ered on the basis that short circuits pro- The transient quadrature-axis reactance
duce currents of low power factor (quad- of salient-pole machines has the same
rature currents predominate). This as- value as the equivalent synchronous reac-
sumption may not be acceptable for dis- tance. Thus salient-pole machines can be
turbances considered in stability analysis. fully modeled as the solid-iron rotor
Therefore, additional synchronous ma- machine by omission of the XA and TAo
chine parameters are required t o more parameters.
accurately model the behavior and ac- 4.9.3.4 Exciter Models.
count for the differences in the magnetic (1) Saturation. The field poles saturate
construction types, such as: salient poles, as the excitation current exceeds a certain
smooth rotor, laminated rotor, solid level (see Fig 39). Computer programs
iron rotor with or without dampers. will usually account for the related non-
Quadrature-axis reactances and open- linearity of air-gap voltage and field cur-
circuit time constants are defined for rent from input data representing two
that purpose. Chapter 1 of [ l l ] is points on the saturation curve. Refer t o
especially recommended as a clear and program instructions for which two
basic text in the subject. points t o use.
The classical model may be improved (2)Standard Models. An IEEE com-
one step by taking account of the varia- mittee has developed a number of models
tion of XA with time from its initial value to represent excitation systems and the
to a steady state value of xd. The varia- dynamic characteristics of synchronous
tion will be an exponential described by machines for stability studies [12]. A
a time constant TAo (transient, open- tutorial paper [13] supplements refer-
circuit time constant). The three para- ence [ 121 by discussing the transfer func-
meters &, X i and TAo will ignore the tion blocks and their practical meanings
major effect of dampers. as well as other topics related t o excita-
Another improvement will involve tion system response. Only type (1)is
adding the effect of dampers which pre- repeated here (Fig 40) t o illustrate the
dominate during fast changing condi- following points.
tions, that is, the subtransient state. The Consider the simple circuit of Fig 41.
additional parameters X: and Tt0 will If the input voltage V is a step function
take care of this effect. (voltage changes suddenly at t = 0 from
The saliency of the rotor will be repre- 0 t o 1.0 pu V), the output voltage V will
sented by the quadrature-axis parameters, be an exponential function of time:
X,,X; and X t and the associated time
constants TAo, TA:.
Adding the parameters X; and to go that may be rearranged

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

NO LOAD SATURATION

C0N STAN T RES I STAN C E

LOAD SATURATION CURVE

A-B - A
S E = f (EFD) = -B
- - -I
B

Fig 39
Saturation Curves

-SE=K(EFD) -

T' - I
I + STR
-
I
KE + STE
- - EFD

SIGNALS
L SKF

Fig 40
IEEE Type 1 Excitation System

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 IEEE
SYSTEM MODELING Std 399-1980

Fig 41
Lag circuit

(Eq 77) system (s = jS2 and TB= RC). Analysis of

the response of this simple RC lag circuit
can therefore be made in the time domain
If the input is sinusoidal voltage, the (Eq 76) or the frequency domain (Eq 78).
output will also be sinusoidal but its It is common practice to use the fre-
amplitude will be reduced by the factor quency domain representation for both
the excitation (as in Fig 40) and the
1 prime mover systems. It pictorializes the
1+ jwCR system.
The lag transfer function just intro-
and phase shifted by a lagging angle duced has many applications, a few of
R which are representations of:
4 = tan-' -
OC (1) The delay for the field current t o
since : change t o a steady state value following
a change of input field voltage
1 (2)The delay of water flow rate
v,=v, 1+ joCR changes in penstocks
(3) The delays inherent in components
of control mechanisms.
where
A similar analysis with the circuit of
w = 21rf and f is frequency. Fig 42 would yield the lead transfer
Dividing both sides of Eq 78 by V , function which has the form s / ( l + sT).
yields : Its response time can be compared with
the previous one. In the type 1 excita-
v, --
_ 1 tion system this function serves the pur-
~ + ~ O C R pose of damping the effect of the ampli-
fication KA of the regulator that forces
This equation has the same form as the the field for faster response. & is the
equation 1/(1 + sTB)(transfer function) fraction of the output field voltage that
in the first block of the type 1excitation is fed back to accomplish this damping.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Fig 42
Lead Circuit

4.9.3.5 Prime Movers and Governor lighting. In utility type networks where
Models. Basic models for speed-governing substations are equipped with voltage
systems and turbines in power system regulators, lighting and heating can be
stability studies have been presented in represented as constant P + jQ.
an IEEE Committee Report [14]. As To calculate the admittances determine
mentioned earlier, the models are in the the watts P and vars Q at rated voltage V
form of block diagrams with transfer and resolve
functions describing the system compo-
nents’ performance. Two more papers P+jQ
Y (siemens) =-
[15], [16] cover some of the basics and E*
will help the novice t o understand the
relationships between the physical ele- The fluorescent and mercury vapor light-
ments and the transfer functions. ing power factors will be determined from
Typical parameter values are also avail- manufacturers’ data in order t o calculate
able in these references. Of course, the the vars Q. Incandescent lights and elec-
analyst will be well advised to seek from tric heating will have unity power factors.
the manufacturer the data applicable to 4.10.2 Electric Furnaces. In load flow
his equipment before compromising with studies this load will usually be repre-
typical data. sented by constant power which will re-
flect a desired controlled operating con-
4.10 Miscellaneous Bus Element Models dition to be analyzed. In the case of
4.10.1 Lighting and Electric Heating. short circuit and stability studies the
Lighting and electric heating often con- electric furnaces may behave like a con-
stitute a large section of a plant load, stant impedance load. It is unlikely that
particularly in commercial buildings. automatic load tap changers and electrode
This type of load can be modeled as position controls will have had time t o
constant admittance as suggested by Figs change from the prefault condition t o
4.10, 4.11,and 4.12 of [17]. The con- the end of the period covered in transient
stant admittance model would seem ap- stability studies. This may very well be
propriate for fluorescent and mercury the case also in dynamic stability studies
vapor lighting as well as for incandescent extending t o several s. Since furnace

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 IEEE
SYSTEM MODELING Std 399-1980

loads can be a large section of a plant Dynamic Modeling of Loads in the

load, it is important that the constant Stability Studies, IEEE Transactions
impedance model be specified in stability Power Apparatus and Systems, May
problems because of its damping effect 1969.
on the power system.
[5] ADLER, R.B., and MOSHER, C.C.
-4.10.3 Shunt Capacitors. Banks of
Steady State Power Characteristics for
capacitors are used extensively t o correct
Power System Loads, IEEE Paper
power factors and as a result, improve
70CP 706-PWR, 1970.
voltage regulation at the point of connec-
tion. They are modeled simply by a con- [6] ILICITO, F., CEYHAN, A., and
stant shunt capacitive susceptance. RUCKSTUHL, G. Behavior of Loads
During Voltage Dips Encountered in
jB = j27rfC Stability Studies - Field and Laboratory
Tests, IEEE Transactions Power Appara-
where C is in farads, f in hertz and B in tus and Systems, Nov/Dec 1972.
siemens.
[7] IEEE COMMITTEE REPORT, SYS-
Often the capacitors will be specified
tern Load Dynamics -Simulation Effects
in kvars. The rated voltage of the bus
and Determination of Load Constants,
where the capacitors are connected must IEEE Transactions Power Apparatus and
be known whether the susceptance or Systems, Mar/Apr 1973.
the equivalent kvars at the base voltage
are used in the study. Remember that [8] FITZGERALD, A.E., and KINGS-
kvars vary proportionally as the square of LEY, Jr, C. Electric Machinery, New
the voltage for a constant susceptance. York, McGraw-Hill, 1961.
4.10.4 Shunt Reactors. These are sel-
[9] ANSI/IEEE Std 112-1978, Standard
dom used in industrial power systems. A
Test Procedure for Polyphase Induction
constant admittance would be the correct
Motors and Generators.
model for reactors that do not saturate.
The same voltage considerations as in the [lo] HUENING, Jr, W.C. Interpretation
last paragraph would apply. of New American National Standards for
Power Circuit Breaker Applications,
4.11 References
IEEE Transactions Industry and General
[l]Electrical Transmission and Distribu-
Applications, Sept/Oct 1969.
tion Reference Book, East Pittsburgh,
PA, Westinghouse Electric Corporation, [ l l ] KIMBARK, E.W. Power System
1964. Stability: Synchronous Machines, vol 3,
[2] PUCHSTEIN, A.F., and LLOYD, New York, Dover Publications, Inc, 1968.
T.C. Alternating-Current Machines, New [12] I E E E COMMITTEE R E P O R T ,
York, John Wiley & Sons, 1974. Computer Representation of Excitation
[3] McFARLAND, T.C., a n d VAN Systems, IEEE Transactions Power Ap-
NOSTRAND, D. Alternating-Curren t paratus and Systems, June 1968.
Machines, New York, John Wiley &
[13] I E E E COMMITTEE R E P O R T ,
Sons, 1948.
Excitation System Dynamic Characteris-
[4] KENT, M.H., SCHMUS, W.R., Mc tics, IEEE Transactions Power Apparatus
CRACKIN, F.A., and WHEELER, L.M. and Systems, Jan/Feb 1973.

89

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

[14] I E E E COMMITTEE R E P O R T , 1191 STEVENSON, Jr, W.D. Elements

Dynamic Models for Steam and Hydro of Power System Analysis, New York,
Turbines in Power System Studies, IEEE McGraw-Hill, 1975.
Transactions Power Apparatus and Sys-
tems, Nov/Dec 1973. [ 201 Standard Handbook for Electrical
Engineers, FINK and CARROL, Editors,
[15] EGGENBERGER, M.A. A Simpli-
fied Analysis of the No-Load Stability New York, McGraw-Hill, 11th Edition.
of Mechanical-Hydraulic Speed Control
Systems for Steam Turbines, ASME [ 211 Industrial Power Systems Data
Paper 60-WA-34. Book, Schenectady, N.Y ., General Elec-
tric Company.
[16] RAMEY, D.G., and SKOOGLUND,
J.W. Detailed Hydrogovernor Representa-
tion for System Stability Studies, IEEE [22] ANSI/IEEE C37.010-1979, IEEE
Transactions Power Apparatus and Sys- Application Guide for AC High Voltage
tems, Jan 1970. Circuit Breakers Rated on a Symmetrical
Current Basis (Consolidated edition).
[17] Industrial Power Systems Hand-
book, BEEMAN, D., Editor, New York,
[23] ANSI/IEEE C37.5-1979, IEEE
McGraw-Hill, 1955.
Guide for Calculation of Fault Currents
[18] Aluminum Electrical Conductor for Application of AC High-Voltage
Handbook , The Aluminum Association, Circuit Breakers Rated on a Total Cur-
750 Third Ave, New York, 1971. rent Basis (Revision of ANSI C37.5-1969).

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 5. Load Flow Studies

5.1 Introduction. Load flow is the ter- requirements change. In any practical
minology applied to the flow of power operating system, load distribution shifts
from one or more sources through avail- each time a user turns a light, a motor,
able paths to loads consuming energy. or other power consuming device on or
Direction and amount of power flowing off. Consequently, load flow is a fluid
in each path or branch can be shown on and ever-changing thing. Where parallel
a system map commonly referred to as paths or circuits exist t o supply power
the system single line (or one-line) dia- loads, the operation of switches, break-
gram - a simplified visual model of a ers, etc (whether manually by an opera-
balanced three-phase electrical system. tor or automatically by relay action)
When the system is radial and has no will change the circuit configuration and
parallel paths, power flows directly to cause a redistribution of power flow
the load. Most systems today, however, through interconnecting lines. Large
are much more complex and have many industrial plants and electric utility com-
paths or branches over which power can panies with complex system netwarks
flow. Such a system forms a network of face a difficult task. They must provide
series and parallel paths. operators and dispatchers with informa-
Electric power flow in a network, like tion necessary to ensure efficient opera-
water flow in a complex water system, tion, minimize losses, maintain reliability
divides the flow among branches accord- of service, and coordinate protective
ing to their respective impedances until relaying for unexpected and emergency
a pressure or voltage balance is reached conditions.
in accord with Kirchhoff’s laws. In addition, the power system planner
As long as the circuit remains un- must look at future power requirements
changed, the balanced conditions hold. and allow for additions and changes. It
The flow will shift however, any time is necessary to meet projected loads
the circuit configuration is changed or when they occur, and still maintain or
modified, generation is shifted, or load improve the efficiency and reliability of

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

the service. Some changes that can be introduced

For many years the only way t o obtain individually, or in combination, t o de-
data t o guide operators and dispatchers termine effect on the system are listed
was from experience gained from emer- below:
gency outages or experimentation, or (1)Take any line or transformer out
both. This method was often costly and of service
sometimes drastic, and was unsatisfactory (2) Add load t o any or all buses
for future planning in that effects of fu- (3) Change regulated bus voltages
ture heavy loads could not be accurately (4) Add new transmission lines
determined without slow and tedious (5) Remove, add or shift generation t o
calculations. any bus
Computer programs t o solve load flows (6) Change transformer taps
are divided into two types -- static and (7) Increase conductor size on lines
dynamic (real time). Most load flow (8) Add rotating or static var supply t o
studies for system analysis are based on buses
static network conditions. Real time (9) Control reactive power distribution
load flows (on line) are used primarily (10) Increase or decrease size of trans-
as operating tools for optimization of formers
generation, var control, dispatch, losses, (11)Change MW or Mvar constraints,
and tie line control. This discussion is or both, between subnetworks
concerned with only the static network System changes can be simulated and
and its analysis. Two types of programs results of such changes analyzed without
are available t o users, time share versions jeopardizing operations or equipment.
and full-fledged batch programs. Where Each case study is accurate and reliable
minimal input and output give a satisfac- for conditions given. Analysis of the re-
tory analysis, time share programs are of sults of a case study often shows condi-
value, particularly when study time is tions which need further study. This can
important. Usually thorough analysis re- show elements of the system that should
quires more detailed input and a com- be changed t o improve performance.
plete output report. Generally, entering
data and printing a large output report is 5.2 System Representation. Present util-
not feasible on a time share basis unless ity and industrial plant electrical systems
the terminal is equipped with card read- can be extensive. A simplified visual
ing and high-speed printing equipment. means of representing the complete sys-
Since the advent of analog network tem is essential t o understand the opera-
analyzers and digital computers, with tion of the system under its various pos-
their ability t o quickly solve load flow sible operating modes. The system single
problems, the picture has changed radi- line (or one-line) diagram serves this pur-
cally. Now, starting with a system pose. The single line diagram consists of
operating under normal conditions, the a drawing, or sketch, identifying buses
flows in all branches can be quickly and interconnecting lines (see Fig 46).
computed for comparison with all other Loads, generators, transformers, reactors,
cases, present and future. It is simple t o capacitors, etc, are all shown in their
introduce one or more changes t o the respective places in the system. It is
present normal system and calculate the necessary t o show equipment parameters
effect on all its buses and branches. as well as their relationship t o each other.

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 IEEE
LOAD FLOW STUDIES Std 399-1980

1 3 . 8 kV
1MAIN
Q I

13.8 kV
7 (24) G:NERATOR I

BUS NAME
BUS NO SYMBOL

1.0 PU VOLTS
8.5 + j 5 . 2 6
GENERATOR 1
(P+Q)
13.8 kV Io
@ FDR 31

Fig 43 Fig 44
Generators Connected Connection of Buses
t o their Bus

Buses can be named as well as numbered. t o bus 9 (FDR 31) and is shown t o be
Interconnecting lines are shown with 650 ft long with R = 0.0845 S2 and X =
their R + jX values entered or cross ref- 0.03074S2.
erenced with tables of values. For in- Transformers are usually shown be-
stance, generators are shown connected tween two buses with the primary on
t o their bus as illustrated in Fig 43 with one bus and the secondary winding
their equipment parameters specified. identified by an auxiliary bus (identified
Each line originates on a bus and termi- by number and a suitable name, see Fig
nates on a different bus as depicted in 45). The auxiliary bus can then be tied
Fig 44. Line 1 runs from bus 3 (main 1) by a line t o the other bus.

Fig 45
Auxiliary Bus

13.8 kV - @ FDR 41
1.5 MVA & TI0

0.48 kL
@TI0

AUXILIARY BUS’
7 h

( TRANSFORM ER
SECONDARY
TERMINALS) 0
.7
+
f
0
0
0
0

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

If the auxiliary bus is used, transform- diverse systems tend to use the more
er impedance is entered along with line sophisticated programs. Industrial plants
impedance. Otherwise, their series com- that use less sophisticated programs find
bination is entered. If the transmission them satisfactory.
or distribution line is long (5 mi or The balance of this section uses one of
more), it will require charging (charging the less sophisticated programs t o illus-
conductance G , and line leakage suscept- trate a load flow study for an industrial
ance B ) . One half of the total for the line plant. Programs are available with various
is usually shown on each of the two levels of sophistication. This one was
buses. arbitrarily chosen for convenience. The
If MVA capability of the line is known, following is a case study for a large in-
it can be entered also. Tap voltages, where dustrial plant and illustrates in detail
required, should be entered to modify how a load flow study is undertaken.
the nominal ratios. If transformers are of
the tap changing under load type, the 5.4 Load Flow Study Example
tap limits and incremental tap values 5.4.1 General. To illustrate the use of a
should be given. If transformer imped- load flow program a typical industrial
ance is given in percent (or per unit), it plant will be studied. The single line con-
is expressed on its own self-cooled MVA nection diagram of the plant electrical
rating as base. system is shown in Fig 46. The base case
solves the system in the normal operat-
5.3 System Data Organization. A load ing mode supplying present maximum
flow solution gives the power flow in all loads. A case identified as case A1 is
branches for a given set of conditions. It solved t o show what happens t o the
represents a steady state in which the in- system when lightning causes relays to
fluential parameters are in balance and a open breakers at bus 3 and bus 26 to
solution has been found. A load flow isolate transmission line 3.
study is a series of such calculations made The impedance diagram in Fig 47 is
when certain equipment parameters are similar to the single line diagram except
set at different values, or circuit config- that impedances of the interconnecting
uration is changed by operning or closing lines, equipment parameters, load re-
breakers, adding or removing a line, etc. quirements, and nominal bus voltages
Many load flow programs have been have been added.
written for digital machines. They differ 5.4.2 Input Requirements. The follow-
in some ways, mainly by solution tech- ing input data apply specifically to this
niques and sophistication (taking into program, but similar data will be required
account more and more influencing para- for almost any load flow program. Three
meters). Power flow is very sensitive to data input forms are used for entering
circuit changes of impedances, intercon- required data in the proper format for
nections, and location of loads and equip- this particular load flow program.
ment. In general, less sophisticated pro- The input data sheet shown in Fig 48
grams will give satisfactory results, al- is used t o identify the company, location,
though more sophisticated ones will have date, and title of the study, and who
increased accuracy. As programs become made the study. Also included is an un-
more sophisticated additional input data limited number of statements defining
is required. Utility companies with large power system conditions under which

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 IEEE
LOAD FLOW STUDIES Std 399-1980

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

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 IEEE
LOAD FLOW STUDIES Std 399-1980

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

calculations were made. Reference t o Fig 1 Unregulated actiue. Buses that

48 gives an example of what is required. supply loads and which nor-
The lower section of Fig 48 is used as mally have no voltage regula-
a matter of convenience t o obtain the tion equipment.
required number of control cards needed
2 Regulated. Buses on which
t o adapt the system t o the program. This
specified voltage is held by
requirement is discussed later in the text.
supplying necessary vars (by
Computer control t o properly read and
some kind of suitable equip-
process input data is effected in this pro-
ment such as generators, ca-
gram by a tag or code number entered
on input data in Figs 49 and 50. The tag pacitors, reactors, etc).
identifies the data and ensures its proper 3 Var Limited. A bus that can
interpretation and storage when read supply vars t o hold the voltage
into the computer. Tag designations are only to specified var limits.
as follows: (Similar t o type 2 except with
limits.)
Tag
- Description 4 Floating. A bus that due to
0 (or blank) Bus data card switching, or error, is discon-
1 Line data card nected from the original sys-
2 Transformer data card tem. (An automatic classifica-
3 Phase shift transformer tion .)
4 Tap changer under load 5 Passiue. A bus that retransmits
5 Low or negative all power received (no direct
reactance line loads on bus).

Figure 49 is used for entering all data Figure 50 is used for entering line and
relating t o system buses, that is, bus transformer data for the system, that is,
name, bus number, bus type (see listing from and to bus numbers, conductance
at bottom), nominal bus voltage and G and susceptance B (usually neglected
angle, generation, loads, and associated for in-plant distribution lines), resistance
capacitors or reactors. and reactance of the line or transformer,
MVA rating, and transformer tap voltages.
Figure 49 shows the information filled
Figure 50 shows data for the illustrative
in with data for the load flow study
example.
example.
Most programs allow changes to be
Bus types are used t o direct the com- made t o a base case with a minimum of
puter t o properly process bus data. Types input data. Change data is entered on
of buses are as follows: Fig 49 for bus changes, and in Fig 50 for
line and transformer changes. A change
Bus Type Function code number must be entered in the
proper column on the figures t o instruct
0 Slack or swing bus. Takes the the computer of the change. The program
swings in loads and adjusts to will recognize the following changes t o a
supply MW and Mvar losses. base case:

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 IEEE
LOAD FLOW STUDIES Std 399-1980

l I 11 11 11 1I J1 11 1 1 1 1 1 I 1 l 1l 11 11 11 11 11 la
0

~
- 3 " ~ ~ ~ 1 1 1 1 =
.*, =" . ,, * >
I I I I I I I I I I I I I I I I I 1 I 1 I . D

Y
7
m
a
E
H
0 , U
Y >

0
0
CL
a

-'rq
0
w R

99

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

p7

m:
S
ag
0
n
CL

100

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 IEEE
LOAD FLOW STUDIES Std 399-1980

Bus Changes Normally the built-in values find a

Change Code Description satisfactory solution. Optimum values
0 Add new bus give a solution with the fewest iterations.
1 Change bus volts Different networks have different opti-
2 Add new generation mum values. Trial and error selection is
3 Add new loads the only practical way t o determine the
4 Change var limits best values. These once found for the
5 Add new capacitors or network, will continue t o be near opti-
reactors mum unless the network is changed
quite substantially. If only specified
Line Changes branch or bus flows are printed rather
Change Code Description than a complete system output, the
0 New line desired buses can be entered on Fig
1 New transformer taps 48 under Bus Select. Up t o 15 buses can
2 Remove be specified. Other special cards are used
line/transformer t o control the computer run. A Compute
3 Restore card must be placed at the end of a case
line/transformer run to instruct the computer that all
4 New line/transformer case data have been read and to start
MVA rating load flow calculations. Case studies can
be stacked when changes t o the first case
5.4.3 Special Data. Data can be entered
are desired. Place the change cards after
t o change the normal built-in constants the Compute card and terminate the
if desired. This program uses the Gauss- change case with another Compute card.
Side1 iteration method of solution and Any number of changes can be stacked.
involves starting the calculations with Two different systems can be stacked by
nominal or input values of voltages as placing a New System card after the last
specified on input data sheets, calculat- Compute card, and giving full system
ing the flow of currents through the data in the cards that follow and again
branches, checking voltage drops in the terminating with a Compute card. After
branches and comparing the resultant data for the last case are terminated, an
voltage at each bus with the bus voltage. End card should follow t o instruct the
If the voltages are not within an accept- computer that all desired work has been
able tolerance, bus voltages are modi- done.
fied by an acceleration factor (real and
imaginary) and calculations are repeated 5.5 Input Card Preparation. Having ob-
until they are within an acceptable tained and entered the system data in
tolerance. Each recalculation is called the input forms, it is necessary t o have
an iteration. If an entry is not made in the data punched into computer input
the special data input sheet for iterations, cards. For in-house computer systems, a
the program will do 500 before aborting. card keypunch and operator are available
This number can be overriden by enter- t o punch the data into cards and verify
ing the desired number on the form. them. For in-house work, cards are
Built-in acceleration factors are 1.6 for arranged in the order specified in the
real values and 1.7 for imaginary values. user’s manual (supplied with the pro-
These can be overriden by entering the gram being used) and submitted to the
preferred factors on the input form. computer center for processing. After

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

processing, the results will be returned numbered bus is shown with name, bus
(with the input cards) to the user. For number and voltage at solution, and
remote terminal entry, the computer phase angle with respect to the swing
service usually has keypunch machines bus. If the bus is a load bus, load MW
and operators, who can punch cards and and Mvar are printed. Printed next is the
verify input data. The computer service bus number of the From bus, then the
will also assist in entering the cards by To bus number and name, MW, Mvar,
remote terminal reader and will notify and MVA flowing in the line. A plus (+)
the user when output results are ready. indicates flow of power from the first
In some instances, data can be punched bus t o the second bus. A negative sign
into paper or magnetic tape and sub- (-) indicates the flow t o be in the oppo-
mitted. However, punched cards are site direction. Note that MW flow and
most frequently used. For the less exper- Mvar flow can be in opposite directions
ienced, there are consultants who can do in the same line. This is not a desirable
the analysis and present the user with a condition, but is entirely possible in
complete report including a technical real systems. For each line the MW and
analysis of the computer output and Mvar line loss is printed. All lines con-
suggestions and advice on system im- nected t o this bus are given. If a trans-
provement. former connects the two buses, the
transformer tap voltages used in the
5.6 Load Flow Results. Output from the calculations are printed. Finally, the bus
computer for each case is printed in error, or mismatch, is printed. When all
report form. For input data checking, a buses with inter-connecting lines have
page of input data is printed from the been printed, the total accumulated bus
computer file for all lines and trans- error is printed. The last item printed is
formers. The number of iterations the the total loss for the system. There are
computer required is also printed (see instances where a solution is found for
Fig 51). specified conditions without exceeding
If a satisfactory solution cannot be the iteration limit, but does have exces-
obtained in the specified number of sive bus error or mismatch (power into
iterations (500), a message is printed the bus does not match power out of the
stating that the number of specified bus, within a reasonable tolerance). When
iterations has been exceeded. In this this occurs, voltage tolerance should be
event, the full report is printed, but decreased for a more accurate solution.
caution should be used, as the values The amount of mismatch is a good indi-
printed do not give a satisfactory bal- cator of the validity of the solution.
anced solution. The full report is often Some programs print certain values
quite helpful in analyzing the system (usually bus voltages) in per unit values
trouble that might have led t o the un- rather than actual. This method allows
satisfactory solution. a relative evaluation. Multiplication by
Assuming a solution has been reached, the per unit value permits determination
the report will be printed on as many of actual values. If the program does not
sheets as required. Printed on the first reach a satisfactory solution (as evi-
line are the case number and description denced by exceeding the specified num-
for identification purposes. Reference t o ber of iterations) the reason can be
Fig 52 verifies the following: The lowest because of incomplete or inconsistent

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 IEEE
LOAD FLOW STUDIES Std 399-1980

O O O O O O O O O o O O O O O O O O O O o o o o o o o * m m m ~ * ~ m ~ m m o
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . .
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4 4

~ o o o o o o o o o o o o o o o o o o o o o o o o o ~ o m m m m m w m m m m m m
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w O 0 0 0 0 0 0 0 0 o O O O O O Q 0 0 0 o o o o o o m m m m m m m m m m m m m m
a .na.4-.44.-I44+-l.4.44
m

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o o o o o o o o o o o o o o o o o o o o o o o o o ~ m ~ ~ m m ~ ~ m t n m m ~ ~
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a 3.4

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........................................
a o o o o o o o o o o o o o o o o o o o o o o o o o ~ ~ m m m m m ~ m m m m m m
a oa.4-.3-.4-.-.4444.4
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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

*a L A S F NO. SAS5 - T Y P I C A L INOLiSTRLAL PLANT E L E C T R I C A L SYSTEM

TI= 1 1 69.60 KV 1.3 DEGREE

GENERATICN 10.00 Wh 5.19 W A R S C h E W L E O BUS V 3 L T A G E 65.00
1- 3 0 YAIPI 1 1o.oc MY 5.19 YVAR 11.56 MVA L O S S E S = 0.09 M b 0.11 WVAR
T R I N S F O R W E Q T A P 69.00 K V 13.eO KV
BUS ERROR -0.00 W -0.00 W A R

0.C JEGREE
GENElATICN 5.32 VU 2.lb WAR
5.32 Yk 2.16 YVAR 5.75 HVA LGSSES = 0.02 Mn 0.1E WAR
T D 4 N S F C d H E S T 4 P 49.30 KV 13.20 KV
R J S ERAOR 0.00 #VI 0.90 WAR

'.4 3 E G R E i
- ~ . 9 i MU -5.03 Y V A R 11.14 V V A = Lrss=s 2 . 0 0 MY 5.71 MVAR
T~ANSFLRUFR T L P 13.90 K V 69.05 KV
1.52 MA 3.93 H V A Q i . e i M V A LPSSES = O.JO wu 0.00 WAR
4.54 Y i 3 . 3 7 YVAR 5.4d CVA LPSSES = 0.01 YW 0.00 MVAR
i.tl 4n 0.9* YVAF 2 - 7 0 MV4 CCSSES = 0.00 YW 0.00 MVLR
1.24 NW 3. 34 MVAP 1.24 MVA L O S S F S = 0.00 MU 3.00 MVAC
qUS E*AClR 0 . 5 3 HU v.33 CVAh

-1.t JEG'I"
-E.>b Uh -1.99 * V A P 5.bC Y V A LGSSES = J.02 Ubi 0.1E WVAF
TF4hS=CPME3 TAD 1 3 . E ~ KV h i . J J KL
1.14 Y n 2 . ~ 7 YVAR 2.72 W 4 LOSSES 0.00 Mh J.00 WAF
7 . 1 : 1.1 -5.4'1 u v A a e.ce W A LOSSZS = u.01 v h J.01 MVbP
3.24 Y.4 2.14 Y V 4 Q 2.80 M V A L O S S E S = 0.31 MW 0.00 MVAR
-t.14 Y * 2 - 7 3 HVAR 5.74 Y V A LGSjcS = 3.05 YW 3.03 YVAQ
3JS E P 9 J P - 3 . l J VU -3.91 WAF

+.A DzLake
-1.52 *d -0.93 UVAK 1.31 W A LCSSCS = 3.Od M k J.00 HVAQ
1.52 *m i.97 F V I R 1.80 M Y 4 LCSSES 0.02 Y h 0.12 YVA"
TQA'!SFO?MER T A P 13.80 KV *.lb KV
9US E F a O R 0.30 Mk 0.01 HVA'

4.+ DCGPFE
- 6 . 5 3 Yn -3.34 dVAE 5.47 MVA LOSSFS = 0.01 Mn 0.00 MVA9
1-25 9h C.39 YVAQ 1.52 WVA Lnsscs = 0.01 w 0.59 YVAR
TKA\j=O2MER T13 13.U~KV 2.40 <V
3.27 Ma 7 - 1 6 MVAG 3.92 nVA LPSSE.2 = 0.03 CW 3.51 W A R
B J S ER4OK -0.00 hk 0.01 YVA4

-1.5 0Fr.2EC
-l.l+ Yrl -2.47 NVAR 7.72 MVA LGSSES = 0.00 YU 0.90 MVbG
0.61 Y.4 5.45 NYAC 3.75 PVA LPSSES = 0.00 M Y 0.QO WVAR
2 - 5 5 yh 2.32 cvp:, 2.09 MVA LCSSES = 0 . 0 0 r(n 0.dO WVAQ

Fig 52
Printed Computer Output

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 IEEE
LOAD FLOW STUDIES Std 399-1980

system data, or the system base might be A case is defined as system power flow
too large or too small for the computer in all branches for given system data. It
t o accurately represent the numbers in- represents a balanced stable flow of
volved. Short, low impedance lines in power distributed throughout the system
close proximity with long lines usually t o satisfy Kirchhoff’s laws and the law of
make convergence more difficult. conservation of energy. Current flow in-
A load flow program requires at least t o a point is equal t o that flowing out of
one swing bus. This is a bus designated the point (within an allowable small
by the user as a bus on which system tolerance) and bus voltages and line drops
losses or excess power can be handled. are compatible throughout the system.
Most programs also allow for a tie inter- When analyzing a system load flow it
change or transfer of power from one should be noted that the real power
system t o another. Problems of converg- (watt) is flowing in one direction from a
ing t o a solution can occur in some pro- given bus t o another, while the imaginary
grams when zero impedance or high power (var) is flowing in the opposite
impedance lines are entered. Usually direction. This results from votlage on
special handling is required for these the second bus being greater than on the
lines and the methods can vary with dif- given bus. The real power must flow to
ferent programs. the load, but t o equalize the voltage,
As mentioned briefly in 5.4.2, change reactive power must flow in the opposite
cases can be run with only minor input direction.
changes on most programs. The usual Proper transformer tap settings can re-
procedure is to run a base case, usually duce or change this condition. Many
an existing operating condition, which is load flow programs have an automatic
checked against known conditions for tap changing feature that changes taps t o
accuracy. Then by changing, adding, or minimize reactive flow. Remember that
omitting lines, changing loads, and equip- var flow can be controlled by tap chang-
ment, &, dimige cases c a i be pun con- ing and that reactive power will flow
secutively as desired. In more sophisti- from the bus with greater (relative) volt-
cated programs, provision is made for a age. The taps must be selected t o equalize
data base where system parameters this difference when done manually. Real
(equipment sizes, line impedances, bus power (watt) will flow t o the load by the
numbers, loads, transformer sizes, volt- difference of the phase angle of the
ages, ratios, taps, etc) are all stored for
supply leading the phase angle of the
use in short circuit programs, load flow load bus.
programs, and stability programs. The
It must be stressed that input data t o a
stored parameters provide data for the
load flow must be real values and as
base case. Then changes are made by
accurate as possible. Rounding off, or
temporarily substituting the change data
not including enough decimal places in
for the permanently stored data for a
change case. Most programs using a data certain parameters can be disastrous t o
base allow for retaining any specified the results in many cases. Do not ignore
case, which can become the base case for influential parameters. Results are no
future changes if desired. better than input.
The study of several such cases of a
5.7 Load Flow Analysis. A load flow system, under the various operating con-
study usually consists of several cases. ditions specified, leads t o a knowledge of

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

expected performance and behavior. illustrates this method using case 1 load
Recognition of, and the appreciation for flow results. In the illustration all perti-
performance and behavior of the system nent system data for equipment and
under desired conditions is defined as a operating conditions are entered 011 the
load flow analysis. system one-line diagram. From the load
A load flow analysis is used to deter- flow report output, then bus voltage,
mine optimum bus voltages for normal voltage angle, load kW and kvar, capa-
operation, and yet continue t o furnish citor kvar, etc are entered. By each inter-
reliable flows through alternate branches connecting line (transmission line) the
when one or more lines become inopera- kW and kvar flowing in the line is
tive due to line damage, lightning strokes, entered. Note that arrows are drawn t o
failure of transformers, etc. The study of show direction of real power. Reactive
multiple load flow cases and analysis of power then carries a positive (+) sign
the results provide operating intelligence when it is flowing to the same bus as real
in a short time that might take years of power. When flowing in the opposite
actual operating experience to obtain. direction a minus (-) sign is shown.
In addition t o optimum bus voltages, a Where sizeable line loss occurs, power
study of reactive power flows in the leaving the bus is shown near that bus,
branches can lead t o reduced line losses, while power arriving at the receiving bus
improved voltage distribution, and less is shown near it with power loss indi-
var supply equipment. Transformer and cated near the center of the line. At a
line capacities are related to their maxi- convenient location on the drawing, or
mum load flow requirements thus pre- on a facing page in the analytical report,
venting burnout from overloads or ad- comments can be entered as t o good or
verse conditions. Transformer tap settings poor conditions, or both, that exist in
should be optimized to reduce reactive circuit parameters or configuration. It is
var flows t o a minimum for practical desirable to list corrective action taken
operation. Knowledge of branch power for the next load flow run t o hopefully
flow supplies the protection engineer improve the operation.
with requirements for proper relay set-
tings t o ensure normal operation and can 5.9 Load Flow Analysis. Now that a load
provide data for automatic load and de- flow has been run for conditions that
mand control if needed. exist, what has been learned about the
system, and what can be done t o improve
5.8 Load Flow Output Presentation. the operation? Analysis of load flow out-
Maximum benefit results from a com- put now presented on the one-line dia-
puter output report when power flows gram shows the following:
are graphically shown on a one-line dia-
gram of the system. System flows can be (1)Voltage on bus 3 is low - 13.3,
quickly analyzed from this visual pre- while voltage on bus 4 is 13.62
sentation which relates system configura- (2) Inspection of all bus voltages sup-
tion, operating conditions, and equip- plied from main bus 3 are relatively low
ment parameters t o an ideal or optimum (3) Voltage on bus 39 is too low for
operation. Another system one-line dia- good operation. This is due partially to
gram is used t o enter the case load flow low voltage on bus 3
results in much the same way the imped- (4) Generator 1 is absorbing vars when
ance diagram was prepared. Figure 53 it should be supplying vars t o the system

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 IEEE
LOAD FLOW STUDIES Std 399-1980

COOP.

-
'
a:
I

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

(5) Var flow from bus 7 t o bus 27 is line diagram.

greater than the real power flow Some typical comments have been
Buses that are being supplied with entered on Fig 53 under Analysis. Each
power from main bus 3 have lower than analysis suggests what system changes
normal voltages. This suggests that taps can be made that would improve opera-
should be changed on transformer T1 to tion and reduce outages. New or larger
raise the voltage on bus 3. This will in- transmission lines, new generation at
crease the voltage on bus 5 and will help optimum locations, new capacitors or
the low voltage condition on bus 39. reactors and power factor improvement
However, changing taps on transformer are some items that analysis might show
T3 could raise bus voltage to a nominal as desirable or necessary changes. In-
4.16 kV. Problem 4 can be remedied by creasing loads over the years requires
increasing generator output voltage t o a analysis to determine when, where, and
level high enough to supply about +j4 how much new generation is required.
vars t o the system. By changing the taps Alternate generating schemes can be
on transformer T12 t o permit 0.48 kV studied and analyzed. New transmission
on bus 30, the var flow through line 7-27 lines may be needed or possibly new tie
can be reduced while allowing it t o re- lines to other utilities may be a solution.
verse the power flow t o bus 38 and to
help supply power to load L16. 5.10 Conclusions. It is evident to opera-
Such analysis of the system after each tors of industrial plant electrical systems,
case run can tune the system gradually as well as utility system engineers, that
to obtain the most efficient and reliable a tool is needed t o study their electrical
operation. systems under operating conditions that
Experience with load flows improves can actually be encountered before the
the engineer’s ability to make corrections condition occurs. Such a tool is used t o
with a minimum number of case runs. prevent expensive outages, damaged
However, it is stressed that any change equipment and possible loss of life. The
affects the whole system, and a cure at load flow solution (usually as obtained
one spot can create unexpected problems from a relatively sophisticated computer
at another location in the system. For program) is available and can.be used t o
this reason, it is better not to make too study systems under real or proposed
many changes in a single run as the ef- conditions. The solution results should
fects on the system may be difficult to be evaluated and analyzed with respect
understand. Each change case should be to optimum present and future opera-
documented showing changes made and tion. This leads to a diagnosis of the sys-
results obtained in order to keep future tem as it exists. The analysis can also
changes consistent with improving the point the way to improved operation
system. A good place to record changes and provide an adequate basis for future
and their results is directly on the one- system planning.

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 6. Short-circuit Studies

6.1 Introduction. Even the most carefully voltage levels in the overall system for
designed power systems are subject t o short circuits in specific areas
damaging effects of high magnitude cur- Details of fundamental concepts in-
rents flowing from short circuits occur- volved in the rigorous calculation of
ring in system components. To ensure short circuit currents are included in
that circuit protective equipment can Section 3. Simplifying techniques and
isolate faults quickly and minimize dam- their limitations, and step-by-step pro-
age and personnel hazard, it is essential cedures t o follow for manual short
that a short circuit analysis be included circuit calculations are given in [ l ] and
in the electrical design of new plants and PI *

also for modifications t o existing plants. The intent of this section is t o comple-
A power system short circuit analysis ment these sources by providing a brief
can be used t o determine any or all of overview of the steps required t o per-
the following: form a short circuit study and then
(1)Calculated system fault current illustrate how the computer can be used
duties which can be compared with the as an effective tool t o aid in the calcula-
first cycle (momentary) and interrupting tions.
short circuit current rating of circuit in-
terrupting devices, such as circuit break- 6.2 Short-circuit Study Procedure
ers and fuses 6.2.1 Preparing a One-Line Diagram.
(2) Calculated system fault current du- The starting point in performing a short-
ties t o compare with short-time, or with- circuit study is the preparation of a basic
stand ratings of system components such system one-line diagram. Accuracy and
as cables, transformers, reactors, etc usefulness of study results depends
(3) Selection and rating or setting of mainly on the reliability of this diagram.
short circuit protective devices, such as All major components such as motors,
direct-acting trips, fuses, and relays transformers, reactors, generators, utility
(4)Evaluation of current flow and supplies, feeder cables and ducts, and

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

overhead lines should be shown. For an grounded wye ( Y ) connection of a

existing plant it is usually possible t o ob- delta-wye (A-Y) transformer of the
tain a one-line diagram from the engineer- three-phase core (three leg) design, (3)
ing records. This diagram should be care- Grounded Y -A tertiary autotransformers,
fully checked t o ensure that it has been or (4)Grounded Y -grounded Y -A tertiary
updated t o reflect accurately the system three winding transformers. In systems
being studied. If such a diagram is not where these conditions exist, it is neces-
available, as may be the case for new sary t o conduct a single line-to-ground
(proposed) plants, it is necessary t o pre- short circuit study.
pare a suitable one-line diagram. Note that in resistance grounded sys-
6.2.2 Determining Depth and Accuracy tems, unless it is essential t o determine
of a Study. The next step is t o determine, specific less-than-maximum, short circuit
from the basic one-line diagram, how values, it is not necessary t o calculate the
extensive the short circuit study must be ground short circuit current since neutral
and what degree of accuracy is required. grounding resistors limit maximum short
There are five possibilities for a short circuit current t o a known value.
circuit in a three-phase system: Careful consideration of the system
(1)Three-phase short circuit. Three- one-line diagram indicates whether a
phase conductors shorted together three-phase short circuit study is adequate
(2) Line-to-line short circuit. Any two- or whether one or more other conditions
phase conductors shorted together must also be studied.
(3) Double line-to-ground short circuit. 6.2.3 Calculating Impedance Values.
Any two-phase conductors shorted to- The next step is t o determine values of
gether and simultaneously to ground impedance for all major passive and ro-
(4)Single line-to-ground short circuit. tating (active) system components which
One-phase conductor shorted t o ground are appropriate for the short circuit
(5) Three-phase t o ground short circuit. study.
For industrial power systems the most The impedance of passive system ele-
common study is the calculation of three- ments is generally considered t o be con-
phase (balanced) short circuit current stant with respect t o time (over the range
for comparison with switching equipment of times considered in short circuit
capability. studies). For three-phase short circuit
The short circuit current determined studies, only positive sequence impedance
from this type of study generally repre- 2, is required. For phase-to-phase short
sents the highest value at a particular circuit studies, positive and negative
location in the system. If information sequence impedances 2, and 2, are re-
regarding lesser balanced short circuit quired. For single and double iine-to-
values, or unbalanced short circuits (line- ground short circuit studies, positive,
to-line, or line-to-ground) is not required, negative, and zero sequence impedance
the basic study is all that is required. 2,, Z,, and 2,are required.
It is important t o realize that single Each rotating (active) component is
line-to-ground short circuit current mag- represented for short circuit purposes as
nitude can exceed three-phase short a constant voltage source behind an im-
circuit current under certain conditions. pedance. This impedance varies with
This can occur near (1)Solidly ground- time (after short circuit) and so in addi-
ed synchronous machines, (2) Solidly tion t o the different impedances listed

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

recommendations for system changes (in used in all other steps in the develop-
the case of existing plants) or for initial ment of a system short-circuit study.
design (in the case of new plants). Various programs are available which can
General guidelines for interpretation be used for:
and application of study results are usu- (1)Complex short-circuit studies using
ally not very useful since sound engineer- fundamental circuit analysis
ing judgment can only be made on the (2) Short-circuit studies using simplify-
basis of treating each case individually. ing techniques for specific use studies
Some important questions t o ask, how- (3) Only certain aspects of a study
ever are: Some of the most common uses rang-
(1)Is circuit interrupting equipment ing from simplest t o most complex are:
adequately rated for maximum short (1)Reduction of a number of system
circuit momentary and interrupting impedances in series or parallel, or both,
availability? If not, what is the most to a single equivalent impedance value
economical method of making system ( 2 ) Calculation of Y or A equivalent
changes while still maintaining a satis- impedances to assist in impedance reduc-
factory degree of system flexibility? tion
(2) Is there any short-circuit capability (3) Simple calculation of three-phase
margin for future expansion? If not, is it faults. No load flow data is required t o
necessary? If it is necessary, what is the establish initial conditions for input t o
most suitable method of effecting the short circuit program. Output gives
changes t o the system? total fault E/X current, line currents to
(3) Is non-interrupting equipment such faulted buses and system voltages.
as reactors, cables, interrupting equip- (4)Calculation of three-phase short
ment bus systems, bus duct, overhead circuit duties for use in comparing with
lines, transformers, etc, adequately rated interrupting device ratings. No load flow
to withstand short-circuit current until data required (see (3)). Output gives
cleared by circuit interrupting equip- total fault E/X current, line current
ment? flows from other selected buses, X / R
(4)Is special protective equipment or ratio values, and applies appropriate
circuitry necessary to provide protective multipliers t o fault values t o allow direct
device selectivity for both maximum and comparison with interrupting device rat-
minimum values of short-circuit current? ings based on applicable American Na-
(5) Does voltage of unfaulted buses in tional Standards.
the system drop to values which will (5) Calculations of three-phase, line-to-
cause motor-starter contactor drop out line, and line-to-ground short circuits in
or unnecessary operation of undervolt- either simple or complex systems. Load
age relays? If so, is special equipment flow data is required for input t o estab-
necessary t o prevent a total system lish initial conditions. Output gives posi-
outage? tive, negative, and zero sequence line
currents, and system voltages.
6.3 Use of the Computer. With the ex- For most computer programs, user
ception of system one-line diagram de- manuals are available for assistance in
velopment and selection of impedance transferring information contained on
values for individual system components, the one-line diagram and the impedance
computer short-circuit programs can be diagram t o a form which can be accepted

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

by the computer. Program limitations 1979 is used to compare short circuit

and output format are generally also values with circuit breakers rated on
explained. total current basis (generally applicable
For some programs it is necessary to for older medium and high voltage
use cards as input data t o the computer, North American breakers in existing
while other programs, usually those used plants).
on a time share basis with small in-house Frequently interrupting current cal-
terminals, use tape input and can be culations are made using [6] as a guide.
conversational. That is, the computer The principal extension this reference
will ask questions which appear typed on makes to American National Standards is
the print-out sheet and the user then a ratio of remote generator fault current
types out answers. This type of program to the sum of local generator fault cur-
is used in the solution of the short-circuit rent and remote generator fault current
study example problem. is used as a measure of electrical distance
from the fault to the generation. The
6.4 Short-circuit Study Example. To il- resulting fault current multiplier takes
lustrate the computer in calculating short into account reactors and line impedances
circuit currents, an example problem will equivalent t o transformer impedance, as
be studied. Basic steps previously de- well as variations in size of transformers.
scribed will be followed. The example The computer program in this example
problem involves a typical industrial uses this interpretation. An interpolation
plant situation where a three-phase short between American National Standard
circuit study is necessary to ensure that Curves is included in the program, and
switchgear and other equipment is ade- the breaker duty, along with X / R ratio
quately rated to withstand and interrupt and breaker speed, is printed with re-
the maximum short circuit current. Con- mote/local-plus-remote interpolated mul-
ditions of maximum load, maximum tipliers applied t o symmetrical current.
utility short circuit duty, and maximum The short circuit program prints enough
generation are considered since this is information so other interpretations of
the most severe fault condition. the American National Standard can be
The computer program used is on a used.
time share basis and is conversational in In the computer, the electrical power
mode. It has been specifically developed system is represented in matrix form.
for calculating momentary (first '/z cycle) Each of the power system components
and interrupting short circuit values (utility sources, generators, motors,
using techniques in accordance with transformers, cables, etc) is represented
ANSI/IEEE C37.13-1980 [3] for low volt- by a resistance value and a reactance
age breakers and ANSI/IEEE C37.010- value.
1979 [4] and ANSI/IEEE C37.5-1979 Note that in this example system X / R
[5] for medium and high voltage break- values are required, so both the reactance
ers. ANSI/IEEE C37.010-1979 is used t o and the resistance of each component
compare short circuit values with cir- arc is required. In studies where X / R
cuit breakers rated on a symmetrical values are not required and when reac-
current basis (generally applicable for tance of a component is very large com-
all new North American medium and high pared to resistance, it is acceptable t o
voltage breakers). ANSI/IEEE C37.5- neglect resistance; its value for computer

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

input becomes zero. actual ohms * base MVA

The computer program places an as- x*uor %U = (base kV)*
sumed three-phase fault at the desired
bus location in the system, and a set of Motors fed from each 480 V substation
short circuit currents is calculated for are grouped (lumped) and a single im-
comparison with published short circuit pedance is based on total connected
ratings of the power system equipment. motor kVA. This impedance was obtained
Figure 54 is the one-line diagram for by using hand calculations because the
the system to be studied. It is the same system is relatively small, but on a larger
diagram used in Section 5, Load Flow system, impedances can be obtained
Example, and elsewhere in this text, using a system data reduction computer
with minor additions for specific use in program. Table 9 lists hand calculations
short circuit study example. and also using such a program, typical
Figure 55 is the impedance diagram for values of subtransient reactance X:
the system. It has been developed from (locked rotor reactance X,) for each
Fig 54. All buses are numbered and all motor within the group are used and the
impedances have been put in a form total equivalent kVA and impedance is
which can be used as input to the com- determined based on the following as-
puter. Major equipment impedances have sumptions when exact motor impedances
been converted from values shown on are not known:
the one-line diagram to per unit on a Subtransient reactance ( X y ) values are
common 100 MVA base. Bus 38 load, used in first cycle (momentary) current
which will not contribute short circuit calculations while a modified subtransient
current is not shown. Selected fault loca- reactance is used in interrupting duties
tions are shown as F 3, F 4, F 24, F 19, for medium and high voltage breakers.
and F 30. These values are in accordance with
The utility system is represented by a applicable circuit breaker application
per unit impedance which is equivalent standards [4], [ 51.
to maximum short circuit duty (1000 American National Standards for cal-
MVA) available from the utility company. culating short circuit duties require
Impedance for computer input is de- actual motor or generator reactances be
rived as follows: modified under certain conditions. Modi-
fication factors are listed in Table 10
base MVA for both momentary (close and latch)
xpu = utility fault availability
and interrupting duty calculations.
Table 10 shows a slight difference be-
- 100 tween momentary calculations using
1000 - Oel ANSI/IEEE C37.010-1979 and ANSI
C37.5-1979 rather than using ANSI/IEEE
01
Rpu = 22 = 0.0045 C37.13-1980. In this example, the latter
calculation is performed using low voltage
calculations since the results are more
System cable impedances are typical conservative.
values taken from Section 5 data. The X / R ratios of induction motors
Impedances for computer input are and transformers were determined by
derived as follows: using medium typical curves from

114

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

Table 9
Assumed Values for Motors when
Exact Impedances are not Known
Induction motor 1 hp = 1 kVA
Synchronous motor, 0.8 PF 1 hp = 1 kVA
Synchronous motor, 1.0 PF 1 hp = C.8 kVA
Lumped induction motors not greater Xz = X1,= 0.25 per unit
than 600 V
Individual induction motors greater X;; = XI,= 0.17 per unit
than 600 V
Synchronous motors not less than X;; = 0.15 per unit
1200 r/min
Synchronous motors less than 1200 % = 0.20 per unit
r/min but greater than 450 r/min
Svnchronous motors 450 r/min and less x1: = 0.28 Der unit
NOTE: Motor impedances are in per unit on motor kVA rating.
Reactances and motor base kVA ratings listed above were taken
from data and assumptions in [ 11.

Table 10
Modification Factors for Momentary and Interrupting Duty Calculations
Impedance Value for
Medium and High Voltage
Calculations per Impedance Value for
Duty ANSI/IEEE C37.010-1979 Low Voltage Calculations
Calculation System Component and ANSI C37.5-1979 ANSI/IEEE C37.13-1980*
First cycle Utility supply 4 4
(momentary) Plant generators X; X;;
calculations Synchronous motors % X;;
Induction Motors
Above 1000 hp > 1200 r/min X;;*** X;;***
Above 250 hp > 1800 r/min X;;*** x;***
All other motors
50-1000 hp 1.2 x;*** X;;***
Less than 50 hp neglect X;;***
Interrupting Utility supply 4 **
calculations Plant generators X; **
Synchronous motors 1.5 X$ **
Induction Motors
Above 1000 hp > 1200 r/min 1.5 Xi*** **
Above 250 hp > 1800 r/min 1.5 X;*** **
All other motors
50-1000 hp 3 xi*** **
Less than 50 hp neglect
*Impedance ( 2 )values can be used for low voltage breaker duties.
**Not applicable.
***X&,for induction motors = locked rotor reactance.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

a
I
0

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

d
ul
m
t

rcl
IJl

$
a I
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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

ANSI/IEEE C37.010-1979. When exact

values can be obtained they should be Xtotal = m2
X l x2

used. - 1 4 * 11.66 = 6.36

Examples of preparation of motor Xmomentary total - 1 4 + 11.66
impedances for input t o the computer
21
21 + 2299 4 2 . 2
a
are as follows: Xiinterrupting total-

(1)13.8kV 9000 hp synchronous 0.84 0.97 = o.45

motors medium and low voltage calcula- Rinterrupting = 0.83 + 0.97
tions. See Fig 55, bus 8.
(3) 2.4 kV motors low voltage calcula-
- motor
-
X
:
base MVA * tion. See Fig 55, bus 20.
Xmomentary motor rated MVA (a) 2 MVA synchronous motor
- 0.20 * 100 = 2.20
-

XinterruDtine.=
. -
1.5
9.1
(see Table 10) 2.20
Xmomentary = 0.28 - -
loo= 1 4
2.0
= 3.30
3.30 - 3.30 - o.094 (b) 1.75 MVA of induction motors
enterrupting - x/R 35 between 50 hp and 1000 hp

(2) 2.4 kV motors medium voltage cal- 100

culation. See Fig 55, bus 20. Xmomentary = 0-17 -
1.75 - 9.7
(2)2 MVA synchronous motor
(c) Total combined motor momen-
\ ,

tary impedance
Xmomentary = 0.28 - loo= 1 4
2 .o
Xinterrupting= 1.5 1 4 = 21 - 14 9.7 = 5.73
21 21
Rinterrupting- x / R - 25 - 0.84
Xmomentary total - 1 4 + 9.7

(4) 480 V motors medium voltage cal-

(b) 1.75 MVA of induction motors culation. See Fig 55, bus 17.
between 50 hp and 1000 hp (a) 1.0 MVA of induction motors 50
t o 150 hp
100
G o m e n t a w lumped = O*I7 1.75
- 1.2 = 11.66 Xmomentary = 0.25 1.0 1 . 2 = 3 0
loo *

100 Xinterrupting= 0.25 -

loo 3 = 7 5
xinterrupting lumped= O.I7 1.75 3*0 1.o
= 29
2929 Rinterrupting --2
x / R = 75
g = 8.33
Rinterrupting lumped= - --
X/R - 30
(b) 0.5 MVA of induction motors
(c) Total combined motor imped- less than 50 hp neglect
ances using the expression for combined (5) 480 V motors low voltage calcula-
X (or R ) tion. See Fig 55, bus 17.

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

-
- 0.25 * 100 rupting duty with its associated multiply-
&omentan
total motor MVA ing factor
- 0.25 100
- - (5) Symmetrical and asymmetrical cur-
1.5 rent for breaker momentary duty
= 16.7 (6) Local and remote fault contribu-
- 16.7 - 1.85
tions.
Rmomentary 9 To arrange system data contained on
the impedance diagram so it can be ac-
NOTE: Interrupting impedances are generally cepted by the computer program, it is
not applicable for low voltage calculations.
necessary t o make up an input data tape
for medium voltage momentary calcula-
For the example all motors and the tion, medium voltage interrupting calcu-
generator are assumed t o be operating. lation, and low voltage calculation. Fig-
This creates the highest possible short ure 56 shows the data arranged for typ-
circuit currents the equipment may be ing paper input data tape for medium
subjected t o since total short-circuit cur- voltage interrupting calculations.
rents from all system motors, generator, Input data tape is a paper tape which,
and utility connection are present. Note, when fed into the computer, becomes a
however, that the 13.8 kV bus tie is file for data storage. Change cases can
normally open and always will be unless then easily be run by modifying data
one utility transformer is out of service. lines in the file. The data file must be
If the tie breaker were closed for normal given a name. In this sample study the
operation the fault duty would be more data file name for medium voltage inter-
severe and the study would be based on rupting calculation is CSP 100.
this operating mode. Figure 57 shows the program listing of
The example study does not inchide input data from data file CSP 100. Data
prefault steady-state load currents. The is usually listed in this way so it can be
effect of system load currents is usually checked for errors before proceeding
negligible in short-circuit current studies with short circuit calculations.
for industrial and commercial power Figure 58 is a sample of the computer
distribution systems. output for the medium voltage interrupt-
ing case giving remote bus voltages in per
6.5 Digital Computer Program Output unit of normal voltage, and short-circuit
Records contributions in MVA.
(1)Total and symmetrical short-circuit Figure 59 is computer output showing
current duty at the faulted bus t o com- total fault level in MVA at each faulted
pare directly with circuit breaker capa- bus, and also contributions from all con-
bility necting buses.
(2) Short-circuit contributions from all Also shown are X I R ratios a t the faulted
buses connected t o the faulted bus or bus, multipliers taken from the standards
between any other two buses specified in t o apply t o the E/X values for both 8
the input, or both cycle and 5 cycle breakers, and the fault
(3) Voltage at the remote buses where duty for direct comparison with the cir-
fault contributions are specified by (2) cuit breaker rating. Remote (in this case
(4)System X / R ratio at the fault point the utility system), and local (in this case
for medium voltage circuit breaker inter- the in-plant generator), sources of short

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

PROGRAM INPUT DATA TO BE TYPED EXPLANATION OF DATA Type o f C a l c u l a t i o n

+ -
LINE NUMBER FOR TAPE /=IInput d a t a t o be l i s t e d
- __ --
__--
+
.
-- -
I

10 JX AND
F
R RED,
I
CHECK, YES*, 100 4------- S t u d y Base MVA
Qemote b u s i n f o . t o h e p r o v i d e d

70 IEEE. ANYWHERE - INTERNATIONAL t--- ?e c-

P r o- t I d- entification
100 l A , INTERRUPTING CASE + Case number and i d e n t i f i c a t i o n
110 0,40,.0045,.1 U t i l i t y s y s t e m bus a n d R a n d x v a l u e s
120 0,o 4 End of u t i l i t y s y s t e m d a t a
121 .
0,24, 0 18,. 9 4 - L o c a l g e n e r a t o r b u s and R a n d X v a l u e s
130 0 , o ri End o f g e n e r a t o r d a t a
131 4 0 , 1 , . 0 1 4 , . 034- U t i l i t y b u s a n d l i n e impedance
132 4 O , l , . 0 1 4 , . 034
133 1,3,.067,.533 U t i l i t y t i e t r a n s f o r m e r b e t w e e n Buses 1 and 3 R a n d X v a l u e s
134 2 , 4 , .067,. 533
135 3,5,.07,.009 f- P l a n t c a b l e R a n d Y b e t w e e n R u s e s 3 and 5
136 3,6,.026,.011 etc.
137 3,9, .044, .016
138 3,26,. 146,.019
139 4,7,.022,.0095
140 4,8,.008,.01
141 4,15,.084,.026
142 4,24,. 1,.064
14 3 5,39,. 463.3.48
144 6 , 1 1 , . 4 5 8 , 3 . 6 7
145 6 , 1 4 , . 1 8 9 , .OS7
146 7 , 1 6 , . 256, . 0 3 3
147 7 , 2 7 , . 0 4 2 , . 0 1 5
148 9 , 1 2 , . 0 3 6 , . 0 0 5
149 9 , 2 5 , . 3 9 5 , . 0 5 1
150 1 0 , 1 3 , . 0 4 3 , . 0 0 6
151 1 0 , 2 7 , . 1 0 2 , . 0 1 3
152 1 2 , 1 7 , . 5 2 9 , 4 . 5
153 1 3 , 1 8 , . 5 2 9 , 4 . 5
154 1 4 , 1 9 , . 2 4 4 , l . 47
155 1 5 , 2 0 , . 2 4 4 , 1 . 4 7
156 1 6 , 2 1 , . 9 5 8 , 7 . 6 7
157 2 4 , 3 1 , . 0 7 4 , . 0 0 9
158 2 4 , 3 2 , . 1 0 4 , . 0 1 4
159 2 5 , 2 8 , . 5 4 8 , 3 . 8 3
160 2 6 , 2 9 , . 5 4 8 , 3 . 8 3
161 2 7 . 3 0 , . 5 4 8 , 3 . 8 3
162 2 8 , 3 8 , . 3 2 2 , . 2 9 2
163 29.38.. 4 2 5 . . 385
164 3 0 , 3 8 , . 3 2 2 , .29 2
165 3 1 , 3 6 , . 3 2 9 , 2 . 3
166 32.37..
, , 82 1.5.75
.
17iO,8,.094,3.3--Motor R a n d X v a l u e s c o n n e c t e d t o Bus 8
176 0 , 1 1 , 1 . 7 , 3 4 etc.
17- 0 , 1 7 , 8 . 3 3 , 7 5
1780,18,8.33,75
175 0 , 1 9 , . 4 1 , 1 0 . 2
180 0 , 2 0 , . 4 5 , 1 2 . 2
181 0 , 2 8 , 1 1 . 9 , 1 0 7
182 0 , 2 9 , 1 1 . 9 , 1 0 7
183 0 , 3 0 , 1 1 . 9 , 1 0 7

-
184 0 , 3 6 , . 2 9 1 , 1 0 . 2
185 0 , 3 7 , 1 1 . 9 , 1 0 7
186 0 , 3 9 , . 4 9 , 1 4 . 6
230 0,O End o f d a t a f i l e

Fig 56
Data Taken from the Impedance Diagram and Arranged €or
Program Input Data Paper Tape Medium Voltage Interrupting Calculation

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

NAME O F DATA F I L E ? CSplOO 4 NOTE: USER MUST TYPE IN ANSWERS

I N P U T DATA TO QUESTION6
B U S TO B U S = R JX
0 40 0.0045 0.1
0 24 0. oia 0.9
1 40 0.014 0.034
2 40 0.014 0.034
1 3 0.067 0.533
2 4 0.067 0.533
3 5 0.07 0.009
3 6 0.026 0.011
3 9 0.044 0.016
3 26 0.146 0.019
4 7 0.022 0.0095
4 a 0.008 0.01
4 15 0.084 0.026
4 24 0.1 0.064
5 39 0.463 3.48
6 11 0.458 3.67
6 14 0.189 0.057
7 16 0.256 0.033
7 27 0.042 0.015
9 12 0.036 0.005
9 25 0.395 0.051
10 13 0.043 0.006
10 27 0.102 0.013
12 17 0.529 4.5
13 18 0.529 4.5
14 19 0.244 1.47
15 20 0.244 1.47
16 21 0.958 7.67
24 31 0.074 0.009
24 32 0.104 0.014
25 28 0.548 3.83
26 29 0.548 3.83
27 30 0.548 3.83
28 38 0.322 0.292
29 38 0.425 0.385
30 38 0.322 0.292
31 36 0.329 2.3
32 37 0.821 5.75
0 a 0.094 3.3
0 11 1.7 34
0 17 8.33 75
0 18 8.33 75
0 19 0.41 10.2
0 20 0.45 12.2
0 28 11.9 107
0 29 11.9 107
0 30 11.9 107
0 36 0.291 10.2
0 37 11.9 107
0 39 0.49 14.6
S Y S T E M HAS 1 LOCAL S O U R C E S A N D 1 REMOTE SOURCES-LOCAL SOURCE = GENERATOR
REMOTE SOURCE = UTILITY
I N P U T DATA CORRECT? yes
I N P U T DATA L I S T E D I N O U T P U T ? yes

P R I N T A L L B U S E S ? no
3 C Y C . MF FOR WHICH 5 B U S E S ? 3,4,24,19,0
P R I N T A L L B U S E S ? no
3 C Y C . MF FOR WHICH 5 B U S E S ? O,O,O,O,O
-- ONLY SELECTED FAULTED
BUSES ARE CONSIDERED IN
THIS EXAMPLE STUDY
P R I N T A L L B U S E S ? NO
I N P U T 5 B U S NUMBERS? 3,4,24,19,0

Fig 57
Program Listing of Input Data from Data Tape
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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

REMOTE MVA CONTRIBUTIONS-CASE IA NOTE : USER MUST TYPE IN ANSWERS

TO QUESTIONS
BUS i: FAULTED ? 3
REMOTE L I N E ? 40,l
CONTRIBUTION FROM 40 ( 0.854 V ) TO 1 ( 0.803 V ) = 150.615 YVA

REMOTZ L I N E ? 40,2
CONTRIBUTION FROM 40 ( 0.854 V) TO 2 ( 0.856 V ) = 4.59 XV.4

RENOTE L I N E ? 2,4
CONTRIBUTION FROM 2 ( 0.856 V ) TO 4 ( 0.88 V ) = 4.59 >!VA

RENOTE L I N E ? 3,15
CONTRIBUTION FROM 4 ( 0.8b V ) TO 1 5 ( 0.88 V ) = 0.676 YVP

REMOTE L I N E ? 4,7
CONTRISUTION FROM 4 ( 0.88 V) TO 7 ( U.879 V ) = 13.283 YVA

REMOTE L I N E ? 4,8
CONTRIBUTION FROM 4 ( 0.88 V ) TO 6 ( 0.8d V ) = 3.627 PlVA

REMOTE L I N E ? 4,24
CONTRIBUTION FROM 4 ( 0.88 V) T U 24 ( 0.889 V ) = 13.372 MVA

REMOTZ L I N E ? 1U,27
CONTRIBUTION FROM 1 0 ( 0.877 V) TO 27 ( 0.677 V ) = 0.154 ?lVA

&EMOTE L I N E 1 0.U

SUS p FAULTED ? 4
REMOTE L I N E ? 4U,1
CONTRIBUTION FROM 40 ( 0.843 V) T O 1 ( 0.84 V ) = 8.233 YVA

REMOTE L I N E ? 40.2
CONTRIBDTION FROI.1 40 ( 0.843 V) T O 2 ( 0.793 V ) = 148.691 MVA

REMOTE L I N E ? 1,3
CONTAIBUTION FROM 1 ( 0.84 v) TO 3 ( 0.796 V I = a.233 YVA

REMOTE L I N E ? 3,5
CONTRISUTION FROM 3 ( 0 . 7 Y 6 V ) TO 5 ( 0.796 V ) = 1.127 MVA

RE:4CTE L I N E ? 3,6
CONTRIBdTIOK FZOM 3 ( 0.796 V ) TO 6 ( 0.797 V ) = 2.275 YVA

REMOTE L I N E ? 3,9
C O N T R I B U T I O d FROM 3 ( 0.’96 V ) TO 9 ( 0.795 V ) = 5.724 YVA

REMOTE L I N E ? 3,26
CONTRIBUTION FROM 3 ( 0.796 V) T O 26 ( 0.795 V ) = 5.958 ?lVA

REMOTE L I N E 1 1U,27
CONTRIBUTION FROI.1 10 ( 0.004 V) TO 27 ( 0.004 V)= 1 . 2 4 8 NVA

REMOTE L I N E ? 0.0

Fig 58
Sample Computer Output Listing of Remote Bus Voltages
and Short Circuit Contributions to the Faulted Bus
Medium Voltage Interrupting Case Short Circuit Study.

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 IEEE
SHORT-CIRCUIT STUDIES Std 399-1980

RESULTS IN MVA
BUS 3
E/X= 183.915 MVA X/R= 8.209
MF FOR 8 CY(.O667 SEC. CONT. PART)TOT CB = 1 ,CB DUTY = 183.915
IYF FOR 5 C Y ( . O ~ O OSEC. CONT. PARTISYM ca = 1 ,CB DUTY = 183.915
CONTRIBUTION :
BUS 1 = 150.613 BUS 5 = 5.5175 BUS 6 = 11.1686
BUS 9 = 8.9544 BUS 26 = 7.6373
B U S NO. LOCAL(MVA) REMOTE(MVA) GEN VOLTS
40 0 146.023 0.854
24 1.38 11.002 0.889
REMOTE / REMOTE+LOCAL = 0.991
BUS 4
E/X= 312.053 MVA X/R= 10.262
M F FOR 8 CY(.O667 SEC. CONT. PART)TOT CB = 1 ,CB DUTY = 312.053
MF FOR 5 CY(.0500 SEC. CONT. PART)SYM CB = 1 ,CB DUTY = 312.053
CONT2IBUTION :
BUS 2 = 148.69 BUS 7 = 14.4201 BUS 8 = 30.2067
BUS 1 5 = 7.2972 BUS 24 = 111.437
BUS NO. LOCAL(MVA) REMOTE(MVA) GEN VOLTS
40 0 156.924 0.843
24 95.827 7.359 0.071
REMOTE / REMOTE+LOCAL = 0.632
BUS 24
E/X= 297.764 MVA X/R= 21.523
NF FOR b CY(.O667 SEC. CONT. PART)TOT CB = 1.048 ,CB DUTY = 312.087
MF FOR 5 CY(.0500 SEC. CONT. PART)SYM CB = 1.018 ,CB DUTY = 303.103
CONTRIBUTION :
BUS 4 = 177.791 BUS 31 = 7.974 BUS 32 = 0.13721
GEN = 111.111
BUS NO. LOCAL(MVA) REMOTE(MVA) GEN VOLTS
40 0 139.068 0.861
24 111.111 0 0
REMOTE / REMOTE+LOCAL = 0.556
BUS 19
E/X= 57.2469 NVA X/R= 7.565
M F FOR 8 CY(.0667 SEC. CONT. PART)TOT CB = 1 ,CB DUTY = 57.247
MF FOR 5 CY(.OSOO SEC. CONT. PART)SYM CB = 1 ,CB DUTY = 57.247
CONTRIBUTION :
BUS 14 = 47.4432 GEN = 9.8039
BUS NO. LOCAL (MVA) REMOTE (MVA) GEN VOLTS
40 0 39.485 0.961
24 0.101 3.247 0.97
REHOTE / REMOTE+LOCAL = 0.998

Fig 59
Computer Output Giving Fault Levels in MVA for
the Four Faulted Buses, Medium Voltage Interrupting Case Short Circuit Study

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Table 11
Sample Summary of Results for Example Short Circuit Study
Short Circuit Duty t o Compare
Directly with Equipment Rating Voltage in Per Unit o n
Associated Buses
Short Momentary Interrupting (Interrupting Case Calculations)
Circuit (first '/i cycle) 5 Cycle
Location Asym kA Sym MVA Bus1 Bus4 Bus3 Bus24
13.8 kV
Bus 3 ( F 3) 13.4 183.9 0.80 0.88 0 0.89
13.8 kV
Bus 4 ( F 4 ) 22.7 31 2 0.84 .o 0.80 .o 4-
13.8 kV
Bus 24 ( F 24) 21.4 303 0.86 0.11 0.82 .o
2.4 kV
Bus 19 (F 19) 26.1 57.2 0.95 0.97 0.74 0.97
480 V
Bus 30 (F 30) 68.9* Not applicable 0.96 0.92 0.92 0.92

*Low voltage calculation in first Im cycle symmetrical kA.

circuit current are listed separately. [2] IEEE Std 242-1975, IEEE Recom-
Table 11 shows a sample summary of mended Practice for Protection and Co-
the short-circuit study results. Not all ordination of Industrial and Commercial
computer output information is shown Power Systems.
since it is not possible to clearly present
this information on one table. Several [3] A N S I / I E E E C37.13-1980, I E E E
tables might be necessary to present Standard for Low Voltage AC Power
complete study results, or in some cases, Circuit Breakers Used in Enclosures.
short circuit diagrams showing all system [4] ANSI/IEEE C37.010-1979, IEEE
voltages and short circuit flows, provide Application Guide for AC High Voltage
the best means of presenting study Circuit Breakers Rated on a Symmetrical
results. Current Basis (Consolidated edition).
Using the complete computer output
information, study results can be ana- [5] ANSI/IEEE C37.5-1979, IEEE Guide
lyzed and applied to specific equipment for Calculation of Fault Currents for
shown on the one-line diagram. Application of AC High-Voltage Circuit
Breakers Rated on a Total Current Basis
6.5 References. The following references (Revision of ANSI C37.5-1969).
were used in the preparation of Section
6. [6] IEEE Transactions Paper 69TP146-
[l]IEEE Std 141-1976, IEEE Recom- IGA Sep/Oct 1969, Interpretation of
mended Practice for Electric Power New American National Standards for
Distribution for Industrial Plants. Power Circuit Breaker Application.

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 7. Transient Stability Studies

7.1 Introduction. For years, system sta- 7.2.2 Steady-State Stability. Although
bility has been a problem almost exclu- the discussioli in the rest of this section
sively t o electric utility engineers. Within revolves around stability under transient
the past decade, however, increasing conditions such as faults, switching oper-
numbers of industrial and commercial ations, etc, there should also be an aware-
facilities have installed local generation, ness that a power system can become un-
large synchronous motors, or both. This . stable under steady-state conditions.
means that system stability is of concern The simplest power system t o which
to a growing number of industrial plant stability considerations apply consists of
electrical engineers and consultants. a pair of synchronous machines, one act-
ing as a generator and the other acting as
7.2 Stability Fundamentals a motor, connected together through a
7.2.1 Definition of Stability. Funda- reactance. See Fig 60. (In this model the
mentally, stability is a property of a reactance is the sum of the transient
power system containing two or more reactances of the two machines and the
synchronous machines. The system is
stable, under a specified set o f conditions, Fig 60
if all of its synchronous machines remain Simplified Two-Machine
in step with one another (or having pulled Power System
out of step, regain synchronism soon
afterwards). The emphasis on specified
conditions in this definition is intended
to stress the fact that a system which is
stable under one set of conditions can be
unstable under some other set of condi- G:
tions.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

mentarily slow down the rotor of a within the steady-state stability limits of
synchronous motor to permit the rotor the system, an overshoot can result in
field to fall farther behind the stator loss of synchronism. If not, both rotors
field and thus increases 6,. The rate at will undergo a damped oscillation and
which rotor speed can change is deter- ultimately settle t o their new steady-state
mined by the moment of inertia of the values.
rotor, plus whatever is mechanically An important concept here is syn-
coupled to it, prime mover, load, reduc- chronizing power. The more real power
tion gears, etc. This means a machine transmitted over the transmission link
with high inertia is less likely to pull out between the two machines, the more
under a disturbance of brief duration likely they are to remain in synchronism
than a low-inertia machine, all other in the face of a transient disturbance.
characteristics being equal. Synchronous machines separated by a
7.2.4 Two-Machine Systems. The pre- sufficiently low impedance behave as
vious discussion of transient behavior of one composite machine, since they tend
synchronous machines is based on a single to remain in step with one another re-
machine connected to a good approxima- gardless of external disturbances.
tion of an infinite bus. An example is the 7.2.5 Multimachine Systems. At first
typical industrial situation where a syn- glance, it appears that a power system in-
chronous motor of at most a few thou- corporating many synchronous machines
sand horsepower, is connected t o a utility would be extremely complex to analyze.
company system with a capacity of This is true if a detailed, precise analysis
thousands of megawatts. Under these is needed; a large digital computer and a
conditions we can safely neglect the sophisticated program are required for a
effect of the machine on the power complete transient stability study of a
system. multimachine system. However, many of
A system consisting of only two ma- the multimachine systems encountered
chines of comparable size connected in industrial practice contain only syn-
through a transmission link, however, chronous motors which are similar in
becomes more complicated, because the characteristics, closely coupled electric-
two machines can affect one another’s ally, and connected to a high-capacity
performance. The medium through utility system. Under most types of
which this occurs is the air gap flux. This disturbance, motors will remain syn-
is a function of machine terminal voltage, chronous with each other, although they
which is affected by the characteristics can all lose synchronism with the utility.
of the transmission system, the amount Thus, the problem is similar to a single
of power being transmitted, and the synchronous motor connected through
power factor, etc. an impedance to an infinite bus. The
In the steady state, the rotor angles of simplification should be apparent. More
the two machines are determined by the complex systems, where machines are of
simultaneous solution of their respective comparable sizes and are separated by
torque equations. Under a transient dis- substantial impedances, will usually in-
turbance, as in the one-machine system, volve a full-scale computer stability study.
the rotor angles move toward values
corresponding to the changed system 7.3 Problems Caused by Instability. The
conditions. Even if these new values are most immediate hazards of asynchronous

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

TORQUE

PULLOUT TORQUE
(MOTOR AC1

Fig 61
Torque Versus Rotor Angle Relationship for
Synchronous Machines in Steady State

a pole. Unless the load torque is reduced a gradual change occurs in one or more
below the 90" level (the pullout torque), of the parameters of the torque equation,
the motor will continue slipping poles the rotor angle will tend t o overshoot the
indefinitely. The problems that can fol- final value determined by the changed
low from extended operation in this out- conditions. This disturbance can be severe
of-step condition will be discussed further enough t o carry the ultimate steady-state
in this section. rotor angle past go", or the transient
A generator operates similarly. Increas- swing rotor angle past 180". Either event
ing torque input until the rotor angle results in the slipping of a pole. If the
exceeds 90" results in pole slipping and conditions which caused the original dis-
loss of synchronism with the power sys- turbance are not corrected, the machine
tem, assuming constant electrical load. will then continue t o slip poles, in short,
Similar relations apply to the other pull out of step with the power system
parameters of the torque equation. For t o which it is connected.
example, air-gap flux &R is a function of Of course, if the rotor angle overshoot
voltage at the machine. Thus if the other does not transitorily exceed 180°,or if
factors remain constant, a change in sys- the disturbance causing the rotor swing
tem voltage will cause a change in rotor is promptly removed, the machine may
angle. Likewise, changing the field excita- remain in synchronism with the system.
tion will cause a change in rotor angle, if The rotor angle then oscillates in de-
constant torque and voltage are main- creasing swings until it settles t o its final
tained. value (less than 90"). The oscillations are
The preceding discussion refers t o damped by mechanical load and losses in
rather gradual changes in the conditions the system, especially in the damper
affecting the torque angle, so that ap- windings of the machine.
proximately steady-state conditions A change in rotor angle of a machine
always exist. The coupling between the generally requires a change in speed of
stator and rotor fields of a synchronous the rotor. For example, if we assume
machine, however, is somewhat elastic. that the stator field frequency is con-
This means that if an abrupt rather than stant, it is necessary to at least mo-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

mentarily slow down the rotor of a within the steady-state stability limits of
synchronous motor t o permit the rotor the system, an overshoot can result in
field t o fall farther behind the stator loss of synchronism. If n o t , both rotors
field and thus increases 6,. The rate a t will undergo a damped oscillation and
which rotor speed can change is deter- ultimately settle t o their new steady-state
mined by the moment of inertia of the values.
rotor, plus whatever is mechanically An important concept here is syn-
coupled t o it, prime mover, load, reduc- chronizing power. The more real power
tion gears, etc. This means a machine transmitted over the transmission link
with high inertia is less likely t o pull o u t between the two machines, the more
under a disturbance of brief duration likely they are t o remain in synchronism
than a low-inertia machine, all other in the face of a transient disturbance.
characteristics being equal. Synchronous machines separated by a
7.2.4 Two-Machine Systems. The pre- sufficiently low impedance behave as
vious discussion of transient behavior of one composite machine, since they tend
synchronous machines is based o n a single t o remain in step with one another re-
machine connected t o a good approxima- gardless of external disturbances.
tion of an infinite bus. An example is the 7.2.5 Multimachine Systems. At first
typical industrial situation where a syn- glance, it appears that a power system in-
chronous motor of a t most a few thou- corporating many synchronous machines
sand horsepower, is connected t o a utility would be extremely complex t o analyze.
company system with a capacity of This is true if a detailed, precise analysis
thousands of megawatts. Under these is needed; a large digital computer and a
conditions we can safely neglect the sophisticated program are required for a
effect of the machine on the power complete transient stability study of a
system. multimachine system. However, many of
A system consisting of only t w o ma- the multimachine systems encountered
chines of comparable size connected in industrial practice contain only syn-
through a transmission link, however, chronous motors which are similar in
becomes more complicated, because t h e characteristics, closely coupled electric-
two machines can affect one another’s ally, and connected t o a high-capacity
performance. The medium through utility system. Under most types of
which this occurs is the air gap flux. This disturbance, motors will remain syn-
is a function of machine terminal voltage, chronous with each other, although they
which is affected by the characteristics can all lose synchronism with the utility.
of the transmission system, the amount Thus, the problem is similar to a single
of power being transmitted, and the synchronous motor connected through
power factor, etc. an impedance t o an infinite bus. The
In the steady state, t h e rotor angles of simplification should be apparent. More
t h e t w o machines are determined by the complex systems, where machines are of
simultaneous solution of their respective comparable sizes and are separated by
torque equations. Under a transient dis- substantial impedances, will usually in-
turbance, as in the one-machine system, volve a full-scale computer stability study.
t h e rotor angles move toward values
corresponding t o the changed system 7.3 Problems Caused by Instability. The
conditions. Even if these new values are most immediate hazards of asynchronous

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

operation of a power system are the high (4)Starting a motor which is large
transient mechanical torques and currents relative t o a system generating capacity
which usually occur. To prevent these (5) Switching operations
transients from causing mechanical and (6) Impact loading on motors
thermal damage, synchronous motors (7) Abrupt decrease in electrical load
and generators are almost universally on generators
equipped with pullout protection. For The effect of each of these disturbances
motors of small t o moderate sizes, this should be apparent from the previous
protection is usually provided by a discussion of stability fundamentals.
damper protection of pullout relay Items (1)through (5) tend t o reduce volt-
which operates on the low power factor age levels, ultimately requiring an increase
occurring during asynchronous operation. in machine angles t o maintain a given
The same function is usually provided load. Items (6) and (7) directly increase
for large motors, generators, and syn- the rotor angles of affected machines.
chronous condensers by loss-of-field re-
laying. In any case, the pullout relay 7.5 Solutions t o Stability Problems. Gen-
trips the machine breaker or contactor. erally, anything which decreases the
Whatever load is being served by the ma- severity or duration of a transient dis-
chine is naturally interrupted. Conse- turbance will make the power system
quently, the primary disadvantage of a less likely t o become unstable under that
system which tends t o be unstable is the disturbance. In addition, increasing the
probability of frequent process inter- moment of inertia per rated kVA of the
ruptions. synchronous machines in the system will
Out-of-step operation also causes large raise stability limits by resisting changes
oscillatory flows of real and reactive in rotor speeds required t o change rotor
power over the circuits connecting the angles.
out-of-step machines. Impedance or dis- 7.5.1 System Design. System design
tance-type relaying protecting these lines primarily affects the amount of synchro-
can falsely interpret power surges as a nizing power that can be transferred
line fault, tripping the line breakers and between machines. Two machines con-
breaking up the system. Although this is nected by a low-impedance circuit such
primarily a utility problem, large indus- as a short cable or bus run will probably
trial systems or those where local genera- stay synchronized with each other under
tion operates in parallel with the utility all conditions except a fault on the con-
can be susceptible. necting circuit, a loss of field excitation,
or an overload. The greater the impedance
7.4 System Disturbances that Can Cause between machines, the less severe a dis-
Instability. The most common disturb- turbance will be required t o drive them
ances that produce instability in indus- out of step. This means that from the
trial power systems are (not necessarily standpoint of maximum stability all syn-
in order of probability): chronous machines should be closely
(1)Short circuits connected t o a common bus. Limitations
(2) Loss of a tie circuit t o a public on short circuit duties, economics, and
utility the requirements of physical plant lay-
(3) Loss of a portion of on-site genera- out usually combine t o render this radical
tion solution impractical.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

7.5.2 Design and Selection of Rotating as rapidly as possible. A system which

Equipment. Design and selection of ro- tends t o be unstable should be equipped
tating equipment can be a major contrib- with instantaneous overcurrent protec-
utor t o improving system stability. Most tion on all of its primary feeders, which
obviously, use of induction instead of are the most exposed section of the
synchronous motors eliminates the po- primary system. As a general rule, in-
tential stability problems associated with stantaneous relaying should be used
the latter. (Under rare circumstances an throughout the system wherever selectiv-
induction motor /synchronous generator ity permits.
system can experience instability, in the 7.5.4 Voltage Regulator and Exciter
sense that undamped rotor oscillations Characteristics. Voltage regulator and
occur in both machines, but the possibil- exciter characteristics affect stability
ity is too remote t o be of serious con- because, all other things being equal,
cern.) However, economic considerations higher field excitation requires a smaller
often preclude this solution. rotor angle. Consequently, stability is en-
Where synchronous machines are used, hanced by a properly applied regulator
stability can be enhanced by increasing and exciter which respond rapidly to
the inertia of the mechanical system. transient effects and furnish a high de-
Since the H constant (stored energy per gree of field forcing. In this respect,
rated kVA) is proportional t o the square modern solid-state voltage regulators and
of the speed, fairly small increases in static exciters can contribute markedly
synchronous speed can pay significant to improved stability. (On the other
dividends in higher inertia. If carried too hand, a mismatch in exciter and regu-
far, this can become self-defeating, be- lator characteristics can make an existing
cause higher speed machines have smaller stability problem even worse.)
diameter rotors. W K 2 varies with the
square of the rotor radius, so the increase 7.6 Transient Stability Studies. Knowing
in H due t o higher speed may be offset how to correct an unstable power system
by a decrease due to the lower WK2 of is not very valuable if, in order to test
a smaller diameter rotor. our proposed recommendations, we have
A further possibility is t o use synchro- t o stage stability tests on the actual sys-
nous machines with low transient reac- tem. This is especially true if the system
tances that permit the maximum flow of in question is still in the design stage.
synchronizing power. Applicability of Consequently, we need a fast, simple,
this solution is limited mostly by short and inexpensive way to simulate transient
circuit considerations and machine de- performance of a power system under a
sign problems. variety of normal and abnormal condi-
7.5.3 System Protection. System pro- tions.
tection often offers the best prospects 7.6.1 History. The first transient stabil-
for improving the stability of a power ity studies responding t o this need were
system. The most severe disturbance done by semieducated guesses. When this
which an industrial power system is likely technique proved insufficiently accurate,
to experience is a short circuit. To pre- and as rotating-machine theory was de-
vent loss of synchronism, as well as to veloped, simple power systems consisting
limit personnel hazards and equipment of only a few machines were analyzed by
damage, short circuits should be isolated manual calculations or mechanical mod-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

As additional data on the machines be- late line t o line or ground faults, the
come available, better approximations effects of these faults on synchronizing
can be used. This permits more accurate power flow can be duplicated by apply-
results which remain reliable for longer ing a three-phase fault with a properly
time periods. Modern large-scale stability chosen fault impedance. This means the
programs can simulate all of the follow- effects of any type of fault on stability
ing characteristics of a rotating machine: can be studied.
(1)Voltage regulator and exciter In addition t o faults, stability programs
(2) Steam system or other prime mover, can simulate switching of lines and gen-
including governor erators. This is particularly valuable in
(3) Mechanical load the load-shedding type of study, which
(4)Damper windings will be covered in the following section.
(5) Salient poles Finally, starting of large motors on
(6) Saturation relatively weak power systems and im-
Induction motors can also be simulated pact loading of running machines can be
in detail, together with speed-torque analyzed.
characteristics of their connected loads. 7.6.5 Data Requirements for Stability
In addition t o rotating equipment, the Studies. The data required t o perform a
stability program can include in its simu- transient stability study, and the recom-
lation practically any other major sys- mended format for organizing and pre-
tem component, including transmission senting the information for most con-
lines, transformers, capacitor banks, and venient use are covered in detail in the
voltage regulating transformers and dc application guides for particular stability
transmission links in some cases. programs. The following is a summary of
7.6.4 Simulation of Disturbances. The the generic classes of data needed. Note,
versatility of the modern stability study that some of the more esoteric informa-
is apparent in the range of system dis- tion is not essential; omitting it merely
turbances that can be represented. The limits the accuracy of the results, espe-
most severe disturbance which can occur cially at times exceeding five times the
on a power system is usually a three-phase duration of the disturbance being studied.
bolted short circuit. Consequently, this The more essential items are marked by
type of fault is most often used t o test an asterisk (*).
system stability. Stability programs can (1)System data.
simulate a three-phase fault at any loca- (a) Impedances (R + jX) of all sig-
tion, with provisions for clearing the nificant transmission lines, cables, reac-
fault by opening breakers either after a tors, and other series components.*
specified time delay, or by the action of (b) For all significant transformers
overcurrent, underfrequency ,overpower, and autotramsformers
or impedance relays. This feature permits (i) kVA rating*
the adequacy of proposed protective (ii) Impedance*
relaying t o be evaluated from the stability (iii) Voltage ratio*
standpoint. (iv) Winding connection*
Short circuits other than the bolted (v) Available taps and tap in use*
three-phase fault cause less disturbance (vi) For regulators and load tap-
t o the power system. Although most changing transformers : regulation range,
stability programs cannot directly simu- tap step size, type of tap changer control*

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

(c) Short circuit capacity (steady- (c) For major induction machines or
state basis) of utility supply, if any* groups of machines
(d) kvar of all significant capacitor (i) Mechanical and/or electrical
banks* power ratings*
(e) Description of normal and alter- (ii) Inertia*
nate switching arrangements* (iii) Speed*
(2) Load data: real and reactive elec- (iv) Positive-sequence equivalent
trical loads on all significant load buses circuit data (for example, R I , X I , X,,
in the system* R2, X2)*
(3) Rotating machine data (v) Load speed-torque curve*
(a) For major synchronous machines (vi) Negative-sequence equivalent
(or groups of identical machines on a circuit data
common bus) (vii) Description of reduced-voltage
(i) Mechanical and/or electrical or other starting arrangements, if used*
power ratings (kVA, hp, kW, etc)* (d) For minor induction machines:
(ii) Inertia constant H or inertia detailed dynamic representation not
W K 2 of rotating machine and connected needed, represent as a static load
load or prime mover* (4) Disturbance data
(iii) Speed* (a) General description of disturb-
(iv) Real and reactive loading, if ance t o be studied, including (as appli-
base-loaded generator* cable) initial switching status; fault type,
(v) Speed-torque curve or other location and duration; switching opera-
description of load torque, if motor* tions and timing; manufacturer, type,
(vi) Direct-axis s u b t r a n si e n t ,* and setting of protective relays and
transient,* and synchronous reactances* clearing time of associated breakers*
(vii) Qua-hature-axis subtransient, (b) Limits on acceptable voltage, cur-
transient,* and synchronous reactances rent, or power swings*
(viii) Direct-axis and quadrature- ( 5 ) Study parameters
axis subtransient and transient* time (a) Duration of study*
constants (b) Integrating interval*
(ix) Saturation information (c) Output printing interval*
(x) Potier reactance (d) Data output required*
(xi) Damping data
(xii) Excitation system type time 7.6.6 Stability Program Output. Most
constants, and limits stability programs give the user a wide
(xiii) Governor and steam system choice of results t o be printed out. The
or other prime mover type, time con- program can calculate and print any of
stants, and limits the following information as a function
(b) For minor synchronous machines of time :
(or groups of machines) (1)Rotor angles, torques, and speeds
(i) Mechanical and/or electrical of synchronous machines
power ratings" (2) Real and reactive power flows
(ii) Inertia" throughout the system
(iii) Speed* (3) Voltages and voltage angles at all
(iv) Direct-axis synchronous reac- buses
tance* ( 4 ) System frequency

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

(5) Torques and slips of all induction disturbance applied. This is a reproduc-
machines tion of an actual computer printout. A
The combination of these results simplified one-line diagram of the system
selected by the user can be printed out appears as Fig 63. Note that while the
for each printing interval (also user- three-phase bolted fault on a synchronous
selected) during the course of the study bus feeder, Case I, cleared by instanta-
period. neous tripping of the feeder breaker,
The value of the study is strongly causes all five generators t o experience
affected by the selection of the proper swings of varying magnitude, the oscilla-
printing interval and the total duration tions in the rotor angles are obviously
of the simulation. Normally a printing damped and can be expected to die out.
interval of 0.01 or 0.02 s is used;longer By contrast, in Case I1 the fault is
intervals reduce the computer costs applied t o the tie between the synchro-
slightly, but increase the risk of missing nizing bus and one of the generator buses
fast swings of rotor angle. The computer and is cleared by tripping the tie circuit
time cost is nearly proportional to the breaker. The swing curves for this con-
total study time, so this parameter dition are shown in Fig 64. Generator
should be closely controlled for the sake No 1 is disconnected from the system
of economy. and suffers a severe overload, causing it
This is especially important if the sys- to decelerate, as shown by a unidirec-
tem and machines have been represented tional negative change in rotor angle.
approximately or incompletely, because The other machines stay in synchronism.
the errors will accumulate and render the
results meaningless after some point. A 7.7 Stability Studies on a Typical System.
time limit of five times the duration of Probably the best way to examine some
the major disturbance being studied is of the typical applications of stability
generally long enough to show whether analysis to industrial power systems is to
the system is stable or not, while keeping look at the stability studies which would
costs t o a reasonable level. go into the design of a typical large in-
7.6.7 Interpreting Results-Swing dustrial system including 20 MVA of lo-
Curves. The results of a computer transi- cal generation and 40 MVA of purchased
ent stability study are fairly easy to power capacity. The stability studies
understand once the user learns the basic which might be applied to this system
principles underlying stability problems. are :
The most direct way t o determine from (1)The basic layout of the primary
the study results whether a system is system can be affected by stability con-
stable is to look at a set of swing curves siderations. For example, an initial de-
for the machines in the system. Swing sign choice might be to connect the
curves are simply plots of rotor angles generated and purchased power buses
against time; if the curves of all the through only one tie circuit. However,
machines involved are plotted on com- stability studies could show that in-
mon axes, we can easily see whether adequate synchronizing power is avail-
they diverge (indicating instability) or able to prevent the generators and the
settle to new steady-state values. utility from losing synchronism during
For example, Fig 62 shows swing curves primary system faults unless two ties are
for a system which is stable under the provided. The same sort of considera-

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

1.0
TIME, S E C O N D S

Fig 62
Computer Printout of Swing Curves for
Case I Fault on System in Fig 63

tions might dictate that the 4160 V bus a selectively coordinated system, how-
ties be operated closed, to ensure the ever, unless expensive zone protection
lowest possible impedance between the schemes (bus differential, pilot wire, etc)
synchronous motors and the power are used. Balancing all of these factors,
sources t o enhance stability. probably the best procedure is t o design
(2) Related to the design of the basic the system layout around process require-
layout is the problem of protective re- ments, provide the fastest relaying pos-
laying. The system can be designed for sible within the constraints of selectivity
maximum inherent stability by closely and economics, and then check the pro-
coupling all machines. Or the same ob- posed layout and relaying by a series of
jective can often be obtained by design- stability studies simulating the more
ing the protective scheme for the fastest probable fault conditions. In the system
possible clearing of faults. Since the shown in Fig 65, three-phase faults are
former choice may involve economic applied on one 138 kV utility line ahead
sacrifices in the form of higher capacity of the plant transformers, on a feeder
switchgear, often the latter choice repre- from each of the 13.8 kV buses, and on
sents the best solution. Extra-fast relay- a feeder from each 4160 V bus. Of
ing can conflict with the requirements of course, the simulation would include

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

ro>
a

k
=!
t-
3

LL

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

37

m 16
W
W
CK
W
W
n
m-
-I
-3
c3
z A GEN NO I
a B GEN NO 2
[ZT
0 a C GEN N O 3
W
0 IX D GEN NO 4
-24 -a U- E GEN NO 5
li d
5 J 5
2 :3 =2
3

- 45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ( 3 1.0
TIME, SECONDS

Fig 64
Computer Printout of Swing Curves for
Case I1 Fault on System Shown in Fig 63

clearing of the fault via the proposed perfectly sound generation is available to
relaying. If any of these studies show an maintain service to the most critical
unstable condition, further stability loads. Obviously, a method of auto-
studies might be required to test the matically interrupting noncritica1 loads
effectiveness of various proposed solu- commensurately with the loss of system
tions. capacity would be valuable.
(3) In the systeni shown in Fig 65 One such possibility would be to trip
some considerations should certainly be noncritical feeders whenever the utility
given to automatic load shedding. If the tie breakers are opened. However, this
power company suffers an outage on the wired-in scheme lacks flexibility. To
138 kV lines while the plant is running permit shedding only the amount of
at nearly full load, the 20 MVA of local load required to prevent system collapse,
generation will abruptly be subjected t o many industrial plants with local genera-
an overload approaching 300%. This tion use underfrequency relaying. This
overload will promptly cause the gener- scheme depends on the fact that an over-
ators to trip off, leaving the plant with loaded generator slows down, dropping
no power at all, even though 20 MVA of the system frequency.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

CURRENT - 0
0
0
LIMITING c;t
Ivm
REACTOR

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 IEEE
TRANSIENT STABILITY STUDIES Std 399-1980

A two-stage load shedding scheme especially under abnormal conditions

might operate as follows: The first-stage when one or more power sources are out
relay operates at 59 Hz and a time delay of service. This effect can be evaluated
of 6 cycles, tripping 1 0 or 1 5 MVA of by a series of stability studies simulating
noncritical load; the second stage oper- motor starting under various conditions
ates at 58 Hz and a delay of 30 cycles, of system capacity, prestart motor
tripping an additional 20 MVA of some- terminal voltage, etc. The study results
what more critical load. yield motor accelerating times, real and
In designing the load-shedding scheme reactive power flows, and bus voltages at
for the system in Fig 65, first run a all critical points in the system.
stability study t o calculate the decay of As this discussion indicates, transient
system frequency when the utility tie is stability analysis should be an integral
lost, without any load shedding. Using part of the design or expansion of any
this frequency decrement curve, estimates industrial power system containing
can be made of the amounts of load t o several large synchronous machines, and
be shed and the frequency and time should be considered even if only one
delay settings for the underfrequency machine is being applied.
relays. Then these data can be used in
the stability study program to calculate 7.8 References
the system frequency versus time curve [ 11 Electrical Transmission and Distribu-
with the proposed load shedding. If suf- tion Reference Book, Westinghouse Elec-
ficient load is shed fast enough to pre- tric Corporation, East Pittsburgh, PA.,
vent system collapse, the validity of the 1964, chap. 13.
proposed relay scheme and settings is
[2] KIMBARK, E. W. Power System
confirmed. Usually several runs are made
Stability, vol 1 , New York, John Wiley,
with different system conditions in each
1948.
load shedding analysis.
(4) In the system shown in Fig 65, the [3] FITZGERALD, A. E. and KINGS-
effect of starting one of the large syn- LEY, CHARLES Jr. Electric Machinery,
chronous motors could be substantial, New York, McGraw-Hill, 1961, chap 5.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

8. Motor Starting Studies

8.1 Introduction. This section discusses widely recognized and studied effect of
benefits obtained from motor starting motor starting is the voltage dip experi-
studies and examines various types of enced throughout an industrial power
computer-aided studies normally per- system as a direct result of starting large
formed. Data or information required t o motors. Available accelerating torque
permit these studies along with expected drops appreciably at the motor bus as
results of a motor starting study effort voltage dips t o a lower value, extending
are also reviewed. the starting interval and affecting, some-
times adversely, overall motor starting
8.2 Need for Motor Starting Studies performance. During motor starting,
8.2.1 Problems Revealed. Motors on voltage level at the motor terminals
modern industrial systems are becoming should be maintained at approximately
increasingly larger. Some are considered 80% of rated voltage or above for a stan-
large even in comparison t o the total dard National Electrical Manufacturers
capacity of large industrial power sys- Association (NEMA) type B motor. This
tems. Starting large motors, especially value results from examination of speed-
across-the-line, can cause severe disturb- torque characteristics of this type motor
ances t o the motor and any locally con- (150% starting torque at full voltage)
nected load, and also t o buses electrically and the desire t o successfully accelerate
remote from the point of motor starting. a fully loaded motor at reduced voltage
A brief discussion of major problems (that is, torque varies with the square of
associated with starting large motors, the voltage). When other motors or
and therefore of significance in power lower shaft loadings are involved, the
system design and evaluation, follows. speed-torque characteristics of both the
8.2.2 Voltage Dips. Probably the most motor and its load should be examined

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

t o specifically determine minimum ac- 8.2.4 Special Torque Requirements.

ceptable voltage. Assuming reduced volt- Sometimes special loads must be acceler-
age permits adequate accelerating torque, ated under carefully controlled condi-
it should also be verified that the longer tions without exceeding specified torque
starting interval required at reduced limitations of the equipment. An example
torque caused by a voltage dip does not of this is starting a motor connected to a
result in the p t damage limit of the load through gearing. This application
motor being exceeded. requires a special period of low torque
8.2.3 Weak Source Generation. Smaller cushioned acceleration to allow slack in
power systems are usually served by limi- the gears and couplings t o be picked up
ted capacity sources, which generally without damage to the equipment.
magnify voltage drop problems on motor Certain computer-aided motor starting
starting, especially when large motors are studies allow an instant-by-instant shaft
involved. Small systems also often have output torque tabulation for comparison
limited on-site generation, which further to allowable torque limits of the equip-
complicates normal problems since addi- ment. This study can be used for select-
tional voltage drops occur in transient ing a motor or a starting method, or
impedances of local generators during both, with optimum speed-torque char-
the motor starting interval. The type of acteristics for the application. The results
voltage regulator system applied with the of a detailed study are used for sizing the
generators can dramatically influence starting resistors for a wound rotor motor
motor starting as illustrated in Fig 66. or in analyzing rheostatic control for a
A motor starting study can be useful, starting wound rotor motor which might
even for analyzing the performance of be used in a cushioned starting applica-
small systems. Certain digital computer tion involving mechanical gearing or a
programs can accurately model exciter/ coupling system that has torque trans-
regulator response under motor starting mitting limitations. High inertia loads
conditions necessary for meaningful re- increase motor starting time, and heating
sults and conclusions. in the motor due t o high currents drawn

Fig 66
Typical Generator Terminal Voltage Characteristics
for Various Exciter Regulator Systems

/-,-

HIGH SPEED REGULATOR /EXCITER SYSTEM

LOW SPEED REGULATOR /EXCITER SYSTEM

NO REGULATOR

I *
0 TIME

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

during starting can be intolerable. A draws an inrush current directly propor-

computer-aided motor starting study tional to terminal voltage, and therefore
allows accurate values of motor acceler- a lower voltage causes the motor to re-
ating current and time. This makes it quire less current, thereby reducing the
possible t o determine if thermal limits voltage dip. Auto-transformer starters
of standard motors will be exceeded for are a very effective means of obtaining a
longer than normal starting intervals. reduced voltage during starting with
Other loads have special starting torque standard taps ranging from 50% to 80%
requirements or accelerating time limits of normal rated voltage. A motor start-
that require special high starting torque ing study is used to select the proper
(and inrush) motors. Additionally, the voltage tap and the lower line current
starting torque of the load or process may inrush for the electrical power system
not permit low inrush motors in situa- during motor start. Other special reduced
tions where these motors might reduce voltage starting methods include resistor
the voltage dip caused by starting a or reactor starting, part-winding starting,
motor having standard inrush character- and wye (Y)-start delta (A)-run motors.
istics. A simple inspection of the motor All are examined by an appropriate
and load speed-torque curves is not suffi- motor starting study and the best method
cient t o determine whether such prob- for the particular application involved
lems exist. This is another area where the can be selected. In all reduced voltage
motor torque and accelerating time study starting methods, torque available for
can be useful. accelerating the load is a very critical
consideration once bus voltage levels are
8.3 Recommendations judged otherwise acceptable. Only 25%
8.3.1 Voltage Dips. A motor starting torque is available, for example, with
study can expose and identify the extent 50% of rated voltage applied at the motor
of a voltage drop problem. The voltage terminals. Any problems associated with
at each bus in the system can, for ex- reduced starting torque imposed by
ample, be readily determined by a digital special starting methods are automatically
computer study. Equipment locations uncovered by a motor starting study.
likely to experience difficulty during Another method of reducing high
motor starting can be immediately inrush currents when starting large
determined. motors is a capacitor starting system
In situations where a variety of equip- [l] . This maintains acceptable voltage
ment voltage ratings are available, the levels throughout the system. With this
correct rating for the application can be method, the high inductive component
selected. Circuit changes such as off- of normal reactive starting current is off-
nominal tap settings for distribution set by the addition, during the starting
transformers and larger than standard period only, of capacitors to the motor
conductor size cable can also be readily bus. This differs from the practice of
evaluated. On a complex power system, applying capacitors for running motor
this type of detailed analysis is very diffi- power factor correction, A motor start-
cult to accomplish with time-consuming ing study can provide information to
hand solution methods. allow optimum sizing of the starting
Several methods of minimizing voltage capacitors and determination of the
dip on starting motors are based on the length of time the capacitor must be
fact that during starting time, a motor energized. The study can also establish

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

I BASIC SPEED-TORCUE CURVt.

100

LII
2W 80
VI
VI
3
g
0
60
e:
c
U
z
% 40
w
z
W
U
4 20
a

0
40 80 120 160 200 240 250
PERCENT FULL-LOAD TORQUE

Fig 67
Typical Wound Rotor Motor Speed-Torque Characteristics

whether the capacitor and motor can information t o assist in selecting proper
be switched together, or because of an taps and ensure that light-load voltages
excessive voltage drop that might result are not excessively high.
from the impact of capacitor transient The motor starting study can be used
charging current when added to the to prove effectiveness of several other
motor inrush current the capacitor must solutions to the voltage dip problem as
be energized momentarily ahead of the well. With a wound rotor motor, differ-
motor. The switching procedure can ing values of resistance are inserted into
appreciably affect the cost of final the motor circuit at various times during
installation. the starting interval t o reduce maximum
Use of special starters or capacitors to inrush (and accordingly starting torque)
minimize voltage dips can be an expen- to some desired value. Figure 67 shows
sive method of maintaining voltage at typical speed-torque characteristic curves
acceptable levels [l]. Where possible, for a wound rotor motor. With appropri-
off-nominal tap settings for distribution ate switching times (dependent on motor
transformers are an effective, economical speed) of resistance values, practically
solution for voltage dips. By raising no- any desired speed-torque (starting) char-
load voltage in areas of the system ex- acteristic can be obtained. A motor start-
periencing difficulties during motor ing study aids in choosing optimum
starting, voltage dip can often be mini- current and torque values for a wound
mized. In combination with a load flow rotor motor application whether resist-
study, a motor starting study can provide ances are switched in steps by timing

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

relays or continuously adjusted values cept for the recognition of generator

obtained through a liquid rheostat-feed- transient impedances when appropriate,
back starting control. machine inertias, load characteristics,
8.3.2 Analyzing Starting Requirements. and other transient effects are usually
A speed-torque and accelerating time ignored. This type of study, while cer-
study often in conjunction with the tainly an approximation, is often suffi-
previously discussed voltage dip study cient for many applications.
permits a means of exploring a variety 8.4.2 The Detailed Voltage Profile. This
of possible motor speed-torque charac- type of study allows a more exact exam-
teristics. This type of motor starting ination of the voltage drop situation.
study also confirms that starting times Regulator response, exciter operation,
are within acceptable limits. The acceler- and sometimes governor action are
ating time study assists in establishing modeled t o accurately represent transi-
the necessary thermal damage character- ent behavior of local generators. This
istics of motors or verifies that machines type of study is similar t o a simplified
with locked rotor protection supervised transient stability analysis and can be
by speed switches will not experience considered a series of voltage snapshots
nuisance tripping on starting. throughout the motor starting interval
Speed-torque/accelerating time motor including the moment of minimum or
starting study is also used t o verify spe- worst case voltage.
cial motor torque or inrush characteris-
tics, or both, specified t o actually pro- 8.4.3 The Motor Torque and Accelera-
duce desired results. Mechanical equip- tion Time Analysis. Perhaps the most
ment requirements and special ratings exacting analysis for motor starting con-
necessary for motor starting auxiliary ditions is the detailed speed-torque
equipment are based on information analysis. Similar t o a transient stability
developed from a motor starting study. study (some can also be used t o accu-
rately investigate motor starting), speed-
8.4 Types of Studies. From the above torque analysis provides electrical and
discussion, it is apparent that depending accelerating torque calculations for spe-
on the factors of concern in any specific cified time intervals during the motor
motor starting situation, more than one starting period. Motor slip, load and
type of motor starting study can be re- motor torques, terminal voltage magni-
quired. tude and angle, and the complex value of
8.4.1 The Voltage Drop Snapshot. One motor current drawn are values to be
method of examining the effect of voltage examined at time zero and at the end of
dip during motor starting is t o ensure the each time interval.
maximum instantaneous drop that occurs Under certain circumstances, even
leaves bus voltages at acceptable levels across-the-line starting, the motor may
throughout the system. This is done by not be able to break away from stand-
examining the power system that corres- still or it may stall at some speed before
ponds t o the worst case voltage. Through acceleration is complete. A speed-torque
appropriate system modeling, this study analysis, especially when performed us-
can be performed by various calculating ing a computer program, and possibly in
methods using the digital computer. combination with one or more previously
The snapshot voltage drop study is use- discussed studies, can predict these prob-
ful only for finding system voltages. Ex- lem areas and allow corrections t o be

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

made before difficulties arise. When C37.010-1979 [4].

special starting techniques are necessary, (3) Other Components. System ele-
such as auto-transformer reduced voltage ments (such as cables) should be speci-
starting, speed-torque analysis can ac- fied as t o the number and size of con-
count for the auto-transformer mag- ductor, conductor material, and whether
netizing current and it can determine the magnetic duct or armor is used. All sys-
optimum time t o switch the transformer tem elements should be supplied with R
out of the circuit. The starting perform- and X values so an equivalent system
ance of wound rotor motors is examined impedance can be calculated.
through this type of study. (4) Load Characteristics. System loads
8.4.4 Adaptations. A particular appli- should be detailed including type (con-
cation can require a slight modification stant current, constant impedance, or
of any of the above studies t o be of constant kVA), power factor, and load
greatest usefulness. Often combinations factor, if any. Exact inrush (starting)
of several types of studies described are characteristics should also be given for
required t o adequately evaluate system the motor t o be started.
motor starting problems. ( 5 )Machine and Load Data. Aside
from base information required for a
8.5 Data Requirements voltage drop type of motor starting anal-
8.5.1 Basic Information. Since other ysis, several other items are required for
loads on the system during motor start- the detailed speed-torque and accelerating
ing affect voltage available at the motor time analysis. These include the WR2 of
terminals, essentially the same informa- the motor and load (with the WR2of the
tion necessary for a load flow or short
mechanical coupling or any gearing in-
circuit study is also required for a motor
cluded), and speed-torque characteristics
starting study. Although this informa-
of both the motor and load. Typical
tion is summarized below, details are speed-torque curves are shown in Fig 68.
available elsewhere in this standard (see
Sections 6 and 7) as well as in [2] and
Fig 68
[31. Typical Motor and
(1) Utility and Generator Impedances.
Load Speed-Torque
These values are extremely significant
Characteristics
and should be as accurate as possible.
Generally they are obtained from local
utility representatives and generator
manufacturers. Where exact generator
data cannot be obtained, typical imped-
ance values are available from 121 and
[31.
(2) Transformers. Manufacturers' im-
pedance information should be obtained
where possible, especially for large units
(that is, 5000 kVA and larger). Standard
impedances can usually be used with
little error for smaller units, and typical "0 40 80 120 160 200 240
X / R ratios are available in ANSI/IEEE TORQUE - PERCENT

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Fig 69
Simplified Equivalent Circuit for a
Motor on Starting

For additional accuracy, speed versus The ratio of 0.746 t o efficiency times
current, and speed versus power factor the power factor approaches unity for
characteristics should be given for as most motors giving the 1 hp/kVA ap-
exact a model as possible for the motor proximation. Therefore, for synchronous
during starting. For some programs, con- motors operating at 1.0 PF, a reasonable
stants for the motor equivalent circuit assumption is 1 hp equals 0.8 kVA.
given in Fig 69 can be either required or ( 2 )Inrush Current. Usually, a conserva-
alternatively utilized as input informa- tive multiplier for motor starting inrush
tion. This data must be obtained from currents is obtained by assuming the
the manufacturer since values are critical. motor to have a code G characteristic
8.5.2 Simplifying Assumptions. Besides with locked rotor current equal to ap-
using standard impedance values for proximately 6 times the full load current
transformers and cables, it is often neces- with full voltage applied at motor ter-
sary t o use typical or assumed values for minals, [6].
other variables when making motor start- (3) Starting Power Factor. The power
ing voltage drop calculations. This is factor of a motor during starting deter-
particularly true when calculations are mines the amount of reactive current
for evaluating a preliminary design and that is drawn from the system, and thus
exact motor and load characteristics are t o a large extent the maximum voltage
unknown. Some common assumptions drop. Typical data [2] suggest the fol-
used in the absence of more precise data lowing:
follow: (a) Motors under 1000 hp, PF = 0.20
(1)Horsepower to kVA Conversion. A (b) Motors 1000 hp and over, PF =
reasonable assumption is 1 hp equals 1 0.15
kVA. For induction motors and synchro-
nous motors with 0.8 leading, running 8.6 Solution Procedures and Examples.
power factor, it can easily be seen from Regardless of the type of study required,
the equation : a basic voltage drop calculation is always
involved. When voltage drop is the only
(kVA) (0.746) concern, the end product is this calcula-
hp = (See Ref [5] .) tion when all system impedances are at
(EFF) (PF) maximum value and all voltage sources

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

are at minimum expected level. In a

more complex motor speed-torque anal-
ysis and accelerating time study, voltage (SOURCE BUS)
drop calculations are required. These are (SYSTEM IMPEDANCE)
performed at regular time intervals fol- (MOTOR TERMINALS BUS)
lowing the initial impact of the motor (MOTOR IMPEDANCE)
starting event and take into account var-
iations in system impedances and voltage
sources. Results of each iterative voltage
drop calculation are used t o calculate
f
output torque which is dependent on the Fig 70
voltage at machine terminals and motor
Simplified Impedance
speed. Since the interval of motor start-
Diagram
ing usually ranges from a few seconds t o
1 0 or more seconds, effects of generator
voltage regulator and governor action are
evident, sometimes along with trans- or, more generally,
former tap control depending on control
settings. Certain types of motor starting
studies account for generator voltage
regulator action while a transient stability
study is usually required in cases where The effect of adding a large capacitor
other transient effects are considered bank at the motor bus is seen by the
important. A summary of fundamental above expression for V. The addition of
equations used in various types of motor negative vars causes X, , or 2, , t o become
starting studies follows, along with ex- larger in both numerator and denomina-
amples illustrating applications of funda- tor so bus voltage V is increased and
mental equations t o actual problems approaches 1.0 per unit as the limiting
which illustrate typical computer pro- improvement. Locked rotor impedance
gram outputs. for three-phase motor is simply
8.6.1 The Mathematical Relationships.
There are basically three ways t o solve rated voltage L-L .
ZLR= in !2
for bus voltages realized throughout the (6
(ILR)
system on motor starting. These are pre-
sented in this section and then examined where
in detail by examples in the next section. ILR=locked rotor current at rated
(1)Impedance Method. This method voltage
involves reduction of the system t o a This value in per unit is equal t o the in-
simple voltage divider network [ 71 where
verse of the inrush multiplier on the
voltage at any point (bus) in a circuit is
motor rated kVA base:
found by taking known voltage (source
bus) times the ratio of impedance t o the
1
point in question over total circuit z,,= ___ in per unit
ILR&L
impedance. For the circuit of Fig 70,
Since a starting motor is accurately repre-
X1
V=E- sented as a constant impedance, the im-
Xl +xz
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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

pedance method is a very convenient and The quantities involved should be ex-
acceptable means of calculating system pressed in complex form for greatest
bus voltages during motor starting. Val- accuracy although reasonable results can
idity of the impedance method can be be obtained by using magnitudes only
seen and is usually used for working for first order approximations.
longhand calculations. Where other than The disadvantage t o this method is
simple radial systems are involved, the that since all loads are not of constant
digital computer greatly aids in obtain- current type, the current t o each load
ing necessary network reduction. To ob- varies as voltage changes. An iterative
tain results with reasonable accuracy, type solution procedure is therefore
however, various system impedance ele- necessary t o solve for the ultimate volt-
ments must be represented as complex age at every bus, and such tedious com-
quantities rather than as simple reac- putations are readily handled by a digital
tances. computer.
(2) Current Method. For any bus in (3) Load Flow Solution Method. From
the system represented in Figs 71 and 72, the way loads and other system elements
the basic equations for the current are portrayed in Figs 71 and 72, it ap-
method are as follows: pears that bus voltages and the voltage
dip could be determined by a conven-
tional load flow program. This is true.
at 1 per
Iperunit = MVA1d .o unit voltage
By modeling the starting motor as a con-
MVAbe
~

stant impedance load, the load flow cal-

culations yield the bus voltages during
starting. The basic equations involved in
v,, = xource - VdOP this process are repeated here [ S I , [ 9 ] .

Fig 71
Typical One-Line Diagram

IO 000 MVA AVAILABLE

Bus I &IO MVA

5000 kVA

Bus 3

0.85 PF 1000 Hp

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

0. 061 + j 0.61

0.1 + j l . 0 0.1 + jl.0

A
4000 kVA 3000 kVA
0.85 PF o m PF 1000 H p
LRA - 6 - F L A
0.15 PF

LRA LOCKED ROTOR C U R R E N T

F L A = F U L LOAD C U R R U T

Fig 12
Impedance Diagram for System
in Fig 71

Kef = voltage of the swing or slack

bus
n = number of buses in the network
z k i = the system impedance between
the kth and ith buses
The load flow solution t o the motor
i=l starting problem is very precise for find-
ing bus voltages at the instant of maxi-
where mum voltage drop. It is apparent from
the expressions for Ik and V, that this
Ik = current in the kth branch of
solution method is ideally suited for the
any network digital computer any time the system in-
4 , Qk = real and reactive powers repre-
volves more than two or three buses.
sentative of the loads at the
kth bus 8.6.2 Other Factors. Unless steady-state
V, = the voltage at the kth bus conditions exist, all of the above solu-
yk = t h e admittance to ground of tion methods are valid for one particular
bus k instant and provide the single snapshot

149

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

A V = 1.0564

O . l + j 1.0 0.1 + j 1.0

4000 kVA
3000 kVA 1000 HP
0.85 PF
0.85 PF LRA = 6 . F L A
0.15 PF
L R A =LOCKED R O T O R C U R R E N T

FLA = FULL LOAD CURRENT

Fig 73
Revised Impedance Diagram Showing
Transient Reactance of Generator

of system bus voltages as mentioned use of the transient reactance as the rep-
earlier. For steady-state conditions it is resentation for the machine results in
assumed that generator voltage regulators calculated bus voltages and, accordingly,
have had time t o increase field excitation voltage drops, that are reasonably ac-
sufficiently t o maintain the desired gen- curate and conservative, even for excep-
erator terminal voltage. Accordingly, the tionally slow-speed regulator systems.
presence of the internal impedance of Assuming for example that bus No 7 in
any local generators connected to the the system shown in Fig 72 is at the line
system is ignored. During motor start- terminals of a 12 MVA generator rather
ing, however, the influence of machine than being an infinite source ahead of a
transient behavior becomes important. constant impedance utility system, the
To model the effect of a close-connected transient impedance of the generator
generator on the maximum voltage drop would be added to the system. The re-
during motor starting requires inclusion sulting impedance diagram is shown in
of generator transient reactance in series Fig 73. A new bus 99 is created. Voltage
with other source reactances. In general, at this new bus is frequently referred to

150

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

t
T= EXCITER

RE GU LATO R

where
XG varies with time as
+ Xi xd, and EG varies with the time
-+

constants Tio TAo+ Tdo

--f

depending on exciter/regulator output

Fig 74
Simplified Representation of Generator
Exciter/Regulator System

as voltage-behind-the-transient-reactance. V = Kerminal+ (jXd)( 4 4 )

It is actually the internal machine transi- = 1 + (JXd) (4oad)
end driving voltage (see Section 3).
When steady-state operating voltage is when
1.0 per unit, it is considered the voltage vT= l.o per unit
that must be present ahead of the gen-
erator transient reactance prior t o supply- and, where
ing power t o the other loads on the sys-
tem and maintain terminal voltage at 1.O
4oad = MVA1& per unit
per unit (within exciter tolerances) during MVAbase
steady-state conditions. The transient
driving voltage V is calculated as follows: Treatment of a locally connected gen-

151

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

erator is equally applicable t o all three the actual inrush multiplier used for de-
solution methods described above. Such termining the appropriate motQr repre-
an approach cannot give any detail re- sentation in the calculations is (6) (0.64)
garding the response of the generator = 4.2 times full load current.
voltage regulator or changes in machine Resistor or reactor starting limits the
characteristics with time. For a more line starting current by the same current
detailed solution which considers time as motor terminal voltage is reduced
dependent effects of machine impedance (that is, 65% of applied bus voltage gives
and voltage regulator action, the appro- 65%of normal line starting current).
priate impedance and voltage terms in Y-start, A-run starting delivers 33% of
each expression must be continuously normal starting line current with full
altered t o accurately reflect changes voltage a t the motor terminals. The start-
which occur in the circuit. This pro- ing current at any other voltage is, cor-
cedure is also applicable t o any solution respondingly, reduced by the same
methods considered. Figure 74 shows a amount. Part winding starting allows
simplified representation of the machine 60% of normal starting line current at
parameters which must be repeatedly full voltage and reduces inrush accord-
modified t o obtain the correct solution. ingly at other voltages.
Some type of reduced voltage starting When a detailed motor speed-torque
is often used t o minimize motor inrush and accelerating time analysis is re-
current and thus reduce total voltage quired, the following equations found in
drop, when the associated reduction in many texts apply [lo]. The equations
torque accompanying this starting meth- in general apply t o both induction and
od is permissible. Representation used synchronous motors since the latter be-
for the motor in any solution method have almost exactly as do induction
for calculating voltage drop must be machines during the starting period.
modified t o reflect the lower inrush cur-
rent. If auto-transformer reduced voltage T a V2
starting is used, motor inrush will be re-
duced by the appropriate factor from T = I,&
Table 12.If, for example, normal inrush
is six times full load current and an 80% WK2
tap auto-transformer starter is applied, I,= -lb-ft-s2
g

Table 12
Auto-Transformer-Line
Starting Current

Autotransformer Tap Line Starting Current

(% Line Voltage) (% Normal at Full Voltage)
50 25
65 42
80 64

152

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

8.6.3 The Simple Voltage Drop Deter-

w 2 = WO' + 201(e - e,) r/s mination. To illustrate this type of a
computer analysis, the system of Fig 71
A0 = w,t + ?h01 t2 r will again be considered. It is assumed
that bus N o 1 is connected t o the tenni-
nals of a 12 MVA generator having 15%
transient reactance (1.25 per unit on a
100 MVA base). Prior t o starting, when
A simplified approximation for start- steady-state load conditions exist, the
ing time is also available: impedance diagram of Fig 72 applies
with the motor disconnected. The im-
WK2 (r/minl - r/min,) (2a) pedance diagram of Fig 73 applies when
t (s) =
60gTl the 1000 hp motor on bus 4 is started.
Bus 99 in Fig 73 has been assigned in
where voltage of 1.056 per unit. This value can
T = average motor shaft output be confirmed using the expression for
torque the internal machine transient driving
V = motor terminal voltage voltage V given in the previous section
I, = moment of inertia with appropriate substitutions as follows:
g = acceleration due t o gravity
w = angular velocity V = (1.0 + j0.G) + (j1.25) (0.060114
01 = angular acceleration
+ j0.042985)
= 1.0564 per unit voltage L 4.08"
t = time in seconds t o accelerate
T, = net average accelerating torque
between rpm, and rpm, where values for the current through the
8 = electrical angle in degrees & 'element correspond to those that
WK2= machine inertia constant exist at steady state prior to motor
The basic equation for use with the starting with generator bus 1 operating
equivalent circuit of Fig 69 is as follows at 1.0 per unit. The computer output
report shown in Fig 75 shows steady-
PI [I11 [I21 :
9 9
state load flow results for this case. All
system loads are connected except the
1000 hp motor. Power flows are expres-
sed in MW and Mvar. Quantities indi-
cated for real and reactive power flow
where
(and, accordingly, the circuit flow at 1.0
T = instantaneous torque per unit voltage) through the line be-
os= angular velocity at syn- tween bus l and bus 2 agree exactly with
chronous speed those used above t o calculate V. Like-
(rl + jXl) = stator equivalent imped- wise, the bus 1 voltage is shown t o be
ance 1.0 per unit while the bus 99 voltage is
(rJs + jX,) = rotor equivalent imped- 1.0564 per unit.
ance For convenience, the angle associated
q1 = number of stator phases with the bus 99 reference voltage is as-
( 3 for a 3 @ machine) sumed t o be zero, which simply results
V = motor terminal voltage in a corresponding shift in all other bus

153

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

W '
0
-0
0
0

*X 0 0 0
-U
0-
W.
X I
zy1 0 0
w
-
C-S 0 0
0

0 1
0 8
0

e.
U
L t
O
. --a -
0 I
"
*.
e-
a?
90-
0
0
...
0 0 0

0 0 0
0

-
c

*NZ

.
0

...
0 nN 0
c--0Q
- 0
c * n
Z >
W X c c u n

e,
zu
W.
.
y1
mm
mm
..
0
N0N

4 -
9oc
In4

....
umnm
0ra.D
0nN-
I
0
--
0 0
cJ
..
O

N
c

I N
1
L.

4 4 - 0 0
bl (DD? 0 0
c 0 0
3

e*
W .1
2 ..
0 0

Q Q
....
0m-N
I--o
0 0 u m

I
5.:
nn
I 1
W

I
0
-
0

0 N
I

0 c
c
0 0
*
-
0
s
.o

0 N '
1
-nu
W

-J xO 1
I I' I l l
NNN
I
n
k

II
I I

v,
.
W

z
-
U
,I
a
I
IC

ffi ul
1

!* I,
, I

1
0 I n :

154

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

1 I
' e ' 0
U 0
c 0
1 :
a x 0 0

-
-U i o
a
w
-
X *L
a m 0

-
w
C -X 0

0
0
0
0
0

I-.
K O
U Z -- --- I

0 I
I
c
a.
=?
%5
-
0 0
0 0
.. ...
0 0 0

0 0 0
0
0
c
I
c
EO
- In**
- aa -y
c f
--.. - ..
a*
ncl
+a
w
Z -X
t-c s
O t O
2
E
0
m
a
0 -
cW
4 e 3
t,
w0
2
6
* ...
3 - -

0 0
1 0
x

VI
a
P
-
0 -0
- 0 0
cm.
....
CY--

...
c
c* oee o c a -
z *1
w
o n e ocni
1 I
w

-
IL' w
VI 0
P
0
a
$Z a c
Z.IU
<

2
W N
*2- 3..
U-
V

on 0 0
>-
,
D N
U:!
L,,
20 -- I 1

L
!
1 I
I
I I
!
f
I

-
a
U 1

z L

U
E
-
z
6

.I

z
3
-, I
I

155

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

GENERATOR
12 MVA

MOTOR INITIAL LOAD

1000 HP 7000 kVA
0.85 PF

Fig 77
Simplified System Model for
Generator Representation During Motor Starting

voltages. It is seen from the motor start- time. The digital computer is used to
ing bus voltage computer report in Fig solve several simultaneous equations that
76 that when this representation is used describe the voltage of each bus in a sys-
and subsequent motor starting calcula- tem at time zero and the end of succes-
tions are made, the voltage at bus No 4 sive time intervals.
is 0.7940 L -9.55' per unit. This voltage Figures 78-81 show in detail the type
is well below the 0.85 criterion establish- of input information required and the
ed earlier for proper operation of ac output obtained from a digital computer
control devices. voltage drop study. The system shown in
8.6.4 Time-Dependent Bus Voltages. Fig 77 contains certain assumptions
The load flow solution method for ex- which include the following:
amining effects of motor starting allows (1)Circuit losses are negligible-reac-
a look at the voltage on the various sys- tances only used in calculations
tem buses at a single point in time. A (2) Initial load is constant kVA type
more exact approach is t o model gen- (3) Motor starting load is constant im-
erator transient impedance characteris- pedance type
tics and voltage sources closer t o give (4) Motor starting power factor is in
results for a number of points in time the range 0 t o 0.25
following the motor starting event. (5) Mechanical effects such as governor
Although the solution methods are response, prime mover speed changes,
applicable t o multiple generator/motor and inertia constants are negligible
systems as well, equations can be devel- Plotted results obtained from the com-
oped for a system of the form shown in puter compare favorably t o those ex-
Fig 77 t o solve for generator, motor, and pected from an examination of Fig 66.
exciter field voltages as a function of In the particular computer program used

156

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

V O L I l u L 10 ktCOYEH FHVH I t i E IMPACT OF IHL MOTOR S T A P I I N C LOAO.

. . - - - -_ - - __ I l l t Y lJU f l l J T COYWtSPDtUJ T U THE TIME RLOUlWtU f O U THE MOTOR 10 START,
NO* b U I r l t l I M P L Y T M A I S U F f I C I L N T TOUOVE IS AWAILAbLE
T I 1 A C C t L t H A f E 1tIE YU10U.

Fig 78
Typical Output-Generator Motor Starting Program

11°F GEIILUATVU E I C l l E U FIELO noion

ISECOhUSI VOLlL f ?.U. I vvL1sIP.u.l VOLTS P. U >
- ._ .

0- 1.00 1.61 0.94

0.0 u.43 1-61 0.7Y
0.1 0.92 2.12 C.78
O.? 0.92 2.62 0.78
U.3 0.02 3.13 0.78
b ... b.'J4 JsIIU 0.80
0 ,'3 lJ.97 3.00 0.83
(1.'. 0.99 3.60 O,C5
0.7 1.00 J.60 0.Hb

Fig 79
Typical Output-Generator Motor Starting Program

157

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

GENERATOR VOLTAGE VS. TIME

W
W
a
0
’0.8

0 I 2 3 4 5 6 7 8 9 IO
TIME IN SECONDS
Fig 80
Typical Output - Plot of
Generator Voltage Dip

MOTOR VOLTAGE VS. TIME

“r

0 I 2 3 4 5 6 7 8 9 IO
TIME IN SECONDS
Fig 81
Typical Output - Plot of
Motor Voltage Dip

158

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

Variations in exciter field voltage

(EFV) over each time interval considered
are used t o calculate system bus voltages
at the end of these same intervals. A
single main machine field circuit time
constant is used in the generator repre-
sentation, and Fromlich's approximation
[14] for saturation effects is used when
the voltage behind the generator leakage
reactance indicates that saturation has
been reached.
The tabulated output stops just short
of full recovery since a more complex
model is necessary t o represent over-
shoot, oscillation, etc, beyond this point.
Of primary concern is this type of study
is the maximum voltage dip and the
length of time to voltage recovery as a
function of generator behavior and volt-
age regulator performance.
8.6.5 The Speed-Torque and Motor
Accelerating Time Analysis. A simplified
sample problem is presented for solution
by hand. In this way it is possible t o ap-
preciate how the digital computer aids in
solving the more complex problems. The
following information applies t o the sys-
tem shown in Fig 83.

Fig 83
Fig 82 Simplified System
Simplified Representation of Model for Accelerating
Typical Regulator/Exciter Time and Speed-Torque
Models for Use in Calculations
Computer Programs
I .o 0"
t o obtain this report, the excitation sys-
tem models available are similar t o those
described in Reference [ 131 . Excitation z sys
system models are shown in simplified
form in Fig 82. Continuously acting reg-
ulators of modern design permit full
field forcing for minor voltage variations
(as little as 0.5%), and these voltage
changes have been modeled linearly for 7000 kVA
1000 HP
simplicity. 0 . 8 5 PF

159

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Table 13
Average Values for Accelerating Torque
Over Time Interval Defined by a
Speed Change
speed Tmotor r
oad Tnet Tnet
0% 100% 30% - -
- - - 77.5% 2260.4 lb-ft2
25% 120% 35% - -
- - - 100% 2916.7lb-ft2
50% 160% 45% - -
- - - 120% 2500.0 lb-ft2
75% 190% 65% - -
- - - 62.5% 1822.9 lb-ft2
95% 80% 80% - -

(1)Motor hp = 1000 (induction) seen how a similar technique can be ap-

(2) Motor r/min = 1800 plied t o the speed-torque starting char-
(3) Motor WK2 = 270 lb-ft2 acteristic of a wound rotor motor (see
(4) load WK2= 810 lb-ft2 Fig 67) t o determine the required time
Assuming Fig 68 describes the speed- interval for each step of rotor starting
torque characteristic of the motor and resistance. The results of such an investi-
the load, it is possible t o find an average gation can then be used t o specify and
value for accelerating torque over the set timers that operate resistor switching
time interval defined by each speed contactors or program the control of a
change. This can be done graphically for liquid rheostat.
hand calculations, and the results are The current drawing during various
tabulated in Table 13. starting intervals can be obtained from a
Now applying the simplified formula speedcurrent curve such as the typical
for starting time provided earlier: one shown in Fig 84. This example has

(270 + 810) (450 -0)

= 0.6981 s Fig 8 4
= (308) (2260.4) Typical Motor Speed-Current
Characteristic
(1080) (900 - 450)
= 0.5410 s I-
t25-s0 = (308) (2916.7)
600
(1080) (1350 - 900)
= 0.4580 s START ING
ts0-75 = (308) (3500.0) 0
a

t75-95 =
(1080) (1710 - 1350)
(308) (1822.9) = 0.6925 s q
c
J

200
\
and therefore, the total time t o 95% of
E
w
100

synchronous speed (or total starting time) a 0 IO 20 40 60 80 100

is approximately 2.38 seconds. It can be PERCENT SYNCHRONOUS RPM

160

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

i
I

I
1
I
I I
i
I
i I
I i I
i
I
I 1
I
I
I
I
I I I
i
I
4
~

i
I

I
I d
Ir zz
I
,
iI
0
.-
I
0
4
D I
Lnc
*z
-a I
0
>
I

0
W
c
I
I ac
U
cI z
2 -0
W
m
0

0
I <
c
i
,
W
3
<
U
I 1 3
u
3Uw
U)
.J
L "
:I
*2 .
O W .*. J
w
W

-c
0 0 '
b-I a
t I
I JJ
2- -
z
I
I
v)
W
3
0
I

-
I 3 U
L >
Jl
c I z I
0 r
0
, ,*
J
0
VI
r
0
c
L
U
I W
w I cc
0
c
n I t
c
>
VI t
3 U
C w
w
I I z

-
L
c * J
a
U
Y .
4
1
' S
c
t
z
z
U
/I-
- 0
I
: I
2
2
;1
r-l
7.
d
.. VI
U-,
a
"
1 l I
r
-
J
a
c
J
n

.,
0
0 I
I
3
I
a

n,
80
1

161

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

assumed full voltage available to the 8.8 References

motor terminals, which is an inaccurate
assumption in most cases. Actual voltage [l]HARBAUGH and PONSTINGL,
available can be calculated at each time How t o Design a Capacitor Starting Sys-
interval. The accelerating torque will tem for Large Induction and Synchronous
then change by the square of the calcu- Motors, IEEE IAS 1975 Annual Meeting
lated voltage. This process can be per- - Conference Record.
formed by graphically plotting a reduced
voltage speed-torque curve proportional [2] Industrial Power Systems Handbook,
t o the voltage calculated at each time D. BEEMAN, Editor, New York, McGraw-
interval, but this becomes tedious in a Hill, 1955.
hand calculation. Sometimes, in the [3] Electrical Transmission and Distribu-
interest of simplicity, a torque corres- tion Reference B o o k , Westinghouse Elec-
ponding to the motor terminal voltage at tric Corporation, East Pittsburgh, Penn-
the instant of the maximum voltage dip sylvania, 1964.
is used throughout the starting interval.
More accurate results are possible with [4] ANSI/IEEE C37.010-1979, IEEE
digital computer program analysis. A Application Guide for AC High Voltage
sample output report for the analysis is Circuit Breakers Rated on a Symmetrical
shown in Fig 85. Current Basis.
[5] CROFT, T., CARE, C., and WATT,
8.7 Summary. Several methods for J. American Electrician's Handbook,
analyzing motor starting problems have New York, McGraw-Hill, 1970.
been presented. Types of motor starting
[6] ANSI/NFPA Std 70-1975, National
studies available range from simple volt- Electrical Code 1975, Boston, Mass.
age drop calculation to the more sophis-
ticated motor speed-torque and accelera- [ 71 MANNING, L. Electrical Circuits,
tion time study which approaches a New York, McGraw-Hill, 1966.
transient stability analysis in complexity. [SI NEUENSWANDER, J. Modern
Each study has an appropriate use and Power Systems, International, 1971.
the selection of the correct study is as
important a step in the solution process [9] STAGG and EL-ABIAD Computer
as the actual performance of the study Methods in Power System Analysis,
itself. Examples presented here should New York, McGraw-Hill, 1971.
serve as a guide for when to use each [lo] WEIDMER, R., and SELLS, R. Ele-
type of motor starting study, what to mentary Classical Physics, 2 v01, Boston,
expect in the way of results, and how Allyn and Bacon, Inc, 1965.
these results can be beneficially applied.
The examples should also prove useful in [ll] FITZGERALD, A., KINGSLEY, C . ,
gathering the required information for and KUSKO, A. Electric Machinery,
the specific type of study chosen. Ex- New York, McGraw-Hill, 1971.
perienced consulting engineers and equip-
[12] PETERSON, H. Transients in Power
ment manufacturers can give valuable
Systems, Dover, New York, 1951.
advice, information, and direction regard-
ing the application of motor starting [13] I E E E POWER GENERATION
studies as well. COMMITTEE Computer Representation

162

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 IEEE
MOTOR STARTING STUDIES Std 399-1980

of Excitation Systems, Paper 31 TP 67- Assemblies; ICs 3-1978, Industrial Sys-

424, May 1,1967. tems; ICs 4-1977, Terminal Blocks for
Industrial Control Equipment and Sys-
[14] KIMBARK, E. Power System Sta- tems; ICs 5-1978, Resistance Welding
bility: Synchronous Machines, Dover, Control; ICs 6-1978, Enclosures for
New York, 1956. Industrial Controls and Systems, Wash-
ington DC.
[ 151 NEMA Standards Publication ICs
1-1978, General Standards for Industrial [ 161 NEMA Standards Publication ICS-
Control and Systems; ICs 2-1978, Indus- 1975, Industrial Controls and Systems,
trial Control Devices, Controllers and New York, New York.

163

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

9. Harmonic Analysis Studies

9.1 Introduction. This section discusses loads or small three phase loads fitting
the basic concepts involved in studies of into the above categories normally have
harmonic analysis of industrial and minimal effect on the system harmonic
commercial power systems. The need for content and therefore are neglected.
such analysis, recognition of potential
problems, corrective measures, required 9.2 History. For years motors and other
data and benefits derived from perform- loads requiring dc power derived their
ance of a harmonic analysis study are energy from ac motor driven dc genera-
also discussed. Benefits of using a com- tors (MG sets). Mechanical linkage be-
puter as a tool for a harmonic analysis tween the two systems transmitted power
study will also be addressed within this between them and at the same time
section. electrically isolated each system from
The prevailing sources of harmonics the other. However, these MG sets were
in a system are rectifiers, dc motor bulky and tended t o be high maintenance
drives (converters/inverters),uninterrupt- pieces of equipment.
ible power supplies (UPS), cycloconvert- The first attempt at electrical rectifica-
ers, arc furnaces, or any other device tion was accomplished through mechani-
with nonlinear characteristics, which cal means. A motor driven cam physically
derive their power from a linear/sinu- opened and closed switches at precisely
soidal electric system. Systems composed the right instant on the voltage wave-
of these types of loads have the potential form to supply dc voltage and current t o
to develop harmonic related problems the load. At best this approach was
and are therefore prime candidates for a cumbersome since timing the switches
harmonic analysis study. Fractional and keeping them timed was extremely
horsepower drives and other single phase difficult. In addition, contact arcing plus

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

mechanical wear also made this equip-

ment a high maintenance item. Mechani-

m+
cal rectifiers were soon replaced by static
equipment including mercury, selenium,
and silicon diodes, and finally thyristors
(SCRs).
Although solid-state rectification ap-
peared t o be the panacea to the problems
of the older methods, other system prob-
lems soon became noticeable especially
as the size of each converter unit and as
the total converter load became a sub- Fig 86
stantial section of the total system power 6-Phase, 6-Pulse
requirements. Rectifier
The most noticeable initial problem
was the inherent poor power factor asso-

b
ciated with static rectifiers. Economics
as well as system voltage regulation re-
quirements made it desirable to improve
the overall system power factor which
normally was accomplished using shunt Iac
power factor correction capacitors. How-
ever, when these capacitor banks were
applied, other problems involving har-
monic voltages and currents affecting
these capacitors and other related equip- Idc
ment became prevalent.
Another initial problem was the exces- I
sive amount of interference induced into
telephone circuits due to mutual coupling Fig 87
between the electrical system and the 6-Phase, 6-Pulse
communication system at these harmonic Rectifier
frequencies.
More recent problems involve the per- of the fundamental (normally 60 Hz)
formance of computers, numerical con- frequency. Typical values are the 5th
trolled machines and other sophisticated (300 Hz), 7th (420 Hz), 11th (660 Hz)
electronic equipment which are very sen- and so on.
sitive to power line pollution. These de- To better understand harmonic related
vices can respond incorrectly to normal problems, it is necessary to understand
inputs, give false signals, or possibly not how and where harmonics are generated.
respond at all. In converting ac power to dc power, a
rectifier effectively breaks or chops the
9.3 General Theory. alternating current waveform by allow-
9.3.1 What are Harmonics? Harmonics ing the current to flow only during a
are voltages or currents, or both, present section of the cycle. The example in
on an electrical system a t some multiple Figs 86 and 87 for a 6-phase, 6-pulse

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

rectifier indicates the waveforms for the for these harmonics to flow. If this
direct current and the corresponding ac occurs, harmonic related problems can
line current. The square alternating cur- have a detrimental effect on the ac sys-
rent waveform represents a distorted tem.
sinusoidal waveform rich in harmonic Various parameters particular to each
content which can be resolved into system determine the magnitude of these
components using Fourier analysis tech- harmonic problems.
niques [ l ] . The Fourier series for this 9.3.2 Resonance. The application of
waveform is : capacitors with harmonic generating ap-
paratus on a power system necessitates
the consideration of the potential prob-
lem of an excited harmonic resonance
1 1 condition.
+ - cos 7e - - cos l i e Inductive reactance increases directly
7 11
1 with frequency and capacitive reactance
+ - cos 138 . . .) decreases directly with frequency. At the
13
resonant frequency of any inductive-
The higher frequency terms are the har- capacitive (LC) circuit, inductive reac-
monic components. tance equals the capacitive reactance.
A similar Fourier analysis of the There are two forms of resonance to
distorted sinusoidal waveforms of other be considered, series resonance and paral-
harmonic generating equipment as men- lel resonance. For the series circuit in
tioned previously will yield similar har- Fig 88, the total impedance at the reso-
monic current components. nant frequency reduces to the resistance
Arc furnaces differ from drives and component only. For the case where this
rectifiers in that harmonic voltages are component is small, high current magni-
generated instead of harmonic currents. tudes a t the exciting frequency will flow.
Arc resistance and the voltage/current Figure 89 is a plot of impedance versus
characteristis are continually varying due frequency of this series circuit.
t o movement of scrap, bubbling of Fig 88
molten metal, magnetic repulsion of the Series Circuit
arc from the other two phases, and so
forth. In addition, magnetic repulsion
forces between furnace flexible cables
cause swinging of these cables resulting
in variation of the reactance of secondary
circuit. The overall result of the non- I '-j\
7'
linearity of the arc and arc furnace
Fig 89
parameters is the generation of harmonic
voltages in the secondary circuit. Because Impedance Versus Frequency

+V
of the unpredictable nature of the arc,
harmonic magnitudes are not readily
determined. Only lower order harmonics IZ I
are generated, however.
With harmonic sources present, all that r
remains is t o have a path in the ac system f +

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

Parallel resonance is similar to series For this same circuit assume a current
resonance in that at its exciting frequen- source equal in magnitude t o l/7 A If/7 at
cy, capacitance reactance equals the in- the 7th harmonic (420 Hz). At this
ductive reactance. However, its parallel frequency the inductive reactance be-
impedance is significantly different. comes 4.2 52 and the capacitive reac-
Figure 91 is a plot of impedance versus tance becomes -4.4 52. The parallel
frequency for the parallel circuit of Fig combination can be calculated to be
90. At the resonant frequency f,, the 92.4 i2. Again, using Ohm's law, the
impedance is very high and when excited voltage across the load (V,) now is
from a source at this frequency, a high 13.20 V with the current through the
circulating current will flow in the capacitor being 3.0 A.
capacitance-inductance loop although In actual electrical systems utilizing
the source current is small in comparison. power factor correction capacitors, either
To illustrate parallel resonance further, type of resonance or a combination of
select 60 Hz reactances of 0.60 i2 and both can occur if the resonant point
-30.23 i2 for X , and X , respectively. happens to be close t o one of the fre-
The parallel impedance of the capacitor quencies generated by harmonic sources
and inductor at 60 Hz can be calculated in the system. The result can be the flow
to +0.61 52. For illustration purposes, in- of excessive amounts of harmonic cur-
ject 1 A (60 Hz) current If into the cir- rent or the appearance of excessive har-
cuit. Using Ohm's law, the voltage across monic overvoltages, or both. Possible
the load V, due to the fundamental consequences of such an occurrence are
frequency is then 0.61 V. excessive capacitor fuse operation, capa-
citor failures, telephone interference, or
Fig 90 overheating of other electrical equip-
Parallel Circuit ment.
9.4 Modeling. To analyze a system for
resonance effects requires calculation of
various harmonic currents throughout
the system and the harmonic voltages
these currents cause. At each frequency,
system impedances are different. For all
conditions the circuit remains the same.
Fig 91 Rectifiers and other similar harmonic
Impedance Versus Frequency generating equipment are represented as
current sources at each harmonic fre-
quency. With reference to the previous
Fourier expansion, the maximum theo-
retical harmonic current magnitude from
each converter equals the fundamental
frequency full load current magnitude
L
r divided by the order of the harmonic.
f+
Harmonic current magnitudes are also
functions of converter pulses. Magnitudes
of system harmonic voltages are a result
of harmonic currents flowing back into

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

the harmonic impedances of the ac sys-

kVA
tem. The order of harmonic currents is
np f 1, where n is any integer and p is
the number of rectifier pulses. Thus, for
a 6-pulse rectifier, the order of harmonics
are 5th, 7th, l l t h , 13th, 17th, 19th etc. I 1
For a 12-pulse rectifier, the order of har- 0 %SPEED 100
monics are l l t h , 13th, 23rd, 25th, 35th,
37th, etc. This procedure using a higher Fig 92
number of phases for lower order har- Typical Thyristor Drive
monic cancellation is referred to as phase Characteristics
multiplication. Although phase multipli-
cation theoretically will cancel normal
harmonics not of the order np f 1, in
practice, both current magnitude and
' tem. For drives with phase retard con-
phase angles deviate enough to allow trol, this loading factor also is propor-
only incomplete cancellation. Most liter- tional to the ac fundamental current
ature on the subject indicates that 10% component but is not necessarily pro-
t o 25% of the maximum harmonic mag- portional to the dc, kW, or hp output.
nitude will remain [ 2 ] . To be as realistic The graph in Fig 92 is typical for thy-
as possible, this factor, sometimes re- ristor drives with the kVA value approxi-
ferred t o as harmonic cancellation factor mately constant over the entire range of
(HCF), should be included. speeds. However, the loading factor in
Additional reduction of the harmonic question is the fundamental component
current magnitude is due to the series in- only and for low speeds, the kvar com-
ductive reactance between the harmonic ponent of the kVA term is very rich in
source and the utility supply. The larger harmonic content. The assumption of
this inductive reactance is (commutating constant kVA and maximum loading at
reactance) the more it impedes that par- maximum phase retard (minimum speed)
ticular harmonic generation. For ex- yields conservative results.
ample, the maximum 5th harmonic cur- The total harmonic current value in-
= 0.2
rent magnitude available is l / h = l / ~ jected into the system by a particular
per unit or 20% (commutating reactance device is then: Ih = (IFL/h) (LDF) (HCF)
= 0). Due to a significant commutating (CRF) where IFL is the fundamental full
reactance, however, the actual magnitude load current of the device and h is the
is only 17%. This reduction is referred to order of harmonic.
as commutating reactance factor (CRF). 9.4.1 Analysis Techniques. With basic
Graphs of per unit Ih (CRF) versus com- system connections (one-line diagram)
mutating reactance are available in the and impedances established, a harmonic
appropriate standards [ 31 . analysis study should analyze the system
The final factor reducing a particular under steady-state conditions for normal
harmonic current is the per unit loading power flow and harmonic current flow
(LDF). If a rectifier is only 50% loaded (sometimes referred to as harmonic load
(fundamental component of current) flow) for all the harmonics being modeled
then the harmonic current will only be for as many system switching conditions
50% of its maximum value on that sys- as required. A typical range of harmonic

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

frequencies modeled can be from 5 (300

Hz) t o 37 (2220 Hz). The harmonic
resonant point at a particular location
will probably differ under each separate The peak is used because of the random
switching condition so all normal modes phase relationships existing between the
of operation should be included. various harmonic components. The third
Since each switching condition requires loading factor is the total rms current
many solved cases of the system for each which connections, bushings, and other
of the harmonics being modeled, the components of the capacitor bank must
digital computer solves the multitude of handle. The current is calculated as:
calculations required for each switching
condition solution. The time required
for all but the simplest systems normally
prohibits manual calculations.
Power factor correction capacitors are Additional problems arise from har-
designed t o continuously carry 135%of monics in motors, lighting ballast trans-
their nameplate rated (fundamental) formers and other similar equipment.
kVA, or kVac, 110% of their rated volt- These problems are essentially excessive
age and 180% of their rated current in heating due t o circulating harmonic cur-
the existing standard (135% current in rents. To evaluate this effect, rms voltages
the pending standard). This overload rather than peak values are required.
capability allows a margin for system Therefore, rms voltages should also be
overvoltages or harmonic voltages, or calculated and printed throughout the
both, which can occur. The total loading system. Total rms voltage can be calcu-
of a bank is calculated as the sum of the lated using the following equation.
kVA loadings of the fundamental and
each harmonic.
This is expressed as

where
h = order of harmonic (including the
first or fundamental)
where V = fundamental or harmonic voltage
I = fundamental or harmonic current
h = order of harmonic (including the X = fundamental or harmonic reactance
first or fundamental) Capacitors must also have sufficient
Detailed results of a computerized har- dielectric to withstand anticipated peak
monic analysis study should include the voltages resulting from the fundamental
four main points mentioned above: total and the harmonics. This peak voltage is
capacitor bank kVac loading, peak volt- calculated as the arithmetic sum of all
ages, rms current, and rms voltage. Volt- the component voltages (not as rms
age and current values should be pro- value).
vided at all critical system locations sus-
ceptible to harmonic problems where 9.5 Solutions t o Harmonic Problems. The
appropriate values can be compared to primary solution to any harmonic related
the device's ratings in question. problem is accomplished by shifting the

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

system resonant point to some other

frequency not generated by the electrical T
equipment of the system. The simplest
and least expensive method is t o alter or
bypass system operating conditions and f
procedures that lead to harmonic reso-
nance.
If this approach is impractical or un-
desirable then quite often additional ap- Fig 93
paratus is required. No 1Scheme for
Remedial measures involving additional Adequate Filtering
equipment generally used to minimize
harmonic effects include shunt L-C filters
located at the harmonic source and tuned
to series resonance at the troublesome
harmonics. This approach makes a low
impedance path for the harmonic cur-
rents t o flow with very little flowing back
into the rest of the ac system. However, IC
a separate filter is required for every Fig 94
major harmonic source. No 2 Scheme for
In other cases where power factor cor- Adequate Filtering
rection capacitors in the ac system cause
resonance at the generated harmonics,
their location or size can be changed to
eliminate the resonance, or series reactors
can be added to detune them at the
troublesome resonant frequency.
There are three different major schemes
which will accomplish adequate filtering. Fig 95
Economic considerations as well as the No 3 Scheme for
particular filtering requirements for each Adequate Filtering
case determine which scheme is most
desirable. Utility requirements for har-
monic content injected into its system another harmonic frequency can then
dictate which scheme is t o be used. Figs become dominant with the resonant
93, 94 and 95 indicate these schemes. point only being shifted to another har-
The least expensive and therefore most monic frequency present on the system.
desirable of these three schemes is that Figures 94 and 95 are used when more
shown in Fig 93. Generally, a carefully stringent harmonic content requirements
selected tuning reactor is sufficient to are in effect. In Fig 95 the two lowest
alleviate harmonic resonance. Careful and most troublesome harmonics are
selection of the tuning reactor is stressed. filtered out individually with one high
If incorrectly selected, the harmonic fre- pass filter.
quency for which it is tuned will probably For new installations or major expan-
be lowered to acceptable levels but sions on existing facilities which have a

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

significant amount of rectification there BUS A

is another method of reducing lower
order harmonics if a harmonic analysis
is incorporated within the design stages.
The concept of phase multiplication
mentioned previously and the inherent

* *
phase cancellation of lower order har-
monics can be employed to greatly re-
duce harmonic magnitudes. From an
economic and manufacturing viewpoint,
it is impractical to construct rectifier
6 Phase 6 Phase
transformers with more than twelve
phases. However, they can be selected
Fig 96
to collectively appear as more phases
6-Phase Rectifier
than they actually are.
Transformers
In Fig 96, both rectifier transformers
are individually 6-phase units but when
viewed from bus A and when they are shifting of the rectifier transformers
both equally loaded, they collectively themselves. For example, one rectifier
appear t o be a 12-phase system. Similarly rated as 12-phase but with six phases
in Fig 97, buses C and D appear to have shifted -30" and six phases at 0" with
12-phase rectification but due to differ- respect t o the primary system will ap-
ing connections of the power trans- pear to be a 24-phase system when
formers, the system becomes a 24-phase operated with another identically rated
system at bus B. and loaded 12-phase rectifier which has
Other methods of accomplishing phase -15" and +15" phase shifts.
multiplication entail different phase It must be stressed that lower order

Fig 97
24-Phase System

BUS B

SHIFT A+-psIL
I 5 O k

A
LYTTC
AA A A

AT+T AT T
6 Phase 6 Phase 6 Phase 6 Phase

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

harmonic cancellation using phase multi- Tables 14 and 1 5 are abbreviated copies
plication techniques is only applicable of the computer solutions for this system.
when each component is equally rated The first solution modeled the system
and loaded. Where not all units are without any filters to determine if a
equally loaded or some are off line only resonant condition would exist after
partial lower order harmonic cancella- application of the proposed capacitor
tion occurs. A harmonic analysis study banks. As indicated by the harmonic
should also include probable imbalanced profile at C3 bus ( 2 banks), the system
loading conditions with only partial lower is resonant very close t o the 7th har-
order harmonic cancellation considera- monic. A comparison of capacitor bank
tions. ratings t o the values listed in the com-
Often an installation using phase multi- puter printout indicated that filtering
plication for harmonic reduction might was indeed required.
not need any filtering at all or requires The application of tuning reactors R3A
only small tuning reactors opposed to a and R3B tuned t o the 4.7th harmonic
complex RLC filtering scheme. The net was sufficient to suppress this resonant
economic effect is significant. condition to acceptable levels. The
Examples: The partial one-line diagram second computer solution indicates the
in Fig 98 was taken from an actual har- 7th harmonic to be almost gone with
monic analysis study performed in the the totalized quantities greatly reduced.
design stages for an electro-chemical The rms voltage was lowered from 1.766
plant. per unit to 1.102 per unit of the system
This particular system required the base value. The current and reactive
addition of tuning reactors in series with power loads were well within ratings.
each capacitor bank to minimize har- The voltage ratings of the proposed banks
monic resonance problems. were increased to 109% of the nominal

Fig 98
Partial One-Line Diagram

UAAJ

12 12
T
20.75
T
20.75
MVA, MVX MVA MVA TO CELL LINES
( d c LOAD)

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

Table 14
First Computer Solution:
Without Filters

W L L ' T I O N FOR 5 Y I T C H I N C C O N O I T I O k 195

BUS N A M E S C 3 c2 C l R3 A2 R 1

STU HARMONIC nUS VOLTAGES AN0 S H U N T L O A D C U R R E N T S

PUS VOLTAGES .1J5 -009 e009 .IS5 e009 .OOY

LOAO C L R R E N T a613 .OU4 .Oh3 .61S .Ob4 .OUl

7Tn H A R W O N I C B U S VOLTAGES AND SHUNT L O A D C U R A E t t T S

RUF VOLTAGES l.QlU -115 -117 l.Ql4 e115 -117

LOAD CLlRQENT 9.196 a805 .a19 9.896 e805 -1119

l l T U HARMONIC BUS VOLTAGES AND SHUNT L O A D CURRENTS

13Tn HARMONIC B U S VOLTAGES AND SHUNT L O A D C U R R E N T S

!!(IS V O L T A G E S a004 .U02 .002 .OOh .no2 -002

LOAD CURRENT .os5 .O~O .oze .oss .OJO .ozn
17Tu H A R M O N I C BUS V O L T A G E S AND S H U N T L O A D C U R R E N T S

BUS V ( A R I T t l ) 2.611 1.1El 1.18~ 2.617 1.18s 1.194

BUS V I R M S ) 1.766 1.058 1.057 1.766 1.056 1.057
L o r 0 IIRHS) 9.975 1.125 1.133 9.975 1.125 lay33
L O A 0 UVA IS*llS 1.196 1.139 e000 .CIOI) *OOlY

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Table 15
Second Computer Solution:
With Filters

YE S T I N G H O U S E lLECTPIC COQPORATION - HARHONXC ANALYSIS STUOY

S O L U T I O N F3R F Y I T C H I N G C O N D I T I O N l 9S

BU’S N A M E S c 3 c2 c1 R3 RI ‘a 1

S T H HARNONIC 3 U S VOLTACfS A N 0 SHUNT LOAO CURRENTS

T i n ,HAR,MONIC gus V O L T A G E S A N O SHUNT L O A O CURRENTS

BUS VOLTAGES .Qlb .U116 .006 .017 .On8 .DO8

L O A D CURRENT .n92 . u r ~ .os3 .09* .OUJ .uas

l l T H H A R M O N I C B U S VOLTAGES A N 0 S H U N T L O A D C U R R E N T S

BUS VOLTAGES .0(12 .OOS .oos .nio .012 .012

LOAD CURRENT .on .ovq .or9 .023 .nw .or9
l l T H H A R M O N I C B U Z V O L T A G E 5 AND S H U N T L O A D C U R R E N T S

RUS V O L f A C t S 0001 .003 .no3 .OD1 0009 -010

L O A D CURRENT 001S .OS6 mO36 .OlS .OS6 ,056

1 7 T H H A R , H O k I C B U S VOLTAGES AN0 S H U N T LOAO C U R R L h T S

1 9 T H H A R N O N I C B U S VOLTAGES AN0 S N U N T L O A O C U R R E N T S

TO T A L I Z E D O U A N f I T I E S INCLUDING ALL A U O V C H A R M O N I C S P L U S ’ r U N O A M C N I A L

FUZ V f A R X T H l 1.180 l.lY7 1.111 1.131 1.120 1.121.

BUI V ( R M S ) 1.’102 1.100 1.100 1.050 1.OSO 1.050
LOAD XIRNS) 1.095 1.057 1.051 1.09s 1 . 0 ~ 7 i.05a
LOAD UvA 1,176 1.1S7 1.157 a076 e057 0057

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 IEEE
HARMONIC ANALYSIS STUDIES Std 399-1980

system voltage, bringing all ratings safely operating in conjunction with capacitor
within limits. banks
The values listed under bus R3 are those Occasionally , when harmonics .appear
of the main bus. Very satisfactory system to be the cause of system problems, it is
harmonic filtering is also achieved. desirable t o determine the system har-
The previous example illustrates how monic resonance point. To determine
effective filtering can be when properly this resonance point, the short circuit
engineered. However, filtering is not al- capacity at each capacitor bank location
ways the best solution. In another electro- is required. A close approximation of
chemical plant with a very large complex this resonance point is the equation:
electrical system, harmonic filtering was
not implemented. The existing system
utilized power factor correction capaci-
tors at each major rectifier location.
Plant expansion required an additional where
rectifier and capacitor bank. Initial filter h, = resonance point in per unit of
design simulation corrected harmonic fundamental frequency
problems for the new bank but shifted MVA = short circuit capacity
the resonant point t o another location MV,, = Mvar rating of the unfiltered
which caused harmonic problems with capacitor bank at that location
existing capacitor banks. The practical
and economical solution in this case was This equation is useful for an initial
to oversize the new capacitor bank’s evaluation. If the resonance point is close
voltage rating to compensate for har- to one of the harmonic frequencies pre-
monic content without filtering. sent on the system, then possible har-
monic related problems could occur.
9.6 When is a Harmonic Study Required? 9.6.1 Data Required. The following
Although a specific answer is not always data are required for a typical study:
available, the following points are indi- (1)Single-line interconnection diagram
cators. (2) Short circuit capacity and X / R ratio
(1)Application of capacitor banks t o of the utility supply system
systems comprised of 20% or more of ( 3 ) Subtransient reactance and kVA of
converters or other harmonic generating all rotating machines. Where possible, all
equipment machines on a given bus should be lumped
(2) History of harmonic related prob- together into one composite equivalent
lems including excessive capacitor fuse machine
operation (4)Percent reactance and resistance of
(3) In the design stage of a facility all lines, cables, bus work, current limit-
composed of capacitor banks and har- ing reactors, and saturable reactors on a
monic generating equipment given kVA base and rated kV of the cir-
(4)Strict electric power company re- cuit in which the circuit element is
quirements which limit harmonic injec- located
tion back into its system to very small (5) The percent impedance and kVA
magnitudes of all power transformers
(5) Plant expansions which add signifi- (6) The three-phase kvar rating of all
cant harmonic generating equipment shunt capacitors and shunt reactors

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

(7) Namplate ratings, number of phases, Systems Using Thyristor Converters,

phase connections, whether diodes or Oct 7-10.1974.
thyristors and if thyristors, the maximum
phase delay angle, per unit loading and [3] IEEE Std 444-1973, IEEE Standard
loading cycle of each rectifier unit con- Practices and Requirements for Thyristor
nected t o the system. Actual manufac- Converters for Motor Drives.
turers’ test sheets on each transformer [4] ADAMSON, C., and HINGORANI,
are also helpful but not absolutely man- N. G., High Voltage Direct Current Power
datory Transmission, London, Garraway, 1960.
(8) Specific system configurations and
operating procedures for the rectifier [5] BORREBACH, E. J. The Effect of
circuits being studied Arc Furnace Loads on Power Systems,
(9) Actual maximum normally ex- IEEE/IAS Conference Record, Paper
pected voltage for the system supplying MI-Thu-Am3 1085, Oct 7-10,1974.
the rectifier loads
(10) For arc furnace installations, [6] McFADDEN, R. H., RAMEY, D. G . ,
secondary impedance from the trans- and SHANKLE, D. F., Electrical Transi-
former to the electrode tips plus a load- ents in Arc Furnace Installations, IEEE/
ing cycle to include arc MW, secondary IAS I and CPS Conference Record, May
voltages, secondary current and furnace 2,1972.
transformer taps [7] SCHIEMAN, R. G. Electrical Circuit
9.7 References. Problems Caused by SCR Drives, IEEE
[ l ] KIMBARK, E. A. Direct Current Pulp and Paper Conference, June 17-19,
Transmission, New York, John Wiley 1970.
and Sons, 1971.
[8] SCHIEMAN, R. G., and SCHMIDT,
[2] STEEPER, D. E., and STRATFORD, W. C. Power Line Pollution by 3-Phase
R. P. Reactive Compensation and Har- Thyristor Motor Drives, IEEE/IAS An-
monic Suppression for Industrial Power nual Meeting, 1976.

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 10. Switching Transient Studies

10.1 Introduction. Compared t o classical or analytically by calculation/modeling

steady-state power system studies (for techniques. This section gives an orienta-
example, short-circuit, load flow, protec- tion of the basic analytical techniques in
tive device coordination, etc) switching general use, their respective areas of ap-
transient investigations in depth are con- plicability, and the associated data and
ducted quite infrequently in industrial equipment requirements; salient consid-
power systems, with arc furnace melt erations in planning and conducting field
shop systems accounting for most such measurements are also presented. The
studies. The relatively high rate of switch- most common approach t o the analytical
ing that occurs in arc furnace systems, determination of transient duties in in-
the prevalence of capacitors, and the er- dustrial power systems, the transient net-
ratic nature of the arc furnace load, all work analyzer, is elaborated upon, in-
lead toward a greater need t o understand cluding excerpts from an actual industrial
the associated transient duties. Relatively transient study.
superficial investigations of limited scope
are commonly undertaken, however, in 10.2 Basic Concept of Switching Transi-
industrial systems, t o assist resolution of ents. The switching event in a power sys-
certain transient behavioral questions in tem initiates the transition between two
conjunction with the application or fail- steady-state conditions, the pre-switching
ure of a particular piece of equipment. condition and the post-switching condi-
Two basic approaches present them- tion. In steady state, the energy stored in
selves in the determination and predic- various inductances and capacitances of
tion of switching transient duties in a the dc circuit are constant. In an ac cir-
power system. They can be determined cuit, energy is continually exchanged
by direct measurements and monitoring cyclically between circuit inductances

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

and capacitances. Depending upon resist- restriking in switches and breakers, inter-
ances present, losses will extract energy mittent or arcing faults, clearing by fuse
which will be supplied by various sources blowing, and so forth. While in this
within the system. Each steady-state broad sense lightning is also a switching-
condition entails its own unique set of produced transient, it is usually listed in
energy storage and exchange rates in and a class by itself.
among the various circuit elements.
Thus a redistribution of energy must 10.3 Control of Switching Transients.
occur among the various system elements The philosophy of mitigation and con-
to change from one steady-state condi- trol of switching transients revolves
tion to another. This change cannot occur around :
instantly; a finite period of time, the (1)Minimizing the number and severity
transient period, prevails during which of switching events
transient voltages and currents develop (2) Limitation of the rate of exchange
to bring about these changes. These of energy that prevails among system ele-
transient voltages and currents develop ments during the transient period
and proceed in an orderly manner, (3) Extraction of energy
prescribed by the network configuration (4)Shifting of resonance points to
and conditions prevailing before and avoid amplification of particularly offen-
after the switching event. The precise sive frequencies
nature and timing of the switching event (5) Provision of energy reservoirs to
itself will profoundly affect the charac- contain released or trapped energy with-
teristics of the ensuing transients. These in safe limits of current and voltage
transient voltages and currents are com- (6) Provision of preferred paths for
posed of damped natural-frequency elevated-frequency currents attending
switching
oscillations which potentially can mag-
This philosophy is implemented prac-
nify to many times normal. The transi-
tically through the judicious use of:
ent environment is based on Kirchhoff’s
(1) Temporary insertion of resistance
law. Since changing quantities and their
between circuit elements, for example,
associated rates of change are involved insertion resistors in circuit breakers
throughout the transient period, the (2) Inrush control reactors
mathematics describing transients in- (3) Damping resistors in filter circuits
volves differential equations. Classical and surge protective circuits
mathematical computation of electrical (4)Tuning reactors
transients, therefore, requires a certain (5) Surge capacitors
degree of mathematical proficiency and (6) Filters
effort. (7) Surge arresters
In the broad sense, virtually all electrical (8) Necessary switching only, with
transients are switching-produced transi- properly maintained switching devices
ents if switching is anything that suddenly (9) Proper switching sequences
changes the network configuration or
any of its elements. Switching, for 10.4 Methods of Analysis. While very
example, is considered to be not only few practicing industrial plant engineers
the intentional actions of opening and are proficient at the type of mathematics
closing circuit breakers and switches, but used in the description and analysis of
also the occasions of fault inception, transients, a very useful insight into the

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

physical aspects prevailing in the net- response (including nonlinearities) t o

work during the transient period can be harmonics, traveling waves, and switch-
obtained with a minimum of mathemati- ing surges. These model components,
cal rigor for the simpler circumstances. composed into a multi-phase analog
In fact, practiced transient analysts use representation of the actual power sys-
known response patterns based on a few tem being investigated, are called a tran-
basic fundamentals to assess general tran- sient network analyzer (TNA).
sient behavior and to judge the validity Digital computers are now being used
of complex transient study results. In- in transient analysis. In limited areas,
deed, simple arrangements composed of digital computers are replacing the tran-
linear circuit elements, and, say, involv- sient network analyzer (TNA). For
ing only one or two switching events, simple system arrangements without
can be processed by hand. Beyond these transformers or other saturating devices,
relatively simple limits, however, the some digital programs now offer an eco-
economical calculation of power system nomical alternative to the TNA. For
switching-produced transients is actually more complex systems arrangements
done with one or more, or a combina- with nonlinear circuit elements, however,
tion of, basic analysis aids that have been progress has been slower but substantial.
developed over several decades. Economical analog-todigital and digi-
tal-to-analog conversion techniques have
10.5 Analysis Aids. Perhaps the earliest permitted interfacing of digital and ana-
aids to analysis of power system transi- log computers for a substantial degree of
ents were so-called mechanical differen- optimization of the most desirable fea-
tial analyzers and later the electronic tures of each. These so-called hybrid
differential analyzer, most commonly computers or simulators have come into
called analog computer. These devices use, principally in the last decade, as
assist the solution of differential equa- another potent tool in the analysis of
tions that evolve in mathematical repre- transients in power systems. They derive
sentation of transient phenomena. their attractiveness from a combination
Early in the application of analog of speed (rapid integrating capability) of
computers it was recognized that many the analog computer with the accuracy
problems involving abnormal voltage and flexibility (through use of memory
conditions could not be solved by con- capability) of the digital computer.
ventional methods. Specifically, systems The model approach of the TNA finds
to be studied for transient voltages due its virtue in the relative ease with which
to system switching operations, as well individual components can duplicate
as certain steady-state problems involv- their actual power system counterparts,
ing nonlinear circuit elements such as as compared with the difficulty of
surge arresters or saturable transformers representing (mathematically) combina-
or reactors, were awkward t o represent tions of nonlinear interconnected ele-
except by model techniques. This led t o ments in an analytical solution; especially
the electromagnetic model approach t o attractive are the relative low cost and
transient analysis wherein individual the speed of solution for individual runs
electric power system elements are repre- on the TNA. Also, the modern TNA has
sented by miniature counterparts with benefited very substantially from aug-
nearly identical electric and magnetic mentation with digital and analog com-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

puters. Such augmentation, for example, minimum and future maximum short-
offers an economical way to obtain a circuit duty conditions, with MVA and
statistical distribution of switching surge voltage bases if impedances are in per
magnitudes. Further, TNA modeling has unit
become a refined art and is becoming in- (b) Voltage spread: maximum and
creasingly enhanced by electronic tech- minimum voltage limits
niques. Traditionally and presently, most (c) Operation: description of reclos-
switching transient studies are conducted ing procedures and contractual or other
through TNA. limitations, if any
There are various equipment approach- (3) Individual power transformer data
es and methods t o aid the calculation of and other transformer data, if any
switching-produced transients to some (a) Rating, connections, no-load tap
extent these methodoligies utilize over- voltages for both positions of the Y-A
lapping technologies. While the TNA switch, if any, and LTC voltages, if any.
continues to be the most used aid in the Location of taps, in LV or HV windings.
calculated determination of transients, Normal position of the no-load tap if
the method employed depends upon seldom varied.
preferences, experiences, and equipment (b) No-load saturation data: Curve of
available to the analysts. The industrial no-load voltage versus exciting current,
plant user should entrust transient anal- additionally specifying rated voltage
ysis only to experts using the particular magnetizing impedance (or exciting
equipment of their preference. current at rated voltage) and air-core
10.6 Data Required for a Switching impedance. Definition of winding ar-
Transient Study. Compared to conven- rangement for which the data apply.
tional power system studies, switching Bases should be given for voltages or
transient analysis data requirements are currents in percent or per unit.
often more detailed and unusual or (c) Positive and zero sequence leakage
special. These requirements remain es- impedances, R and X,, for all trans-
sentially unchanged regardless of basic former tap connections. Impedance of
analysis tools and aids that are employed, series reactor, if any
be they digital computer, hybrid simu- (d) Neutral grounding details
lator, or transient network analyzer, or (4)Capacitor data, for each Mvar sup-
a combination of these. The generalized ply bank and surge protection unit
data listed below encompass virtually all (a) Mvar or microfarad rating, volt-
information areas required in an indus- age rating, catalog number, connections,
trial power system switching transient neutral grounding details
study : (b) Description of switching device
(1)One-line diagram of the system for Mvar supply bank
showing all circuit elements and connec- (c) Description of tuning reactors, if
tion options any, for Mvar supply bank
(2) Utility information, for each tie, at (5) Feeder cables or lines: Impedances
the connection to the plant, exclusive of per phase, R , X,, X,, both positive and
the plant load or backfeed zero sequence, for each circuit of appre-
(a) Impedances R , X,, Xc, both pos- ciable length. If these impedances are
itive and zero sequence, representing not available directly, t o permit their cal-
utility system or systems under present culation, data must be given as follows:

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

(a) Length of circuit, wire size, con- release relatively large quantities of
ductor arrangement and material, for energy. Similarly, highly inductive ap-
phase conductors and ground conductors, paratus possesses energy storage capabil-
or other return circuit paths. If cable, ity which can release large quantities of
whether in magnetic or non-magnetic electromagnetic energy during a rapid
duct, voltage rating, insulation specifica- current decrease. Since transient voltages
tion, shield and sheath description. and currents arise in conjunction with
(b) If multiple conductors per phase, energy redistribution that occurs during
a dimensioned cross section of the feeder the transient period between steady-state
installation (for example, of a duct bank conditions, the greater the energy storage
for multiple under ground cables) show- in associated system elements, the greater
ing several conductors of each phase and the transient magnitudes become. This
ground return conductors. has been confirmed countless times in
(6) Other power system elements. studies.
(a) Surge arresters: location, rating, Generalized switching transient studies
catalog or model number have provided many important criteria
(b) Grounding resistors (and reactors, to enable system designers t o avoid ex-
if any): rating, impedance of each cessive transients in most common cir-
(c) Buffer reactors: rating, imped- cumstances. Criteria for proper system
ance for all taps of each grounding t o avoid transient over voltages
(d) Rotating machines: rating of on the occasion of a ground fault are a
each, subtransient and transient react- prime example. Results of these general-
ance, type of regulator. ized studies have formed the basis of
(7) Operating modes and procedures. several IEEE Committee reports on
(a) Sequence and occasion for clos- switching surges. There are also several
ing each switch and circuit breaker not-to-common potential transient prob-
(b) Action of existing protection lem areas that are analyzed on an indi-
scheme during system overvoltages and vidual basis. The following is a partial
undervoltages list of transient-related problems which
Transformer data requirements (3) in- can, and have been, analyzed in com-
clude items which require considerable puter studies:
time for the transformer manufacturer (1)Energizing and deenergizing transi-
to develop. This should be factored into ents in arc furnace installations
the lead time in projecting the date of (2) Ferroresonance
study completion. (3) Lightning and switching surge
response of motors, generators, trans-
10.7 Switching Transient Problem Areas. formers, transmission towers, cables, etc
Switching of predominately reactive (4)Lightning surges in complex station
equipment represents the greatest poten- arrangements and optimum surge arrester
tial for creating excessive transient duties. location
Principal offending situations are switch- ( 5 ) Surge transfer through transformers
ing capacitor banks with inadequate or ( 6 ) Switching of large-magnitude induc-
malfunctioning switching devices and tive current
energizing and deenergizing transformers (7) Switching capacitors
with the same switch deficiencies. Capa- (8) Restrike phenomena in dropping
citors can store, trap, and suddenly lines, cables, and capacitor banks, includ-

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

ing modification by nonlinear trans- grounding, and application of surge

former and arrester elements arresters and surge protective capacitors
(9) Neutral instability and reversed (4) Recommendation of alternative
phase rotation operating procedures, if necessary, to
(10) Rectifier transients minimize transient duties
(11) Voltage flicker (5) Document results of study on case-
(12) Magnification of switching surges by-case basis in a readily understandable
(13) Energizing and reclosing transients form for those responsible for system
on lines or cables, either open-ended or design and operation. Such documenta-
transformer-terminated tion usually includes reproductions of
(14) Switching surge reduction by wave shape displays of oscilloscopes or
means of controlled closing of circuit various recorders and reproductions of
breaker or resistor pre-insertion, or both digital tapes, or both. Documentation
(15) Statistical distribution of switch- must include interpretation of at least
ing surges the limiting cases.
(16) Recovery voltages on distribution Industrial use of transient studies has
and transmission systems been limited primarily to arc furnace
(17) Energizing transients on systems melt shop systems which entail a high
using phase-shifting transformers rate of furnace switching, usually via
vacuum switches, and usually in the
10.8 Switching Transient Study Objec- presence of significant amounts of power
tives. The basic objectives of a switching capacitors which are sometimes also
transient investigation are to identify switched. In these applications study
and quantify transient duties that may objectives typically determine:
arise in a system as a result of intentional (1) Transient and harmonic sensitivi-
and non-intentional switching, and to ties associated with furnace and capa-
prescribe economical corrective measures, citor switching
if necessary. Results of a switching tran- (2) Preferred switching sequences
sient study can affect operating proced- (3) If tuning reactors for capacitors are
ures &swell as the equipment in the sys- justifiable
tem. The following include specific (4) Effect of resistor insertion
broad objectives, one or more of which (5) Proper surge protective equipment
are included in a given study: specifications
(1) Identify nature of transient duties (6) Transient duties associated with in-
(that is, magnitude, duration, and fre- ception of faults (line to ground and
quency) which can occur for any realistic multi-phase) and fault clearing
operational (that is, intentional) switch-
ing 10.9 Switching Transient Study Via
(2) Determine if abnormal transient Transient Network Analyzer (TNA). The
duties are likely t o be imposed on equip- TNA is the most used method of con-
ment by the inception of faults and their ducting calculated predictions of transi-
removal ent behavior in a power system. Accord-
(3) Recommend corrective measures to ingly the TNA will be elaborated upon in
mitigate excessive transients, such as this section, followed by an example of a
resistor insertion, tuning reactors (for case selected from an actual industrial
capacitor banks), appropriate system system study. The TNA uses electromag-

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

netic models primarily in representing a significant influence on the transients.

the system to be studied whereas digital Two- or three-winding transformers or
and analog or hybrid computer analysis autotransformers are represented by
is based on mathematical modeling. The models which accurately match positive,
hybrid simulator, while composed of negative, and zero sequence leakage
general purpose components, can still be impedances; as well as complete positive
special purpose to a degree depending on and zero sequence saturation character-
special components that are included. istics for single- or three-phase core or
The TNA is basically special purpose in shell-type designs. Phase-shifting trans-
nature, being devoted virtually entirely formers can also be modeled.
t o switching transient analysis. The fol- Series reactors are modeled using model
lowing discusses salient aspects of a TNA reactors which are linear. Shunt reactors
facility and associated study procedures. are modeled as linear or saturable, as
10.9.1 Model Components. Power for required.
the model system is supplied from a low- Shunt capacitor banks can be modeled
impedance three-phase sine-wave source, using miniature model capacitors.
sufficiently large to appear as a virtual Series capacitors can be accurately
infinite source to the model system. modeled, including their protective by-
System equivalent impedances at points pass and reinsertion switches.
of infeed are represented by linear reac- Harmonic filters, including tuned ca-
tances supplied from the infinite source pacitor banks for harmonic resonance
in the associated positive, negative, and control, are modeled using combinations
zero sequence component networks. In a of model resistors, reactors, and capaci-
similar manner, generators are usually tors.
represented by their direct-axis transient It is possible t o accurately represent
or subtransient reactances. Transfer im- any surge arrester design, including the
pedances between buses are represented complex, current-limiting valve type and
when their contribution is considered zinc oxide valve type. However, detailed
significant . application of each type is usually not
Because of the effect of traveling waves, warranted; instead, a relatively simple
transmission lines and cables are repre- representation consisting of a model
sented by a quasi-distributedconstant voltage-sensitive gap in series with a non-
model composed of a number of cas- linear resistor forms an adequate base
caded three-phase, four-wire L or pi from which evaluations of specific surge
sections. Each section consists of a series arrester designs can be made.
of resistance and inductance plus shunt Circuit breakers or other switching de-
capacitance to simulate positive and vices are represented by either a mechani-
zero sequence line constants. Depending cal or electronic-controlled multi-contact
on system configuration and objectives switch which operates in synchronism
of the study, each section can be made with the TNA power supply. This TNA
t o represent widely varying lengths of switch can be adjusted t o independently
circuit. Models representing completely represent the three poles of the power
untransposed lines or coupled lines on system switching device for either open-
the same right-of-way, or both, can be ing or closing operations and can be
modeled in greater detail when these direct acting or can accommodate single-
effects are considered sufficient t o have or multi-step resistor pre-insertion.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Where loads significantly influence within the capability of the conventional

transients, a static representation via TNA switching representation. However,
combinations of model resistors, reactors, modeling numerous reignitions in a
and capacitors is made. Load flows in a switching device within a very small part
multi-terminal system are represented o f a cycle of fundamental frequency,
through phase-angle regulators at appro- such as may occur in some vacuum
priate model system infeeds. switching circumstances, requires elec-
For convenience of interconnection tronic augmentation of the TNA switch
and instrumentation, all various indi- representation.
vidual components are connected to a High voltage transmission transient
plug board or patch panel. measurements have confirmed TNA pre-
10.9.2 Model Scale Factors. Generally, dictions within 4% magnitude deviation.
a voltage scale factor is introduced on Limited transient measurements on arc
transient network analyzer representa- furnace systems in industry indicate TNA
tions. For example, 100 V on the TNA predictions to be modestly higher, say
model might represent 34.5 kV on the within lo%, than actual prevailing transi-
actual system. ent duties. This, to a large extent, is
Transient network analyzer representa- expected because TNA results are most
tions of systems can be made with model often maximized, that is, assuming the
elements of the same ohmic values as most unfavorable combination of switch-
their system counterparts. However, t o ing device pole-closing electrical angles.
minimize the number of model elements As such they are expected to be higher
required for system parameters, other than that indicated by field measure-
electrical scale factors are introduced in ments where it is unlikely that the worst
accordance with established theories of (most pessimistic) pole closing angle
modeling. Impedance scale factors are combination will occur, at least during
given for convenience. Time scale fac- a staged field test.
tors have been advantageous for some It is mandatory that all TNA model
studies. components possess the same high-
10.9.3 Accuracy. In general, where re- frequency characteristic as individual
liable measurements of transients in the items of system apparatus that they
field have been conducted under condi- represent. Thus the models must entail
tions and switching circumstances dupli- appropriate capacitive, inductive, and
cating that of TNA analysis, correlation resistive elements t o duplicate the fre-
of results has been remarkably good. Of quency response over the range of fre-
course, accuracy of TNA results depends quencies of interest, model electrical
on the accuracy of data and the degree scale factors being considered. Perhaps
to which models can be made to approach the most difficult quantity to model is
the desired characteristics. In the typical the resistance of some reactors and trans-
industrial system, modeling system com- formers, which tends to be proportion-
ponents is usually a straightforward pro- ately higher in the model than in the
cedure with transformers being the most represented equipment. This circum-
complex and requiring the most data. stance is a challenge to the TNA model-
Modeling switch characteristics confined ing specialist. In fact, the reasonably pre-
to a limited number of reconductions cise simulation of transformers is gen-
(reignitions, preignitions, restrikes) is erally the most difficult area of TNA

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

modeling. Nonlinear magnetic character- breaker.

istics, losses, leakage inductance, distrib- Analog computer controlled switching
uted capacitance - all must be accom- is used t o generate a statistical overvolt-
modated within reasonable limits. Elec- age distribution on the TNA. One such
tronic circuit modeling is sometimes facility utilizes two analog computers,
used to achieve desired nonlinearities one to simulate natural variations in
and losses and to exhibit correct termi- actual switching device closing angles
nal behavior. and closing span, and the other to
10.9.4 Study Procedures. After all establish actual overvoltage distribution
model components have been intercon- produced on the TNA. Experience with
nected t o properly represent the actual many distribution curves and correspond-
system t o be studied, the switching oper- ing hand-maximized transients indicates
ation is performed. With this model tran- that a hand-maximixed transient is
sient voltages and currents can be ob- attained in only a small fraction of 1% of
served and measured on an oscilloscope the switching events in actual system
or by means of digital metering by con- service.
necting measuring probes directly to Where surge arrester operation is ex-
various locations in the model system. pected to make important modifications
For energizing, reclosing, or restriking of the transient under consideration, the
investigations, positions of the individual TNA model surge arrester can be sparked
closing contacts on the TNA switch over at some point between reseal rating
(representing the three phases of the and maximum guaranteed sparkover
power system switching device) are voltage of the arrester for maximum
varied and adjusted both with respect magnitude t o successive voltage crests in
to the driving voltage sine wave and to the modified transient voltage wave.
each other. For a given set of conditions Arrester discharge currents and the mod-
there exists a particular combination of ified transients are observed and recorded.
pole-closing angles which produces the Such records are examined t o determine
maximum closing transient. Searching the minimum applicable surge arrester
out this maximum transient pole-closing ratings consistent with reasonable system
combination within the allowable time operating procedures.
span between poles is called maximizing A permanent record of the transients
the transient. Maximizing is done man- is usually made by photographing the
ually and requires considerable practice traces on the oscilloscope screen.
t o accomplish it efficiently and de- 10.9.5 Example of TNA Study Case
pendably. Maximizing accomplishes in a Documentation. Figure 99 illustrates one
few minutes what otherwise could re- particular form of a TNA study case data
quire many computer runs if done sheet. The left half illustrates an abbrevi-
digitally. ated one-line diagram containing essen-
For investigations of overvoltages fol- tial components of the case. Provision
lowing switching device opening opera- for describing the switching event and
tions, the model system is first energized, the system arrangement along with the
and after all energizing transients have disposition of loads is included immedi-
subsided, contacts of the TNA switch are ately below the one-line diagram. For
adjusted to interrupt on successive cur- the case illustrated, the switching event
rent zeros, just as on an actual circuit is the simultaneous energizing of a capa-

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Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

citor and a furnace transformer by clos- 99, only one run was conducted and the
ing a breaker wherein one pole (phase C) most severe overvoltage was 2.87 per
remains open. The description also indi- unit as a result of ferroresonance which
cates the breaker used no resistor inser- developed as a consequence of breaker
tion and a pole-closing span of 180' was malfunction (one pole remaining open).
searched t o attain a maximized transient The magnitude of this overvoltage is
of 2.87 per unit voltage which occurred determined by scaling the oscillogram
at the energized transformer primary which displays the greatest instantaneous
(that is, location 2; the measuring probe voltage or by direct read-out from a
locations are indicated by circles). digital peak-holding voltmeter. Figure
The right half of the case sheet consists 100 shows an oscillogram which discloses
of a tabulated format so transient and the characteristic ferroresonant pattern
sustained voltage magnitudes can be as well as the magnitude of associated
recorded up t o ten probe locations each. peaks. It also discloses that the predomi-
Provision is made to show both pre- nant frequency of the ferroresonance is
switching and post-switching (and pre- 60 Hz. Those familiar with switching
fault and post-fault) sustained voltage transient analysis will immediately recog-
levels. Also, an index is included for nize that ferroresonance has developed
oscillograms (which in the TNA report as a result of a 60 Hz impedance match
are generally reproduced on the page(s) (or a near match) between the magnetiz-
immediately following the case sheet). ing reactance of the transformer being
Oscillograms are photos of CRO displays, energized and its p F surge capacitor.
generally a separate photo for each phase. This inductive-capacitive combination is
At the bottom right half sheet there is excited by a zero-sequence driving volt-
a listing of electrical scale factors used in age occasioned by the open breaker pole.
the modeling, that is, the relationship The multi-frequency nature of the oscil-
between the TNA model and system logram is a result of the nonlinear mag-
electrical quantities. netizing reactance of a transformer,
Note in the case sheet illustrated in Fig particularly in the period immediately

Fig 100
Oscillogram 12-10-2 as Described
in TNA Case Sheet of Fig 99

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

following energizing. ventional CTs and potential transformers

Complete switching transient study PTs can be suitable for harmonic investi-
documentation includes not only de- gations involving up t o only a few kilo-
tailed individual case study sheets for hertz, their frequency response is usually
transient responses associated with vari- inadequate for switching transient mea-
ous arrangements and conditions sur- surements.
veyed, but also analysis, recommenda- In transient switching field measure-
tions, and conclusions of the study. ments, voltage signals are derived from
Finally, the study documentation should the power circuit via compensated capa-
include a complete listing of parameters citor divider and conveyed t o the measur-
( R , L, and C ) of various system compo- ing equipment via shielded (or double
nents, characteristics of protective de- shielded) coaxial cable. Sometimes so-
vices, and a description of any unusual called cuptup dividers are used for deriv-
or special representations used in the ing voltage signals at apparatus bushings
study. provided with capacitance taps or power
factor taps. The captap device consists of
10.10 Field Measurements. The impor- a known value of capacitance made. up
tant role of field measurements in of capacitors arranged in a coaxial array
switching transient investigations has and fitted into a shielding container. This
been noted earlier in this section. The container includes a special adapter which
choice of measurement equipment, aux- is screwed into the capacitance tap or
iliary equipment selection, and tech- power factor tap of the respective bush-
niques of setup and operation is in the ing. This external known capacitance,
domain of practiced measurements spe- together with the inherent known capa-
cialists. No attempt will be made here to citance of the bushing, forms a capaci-
delve into such matters in detail, except tive voltage divider. The divider is formed
from the standpoint of conveying the by the internal line-to-tap bushing capa-
depth of involvement entailed by switch- citance and the much greater capacitance
ing transient measurements and from the of the external adapter capacitance from
standpoint of planning a measurements tap to ground. The geometry of the
program to secure reliable transient in- adapter can be made such that this
formation of sufficient scope for pur- bushing-adapter system is capable of
poses intended. responding to very short-time wavefronts,
10.10.1 Signal Derivation. Field mea- less than 100 nanoseconds (0.1 ps). This
surements are conducted with staged response is more than adequate for faith-
tests wherein a prescribed sequence of ful recording of switching transient volt-
switching operations are conducted for ages encountered in power systems.
various system operating modes, or they 10.10.2 Signal Circuits, Terminations,
may relate to monitoring day-by-day and Grounding. Due to very high currents
operating conditions. In any case, switch- with associated high magnetic flux con-
ing transients involve natural frequencies centrations that may attend transient
of orders of magnitude such that signal phenomena in power systems, it is essen-
sourcing must be by special current trans- tial that signal circuitry be extremely
formers CTs, noninductive resistance well shielded and constructed t o be as
dividers, non-inductive shunts, or com- interference-free as possible. Double-
pensated capacitor dividers. While con- shielded coaxial low-loss signal cable is

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 IEEE
SWITCHING TRANSIENT STUDIES Std 399-1980

satisfactory for this purpose. Addition- single-trace surge test oscilloscope with
ally, it is essential that signal circuit direct CRT (cathode ray tube) connec-
terminations be made carefully with high tions is sometimes used to record such
quality hardware and be carefully imped- transients with least possible distortion
ance matched to avoid spurious reflec- (2) A multi-channel magnetic light
tions. It is desirable that signal circuits beam oscillograph with high input im-
and instruments be laboratory tested as pedance amplifiers
an assembly before field measurements (3) A peak-holding digital-readout
are undertaken. This testing should in- memory voltmeter (sometimes called
clude the injection of a known steep peak picker), usually manually reset
wave into the input end of the signal The storage scope should have at least
circuit and comparison of this wave threechannel capability to permit simul-
shape with that on the receiving instru- taneous display of the three phase-voltage
ments (scopes). Only after a close agree- signals. An additional channel is desirable
ment between the two wave shapes is to allow a spare or to display another
achieved should the assembly be approv- signal of interest. The single-trace surge
ed for switching transient field measure- test oscilloscope with direct CRT input
ments. These tests also aid overall cali- is capable of producing the highest
bration. resolution of specific signals of interest
All the components of the measure- on faster sweep speeds, normally from
ments system should be grounded via a 10 to 200 ps/divisions.
continuous conducting grounding system From the standpoint of conducting
of lowest practical inductance to mini- switching transient field measurements,
mize internally induced voltages. The one of the most difficult aspects is secur-
grounding system should be configured ing an acceptable and reliable triggering
to avoid so-called ground loops which method for the storage scope when multi-
can result in noise injection. Where signal channel switching is used t o record more
cables are unusually long, excessive volt- than one signal. Considerable experi-
ages can become induced in their shields, menting may be necessary in order t o
but industrial switching transient mea- catch the transient activity due to its
surement systems have not as yet in- short duration. One successful approach
volved such cases. in some tests on systems with open (non-
10.10.3 Transient Measurement/h4oni- shielded) bus has been to use a simple
toring Instrumentation. The complement wire antenna connected to the external
of instruments used depends on circum- trigger of the scope. The antenna will
stances and purpose of the test program. sense air-born signals emanating from the
Major items comprising the total comple- power circuit bus in concert with initia-
ment of display and recording instru- tion of the switching. Associated sweep
mentation for transient measurements speeds of 200 t o 1000 psldivisions have
are one or more of the following: been found generally most useful for
(1)One or more oscilloscopes including recording all but the very fastest switch-
a storage-type scope with multi-channel ing transient voltages.
switching capability. When the presence The magnetic oscillograph displays all
of the highest speed transients (that is, voltages and signals being monitored.
with front times of a small fraction of a Current signals derived from special cur-
microsecond) is suspected, a high-speed, rent transformers or shunts are fed

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

directly t o oscillograph galvanometers evaluation of the severity of transients

through appropriate damping resistors. produced by a particular switching oper-
Voltage signals derived from capacitive ation. This permits a quick comparison
dividers are isolated from low-impedance between test runs and also can be left
galvanometers by high input-impedance on for extended periods, sometimes un-
(megohm range) oscillograph amplifiers. attended, t o obtain a reading of the high-
Oscillograph records are virtually indis- est transient occurring during that
pensable in the efficient interpretation period.
of transient phenomena recorded through 10.10.4 Objectives of Field Measure-
the orientation of the broad perspective ments. See the foregoing section on
they provide. Such oscillograph traces switching transient study objectives. Field
also give records of slow-speed switching measurements seldom, if ever, include
transients, system oscillations, and har- fault switching, and often recommended
monics. corrective measures are not in place t o be
Finally, the peak-holding voltmeter put into the test program, except on a
allows a valuable quantitative on-the-spot follow-up basis.

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 11. Reliability Studies

11.1 Introduction. An important aspect cluding maintenance practice. A detailed

of power system design involves consid- treatment of reliability evaluation meth-
eration of service reliability requirements ods is given in the IEEE Recommended
of loads to be supplied and service reli- Practice for Reliability Evaluation of
ability provided by any proposed system. Industrial and Commercial Power Sys-
System reliability assessment and evalua- tems El].
tion methods based on probability
theory allow the reliability of a proposed 11.2 Definitions. The definitions pre-
system t o be assessed quantitatively. Such sented here provide much of the re-
methods permit consistent, defensible, quired nomenclature for discussions of
and unbiased assessments of system reli- power system reliability.
ability which are not otherwise defensible,
availability. A term which applies either
and which are not otherwise possible.
Quantitative reliability evaluation
to the performance of individual com-
ponents or t o a system. Availability is
methods permit reliability indexes for
the long-term average fraction of time
any electric power system computed
that a component or system is in service
from knowledge of the reliability per-
satisfactorily performing its intended
formance of the constituent components
function. An alternative and equivalent
of the system. Thus, alternative system
definition for availability is the steady-
designs can be studied to evaluate the
state probability that a component or
impact on service reliability and cost of
system is in service.
changes in component reliability, system
configuration, protection and switching component. A piece of equipment, a line
scheme, or system operating policy in- or circuit, or a section of a line or circuit,

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

or a group of items which is viewed as interruption. The loss of electric power

an entity for purposes of reliability eval- supply t o one or more loads.
uation. interruption frequency. The expected
expected interruption duration. The ex- average number of power interruptions
pected, or average, duration of a single to a load per unit time, usually expressed
load interruption event. as interruptions per year.
exposure time. The time during which a outage. The state of a component or sys-
component is performing its intended tem when it is not available t o properly
function and is subject t o failure. perform its intended function.
failure. Any trouble with a power system repair time. The clock time from the
component that causes any of the fol- time of component failure to the time
lowing t o occur: when the component is restored to ser-
(1)Partial or complete plant shutdown, vice, either by repair of the failed com-
or belowstandard plant operation ponent or by substitution of a spare
( 2 ) Unacceptable performance of user’s component for the failed component. It
equipment is not the time required to restore service
(3) Operation of the electrical protec- to a load by putting alternate circuits
tive relaying or emergency operation of into operation. It includes time for diag-
the plant electrical system nosing the trouble, locating the failed
(4)Deenergization of any electric cir- component, waiting for parts, repairing
cuit or equipment or replacing, testing, and restoring the
A failure on a public utility supply sys- component t o service. The terms repair
tem can cause the user t o have either of time and forced outage duration can be
the following: used synonymously.
(1)A power interruption or loss of
service scheduled outage. An outage that results
(2) A deviation from normal voltage or when a component is deliberately taken
frequency of sufficient magnitude or out of service at a selected time, usually
for purposes of construction, mainten-
duration
ance, or repair.
A failure on an in-plant component
causes a forced outage of the component, scheduled outage duration. The time
that is, the component is unable t o per- period from the initiation of a scheduled
form its intended function until repaired outage until construction, preventive
or replaced. The terms failure and forced maintenance, or repair work is complet-
outage are often used synonymously. ed and the affected component is made
available to perform its intended func-
failure rate (forced outage rate). The
tion.
mean number of failures per unit of ex-
posure time for a component. Usually scheduled outage rate. The mean number
exposure time is expressed in years and of scheduled outages per unit of exposure
failure rate is given in terms of failures time for a component.
per year. switching time. The period from the
forced unavailability. The long-term time a switching operation is required
average fraction of time that a com- because of a component failure until
ponent or system is out of service as a that switching operation is completed.
result of failures. Switching operations include such opera-

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 IEEE
RELIABILITY STUDIES Std 399-1980

tions as: throwover to an alternate cir- 11.4 Data Needed for System Reliability
cuit, opening or closing a sectionalizing Evaluations. Data needed for quantitative
switch or circuit breaker, reclosing a cir- evaluation of system reliability depends
cuit breaker following a trip-out from a t o some extent on the nature of the sys-
temporary fault, etc. tem being studied and the detail of the
system. A group of components con- study. In general, however, data on the
nected or associated in a fixed configura- performance of individual components
tion t o perform a specified function of together with the times required to per-
distributing power. form various switching operations are
required.
unavailability. The long-term average System component data generally re-
fraction of time that a component or quired are summarized as follows:
system is out of service caused by fail- (1)Failure rates (forced outage rates)
ures or scheduled outages. An alternative associated with different modes of com-
definition is the steady-state probability ponent failure
that a component or system is out of (2) Expected average time to repair or
service. Mathematically, unavailability = replace failed component
(1- availability). (3) Scheduled maintenance outage rate
of component
11.3 System Reliability Indexes. The (4)Expected average duration of a
two basic system reliability indexes scheduled outage event
which have proven most useful and If possible, component data should be
meaningful in power distribution system based on historical performance of com-
design are load interruption frequency ponents in the same environment as
and expected duration of load interrup- those in the proposed system being
tion events. These indexes can be readily studied. The reliability surveys conducted
computed using the methods in [l]. The by the Power Systems Reliability Sub-
two basic indexes of interruption fre- committee [2], [3] allow a source of
quency and expected interruption dura- component data when such specific data
tion can be used t o compute other in- is not available.
dexes which are also useful: Switching time data needed includes :
(1)Total expected average interrup- (1)Expected times t o open and close a
tion time per year, or other time period circuit breaker
(2) System availability or unavailability (2) Expected times to open and close a
as measured at the load supply point in disconnect or throwover switch
question (3) Expected time to replace a fuse link
(3) Expected energy demanded, but (4)Expected times to perform such
unsupplied, per year emergency operations as cutting in clear,
Note that the disruptive effect of installing jumpers, etc
power interruptions is often non-linearly Switching times should be estimated
related t o the duration of the interrup- for the system being studied based on
tion. Thus, it is often desirable t o com- experience, engineering judgment, and
pute not only an overall interruption fre- anticipated operating practice :
quency but also frequencies of irter-
ruptions categorized by the appropriate 11.5 Method for System Reliability Eval-
durations. uation. The general method for system

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

reliability evaluation which is recom- (voltage dip) together with the minimum
mended has evolved over a number of duration of such reduced voltage period
years. The method is well suited t o the which results in substantial degradation
study and analysis of electric power or complete loss of function of t h e load
distribution systems as found in indus- or process being served. Frequency reli-
trial plants and commercial buildings. ability studies are conducted on a con-
The method is systematic and straight- tinuity basis in which case interruption
forward and lends itself t o either manual definitions reduce t o a minimum dura-
or computer computation. An important tion specification with voltage assumed
feature of the method is that system t o be zero during the interruption.
weak points can be readily identified, 11.5.2 Failure Modes and Effects
both numerically and non-numerically , Analysis. Failure modes and effects
thereby focusing design attention on analysis (FMEA) for power distribution
those sections of the system which con- systems amount t o determination and
tribute most t o service unreliability. listing of those component outage events
The procedure for system reliability or combinations of component outages
evaluation is outlined as follows: which result in an interruption of service
(1) Assess the service reliability require- a t the load point being studied according
ments of the loads and processes supplied t o the interruption definition adopted,
and determine appropriate service inter- This analysis must be made considering
ruption definition or definitions the different types and models of out-
(2) Perform a failure modes and effects ages which components can exhibit and
analysis (FMEA) identifying and listing the reaction of the system’s protection
those component failures and combina- scheme t o these events. Component out-
tions of component failures which result ages are categorized as:
in service interruptions and constitute (1)Forced outages or failures
minimal cut-sets of the system (2) Scheduled or maintenance outages
( 3 ) Compute interruption frequency (3) Overload outages
contribution, expected interruption dur- Forced outages or failures are either
ation, and the probability of each of the permanent forced outages or transient
minimal cut-sets of (2) forced outages. Permanent forced out-
(4)Combine results of ( 3 ) t o produce ages require repair or replacement of the
system reliability indexes failed component before it can be re-
The above steps are discussed in more stored t o service while transient forced
detail in later sections. outages imply no permanent damage t o
11.5.1 Service Interruption Definition. the component thus permitting its restor-
The first step in any electric power system ation t o service by a simple re-closing or
reliability study should be a careful re-fusing operation. Additionally, com-
assessment of the power supply quality ponent failures can be categorized by
and continuity required by the loads physical mode or type of failure. This
which are served. This assessment should type of failure categorization is important
be summarized and expressed in a ser- for circuit breakers and other switching
vice interruption definition used in the devices where the following failure
succeeding steps of the reliability evalua- modes are possible:
tion procedure. The interruption defini- (1)Faulted, must be cleared by back-up
tion specifies the reduced voltage level devices

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 IEEE
RELIABILITY STUDIES Std 399-1980

Table 16
Frequency and Expected Duration Expressions for
Interruptions Associated with Forced Outages Only

First-Order Minimal Cut-Set Second-Order Minimal Cut-Set

fa= hi f , = X i hj (ri + 9)
r, = ri r, = ri 5 1 (ri + rj)
Third-Order Minimal Cut-Set
f, = XiA j (ri rj + ri rk + 5 ‘k)
rcs = rir j. rk / ( r i r j + r i r k + r j r k )
Symbols: f, = frequency of cut-set event
r, = expected duration of cut-set event
hi = forced outage rate of ith component
ri = expected repair or replacement time of ith com-
ponent

NOTE: The time units of r and h in expressions for f, must be

the same. Once frequencies and expected durations have been
computed for each minimal cut-set, system reliability indexes at
the load point in question are given by:
f, = interruption frequency
= c
min
fCsi

cutsets
rs = expected interruption duration
= f a i r c s i / fs
min
cutsets
f, rs = total interruption time per time period

(2) Fails t o trip when required An important non-quantitative benefit

(3) Trips falsely of FMEA is the thorough and systematic
(4)Fails t o re-close when required thought process and investigation it re-
Each will produce a varying impact on quires. Often weak points in system de-
system performance. sign are identified before any quantita-
The primary result of the FMEA as far tive reliability indexes are computed.
as quantitative reliability evaluation is Thus, the FMEA is a useful reliability
concerned is the list of minimal cut-sets design tool even in the absence of the
it produces. A minimal cut-set is defined data needed for quantitative evaluation.
t o be a set of components which if re- 11.5.3 Computation of Quantitative
moved from the system results in loss of Reliability Indexes. Computation of reli-
continuity to the load point being in- ability indexes can proceed once the
vestigated and does not contain as a sub- minimal cut-sets of the system have been
set any set of components that is itself a found. The first step is t o compute the
cut-set of the system. In the present con- frequency, expected duration, and ex-
text the components in a cut-set are just pected down-time per year of each mini-
those components whose overlapping out- mal cut-set. Note that expected down-
age results in an interruption according time per year is the product of the
t o the interruption definition adopted. frequency expressed in terms of events

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

per year and the expected duration. If maintenance outages, switching after
the expected duration is expressed in faults t o restore service, and incomplete
years, the expected down-time will have redundancy of parallel facilities is given
the units of years per year and can be in [l].
regarded as the relative proportion of
time or probability the system is down 11.6 References
due t o the minimal cut-set in question. [l] IEEE Std 493-1980, Recommended
More commonly, expected duration is Practice for the Design of Reliable In-
expressed in hours and the expected dustrial and Commercial Power Systems.
down-time has the number of hours [2] IEEE COMMITTEE REPORT, Re-
per year. port on Reliability Survey of Industrial
Approximate expressions for frequency Plants, Part I: Reliability of Electrical
and expected duration of the most com- Equipment, IEEE Transactions on Indus-
monly considered interruption events try Applications, pp. 213-235, March/
associated with first-, second-, and third-
April 1974.
order minimal cut-sets are given in Table
16. Note that expressions for the calcula- [3] IEEE COMMITTEE REPORT, Reli-
forced outages (failures) only. A detailed ability of Electric Utility Supplies to
treatment of expressions for the calcula- Industrial Plants, Conference Record
tion of interruption frequency and dura- 1975 I & CPS Technical Conference,
tion considering forced outages as well as pp. 131-133.

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 12. Grounding Mat Studies

12.1 Introduction. A grounding mat healthy person can feel a current of

study has one primary purpose: t o en- about 1 mA.3 Currents of approximately
sure that the ground mat design provides 10-25 mA can cause lack of muscular
for the safety and well being of linemen, control. In most men 100 mA will cause
maintenance personnel, operators, and ventricular fibrillation. Higher currents
the public, anyone who comes near an can stop the heart completely or cause
electrically conductive object tied t o a severe electrical burns.
ground mat under the influence of a For practical considerations, the thresh-
major ground fault. Equipment protec- old of fibrillation is the major concern of
tion or system operation is rarely an most grounding mat studies. Ventricular
objective of a grounding mat study, fibrillation is a condition where the heart
which makes this particular type of beats in an abnormal and ineffective
analysis rather unique. An increasing manner, with fatal results. Accordingly,
concern of industry and utilities for the most ground mats are designed t o limit
safety of their employees has led t o body currents t o values below this thresh-
greater interest in predicting voltage old. Probably the most useful informa-
characteristics of grounding mats ex- tion on this subject can be found in [ l ]
periencing heavy fault currents. [ 2 ] , [ 3 ] , and [4] (the figures cited in
the preceding paragraph were taken
12.2 The Human Factor. To properly
understand the analytical techniques in-
volved in a grounding mat study, it is 'Numbers in brackets correspond to those in
the References at the end of this Section.
necessary to understand the electrical
%ests have long ago established the now well-
characteristics of the most important known fact that electric shock effects are the
part of the circuit - man. A normally result of current and not voltage [ 51.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

from these references). Although the test the sum of the intervals of the individual
results on ventricular fibrillation were shocks. The same series of tests also
actually taken from animals with body showed that the body can tolerate much
and heart weights comparable t o those more current flowing from one leg to the
of a man, the results have been generally other than it can when current flows
accepted as being valid for human beings. from one hand to the legs.
These studies have determined that 99.5 Figures 101 and 102 show two typical
percent of all healthy men can tolerate a shock hazard situations and the equiva-
current through the heart region defined lent resistance diagrams. Figure 101
by shows a touch contact with current flow-
ing from operator’s hand t o his feet. Fig-
ure 102 shows a step contact where cur-
rent flows from one foot t o the other. In
each case the body current Ib is driven
where by the potential difference between
= maximum body current in amperes points A and B. Exposure t o touch po-
tential normally poses a greater danger
T = duration of current in seconds than exposure to step potential. The step
potentials are usually smaller in magni-
without going into ventricular fibrilla- tude, the corresponding body resistance
tion. Obviously, this equation precludes greater, and the permissible body current
choosing a single value for the fibrilla- higher than for touch contacts. (The cur-
tion threshold current. Even a high cur- rent magnitude in the heart region that
rent through the heart region can be causes fibrillation is the same for both
tolerated for a brief period. Other tests types of contacts. In the case of step
show that this threshold current is ap- potentials, however, not all current flow-
proximately five times greater for direct ing from one leg to the other will pass
current [5] and as much as 25 times through the heart region.) The worst
greater for 3000 Hz [6]. Therefore, Eq 1 possible touch potential (called mesh
should embody sufficient conservatism potential) occurs at or near the center of
for all cases where an individual might be a grid mesh. Accordingly, industry prac-
exposed to 60 Hz ac fault potentials tice has made mesh potential the standard
(the dc component of asymmetrical fault criterion for determining safe ground mat
current is accurately recognized by a design. In most cases, controlling mesh
suitable correction factor described in a potential will bring step potentials well
later section). within safe limits inside the area defined
Tests indicate that the heart requires by the grounding mat. Step potentials
about five minutes to return t o normal can, however, reach dangerous levels at
after experiencing a severe shock [l]. points immediately outside the grid.
This implies that two or more closely Since the body of a man exposed to an
spaced shocks (such as those that would electrical shock forms a shunt branch in
occur in systems with automatic re- an electrical circuit, the resistance of this
closing) would tend to have a cumulative branch must be determined to calculate
effect. Present industry practice considers the corresponding body current. Gen-
two closely spaced shocks to be equiva- erally, the hand and foot contact resis-
lent to a single shock whose duration is tances are considered to be negligible.

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

Fig 101
Touch Potential

Fig 102
Step Potential

However, resistance of the soil directly mate resistance of 3p, where ps is the soil
underneath the foot contact area is con- resistivity [ 3 ] . The body itself has a
sidered significant. Treating the foot as a total measured resistance of about 2300
circular plate electrode gives an approxi- 52 hand to hand or 1100 52 hand t o foot.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

In the interest of simplicity and con- therefore depends solely upon the char-
servatism, IEEE Std 80-1976 [6] recom- acteristics of the permanent physical
mends the use of 1000 S2 as a reasonable installation. Grid voltages depend upon
approximation for body resistance. This three basic factors: ground resistivity,
yields a total branch resistance of available fault current, and grid geometry.
Proper consideration of each of these
factors allows the analyst t o recognize
both hazardous and overly conservative
for foot t o foot currents and designs.
12.3.1 Ground Resistivity. Obviously,
the simplest grounding mat analysis in-
volves a grid in a homogeneous medium.
for hand t o foot currents where p, is the
Unfortunately, substations must be
surface resistivity in ohm meters and R is located according to factors other than
expressed in ohms. If the station surface the ease of calculating grid voltages.
has been dressed with crushed rock or Fortunately for those concerned with
some other high resistivity material, such calculations, the homogeneous
resistivity of the surface layer material medium assumption is sufficiently accu-
should be used in Eq 2 and Eq 3. rate for most soils. Also, a number of
Because potential is easier to both cal- nonhomogeneous soils can be modeled
culate and measure than current, the by two-layer techniques [7], [8] . Al-
fibrillation threshold given by Eq 1 is though reasonably straightforward, these
normally expressed in terms of voltage. methods involve many tedious calcula-
Combining Eq 1, Eq 2, and Eq 3 gives tions making computation by hand diffi-
the maximum tolerable step and touch cult. The two-layer model is necessary
potentials: only for locations where bedrock and
other natural soil layers are close enough
to the surface to severely affect the dis-
tribution of current.
Of far more serious concern are soils
which experience drastic and unpredict-
(1000 S2 + 1.5pS)(0.116)
Etouc h = (Eq 5) able changes in resistivity at the earth’s
0 surface. These situations present prob-
lems :
12.3 The Physical Circuit. Although in (1)Difficulty of modeling soil in calcu-
each of the cases discussed above man’s lations
body resistance shunts a part of the (2) Physical difficulties in finding dis-
ground resistance, its actual effect on continuities in the field and measuring
voltage and current distribution in the local soil resistivity.
overall system is negligible. This becomes At present, these cases are normally
obvious when the normal magnitude of handled by the inclusion of a safety
the ground fault current (as much as margin in the value used for the soil
several thousand amperes) is compared resistivity.
to the desired body current (usually no A description of a simple method of
more than several hundred milliamperes). measuring soil resistivity of homogene-
Voltage rise of any point within the grid ous soils is given in [ 6 ] . Techniques also

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 IEEE
GROUNDING MAT STUDIES Sts 399-1980

Table 1 7 maximum ground fault current (assum-

Representative Values of Soil Resistivities ing a bolted fault) is given as:
Type of Ground Resistivity in ohm-meters
3v
Wet organic soil 10 I = 3Rg + (RI + R2 + R,) +j (x? + x2 + XO)
Moist soil lo2
Dry soil 103
Bed rock 104

where
exist for measuring the resistivity of each
layer of two-layer soils [ 8 ] . Because soil I = maximum fault current, amperes
resistivity varies with moisture content (note that this is not the same as
and, to a lesser degree, with temperature, the current, Ib,in Eq 1)
these measurements should be made over V = phase to neutral voltage, volts
a period of time under different weather Rg = grid resistance t o earth, ohms
conditions. If for some reason actual R, = positive sequence system resis-
measurement of resistivity is impractical, tance, ohms
tables of approximate values of resistivity R2 = negative sequence system resis-
for soils of various composition have tance, ohms
been compiled by several sources. Table
Ro = zero sequence fault path resis-
1 7 is a sample table [9]. These values are
tance, ohms
only approximations and should be re-
placed in the study by more accurate X y = positive sequence subtransient
figures whenever possible. system reactance, ohms
12.3.2 Fault Current-Magnitude and X 2 = negative sequence system reac-
Duration. Determination of ground fault tance, ohms
current normally entails a separate study. X o = zero sequence fault path reac-
Techniques and problems of making fault tance, ohms
studies are covered in numerous sources.
This section will only cover aspects This current will, in general, be a sinu-
peculiar t o grounding grid studies. soidal wave with a dc offset. Since dc
After the system impedance and grid current can also cause fibrillation, the
resistance have been determined, the current value I must be multiplied by an

Table 18
Decrement Factor for Use in Calculating
Electrical Shock Effect of
Asymmetrical ac Currents
Shock and Fault Duration
Seconds Cycles (60 Hz) Decrement Factor
0.008 Ih 1.65
0.1 6 1.25
0.25 15 1.10
0.5 o r more 30 or more 1.o

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

appropriate correction factor for this Study of maximum ground fault cur-
effect. This multiplier is called the decre- rent alone is not sufficient. Any low mag-
ment factor in [ 6 ] , and a table of ap- nitude ground fault current that might
proximate values for it is provided (re- persist for several minutes or more also
produced in Table 18). For more ac- presents the very real danger of asphyxi-
curate results, the exact value for the ation. A fault current capable of induc-
decrement factor D is given by the ing body currents of 10 to 25 mA can
equation cause muscular paralysis in a man, in-
cluding his lungs. Since the majority of
people resume normal respiration upon
removal of the current, interruption
times of a minute or so at this level
where should prevent any lasting injury from
this particular effect. A grounding mat
T = duration of fault, seconds design can be checked for this hazard by
o =system frequency in radians per first finding the ground fault current
second that will result in a body current of 10
X =total system reactance, ohms mA, then considering the protective re-
R =total system resistance, ohms laying scheme to determine the time
The current value calculated in Eq 6 required to detect and interrupt this
must be multiplied by this factor to find current. If the time is one minute or less,
the effective fault current. Note that asphyxiation should not be a danger.
time T in Eq 7 is the same as that used in An accurate estimation of the ultimate
Eqs 1, 4, and 5. To determine the fault system fault capability is necessary to
duration it is necessary t o analyze the ensure a safe design throughout the life
relaying scheme t o find the interrupting of the substation or plant. Normal indus-
time for the current calculated by Eq 6. try experience indicates that fault cur-
Substitution of this time into Eqs 4 and rents rise as power systems are expanded
5 will fix the maximum allowable step and modernized. After the initial con-
and touch potentials at the appropriate struction phase, however, changes t o the
values. These maximum allowable poten- ground mat are prohibitively expensive.
tials are used t o check the voltages actu- Therefore, it is vital to consider the total
ally present within the grid. If any volt- future expansion in the initial ground
ages exceed maximum limits, the grid mat design.
should be redesigned. 12.3.3 Fault Current-The Role of Grid
The choice of the clearing time of Resistance. Accurate calculation of
either the primary protective devices or ground fault currents presupposes that
the backup protection for the fault dura- an accurate and dependable value for the
tion depends on the individual system. grid resistance can be calculated. More
Designers must choose between the two literature exists on this aspect of ground-
on the basis of the estimated reliability ing mat design than any other, so finding
of the primary protection and the desired an approximate value for the required
safety margin. Choice of backup device grid resistance is not particularly diffi-
clearing time is more conservative, but it cult. Most of the equations and tech-
will result in a more costly ground mat niques developed to calculate grid re-
installation. sistance are based on several simplifying

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

assumptions, however, and produce re- Another method for determining grid
sults that are, by necessity, both con- resistance (with greater accuracy than
servative and somewhat inaccurate. For the previously described method) offers
the most part the accuracy of the grid re- the advantage of lending itself t o use in a
sistance equations depends upon how computer program that can precisely cal-
well they account for the different grid culate voltages at any location within a
configurations likely to be encountered. general grid configuration. It simply ex-
A formula for a quick simple calcula- presses grid-to-ground resistance as the
tion of resistance when a minimum of total voltage rise of the grid (relative t o a
design work has been completed is given “remote” ground reference) divided by
in [GI total fault current. This method can be
applied t o any grid configuration with
R = -P+ - P any number of conductor elements.
4r L However, because an accurate determin-
ation of the total voltage rise depends on
where the solution to a potentially overwhelm-
R = grid resistance t o ground, ohms ing array of involved mathematical ex-
p = soil resistivity, ohm meters pressions, this method is not well suited
L = total length of grid conductors, for hand calculations.
meters Since grid resistance is viewed as a
r = radius of a circle with area equal measure of the grid’s ability to disperse
to that of the grid, meters ground fault current, many designers are
Grid resistance depends on soil resistiv- tempted t o use resistance as an indicator
ity, grid area, and total length of the of relative safety of a ground mesh. In
conductors forming the grid. These vari- general, however, there is no direct cor-
ables influence the resistance so heavily, relation between grid resistance and
that Eq 8 does not consider any others. safety. At high fault currents, dangerous
By inspecting Eq 8 it also becomes evi- potentials exist within low resistance
dent that adding grid conductors to a grids. The only occasion when a low grid
mat to reduce its resistance eventually resistance can guarantee safety is when
becomes ineffective. As the conductors maximum potential rise of the entire
are crowded together, their mutual inter- grid (that is, grid potential) is less than
ference increases to the point where new allowable touch potential.
conductors tend only to redistribute 12.3.4 Grid Geometry. The potential
fault current around the grid, rather than rise of points protected by a grounding
lower its resistance. mat depends on such factors as: grid
The first term of Eq 8 gives the resis- burial depth, length and diameter of con-
tance of a circular plate with the same ductors, spacing between each conductor,
area as the grid. The second term allows distribution of current throughout the
for the grid’s departure from the idealized grid, proximity of the fault electrode
plate model. The more the length of the and the system grounding electrodes to
grid conductors increases, the smaller the grid conductors, along with many
this term becomes. This equation is ideal other considerations of lesser importance.
for the initial stages of a study where A perfectly rigorous analysis of all these
only the most basic data about the ground variables for a grounding grid with any
mat are available. number of conductor elements would,

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

at the very least, involve solving a like Coefficients K, and & are calculated
number of (1)differential equations (to by two reasonably simple equations based
find the current distribution along each upon the number of grid elements, their
line) [ 8 ] , [5], and (2) simultaneous spacing and diameter, and depth of burial
linear algebraic expressions (to find the of the grid. Many assumptions made in
current distribution throughout the developing these equations were not
entire grid) [ 161 . Although unfortunate, meant to describe rigorously either
it is hardly surprising that the quantita- industry practices or physical law, but
tive effect of these factors upon touch were instead intended to simplify and
and step potentials is one of the most make manageable what would otherwise
infrequently discussed aspects of grid be a very involved analytical procedure.
analysis. Equations 9 and 10 incorporate an irreg-
Paradoxically, these factors include ularity factor Ki to compensate for the
most of the elements of grid design that inaccuracies introduced by these simpli-
normally must be changed to control fying assumptions. Except for applica-
grid voltages. Obviously, any analytical tions involving very simple grid config-
method that cannot predict the effect urations, proper selection of a value for
of important changes in grid geometry is Kiis totally dependent upon the experi-
of limited utility for design purposes. ence and judgment of the designer. Most
Fortunately, some of these factors can choose to err on the side of safety and
be (and, for the sake of practicality, make Ki large, which results in an over
should be) safely ignored, while (un- designed ground mat installation-usually
fortunately) others are vitally important safe, but often expensive.
to a reliable and accurate analysis. Equations 9 and 10 yield a single value
Until recently, [6] provided the only of Emeshand Esteprespectively, for any
practical formulas for computing the ef- particular ground grid system. Values
fects of the grid geometry upon the step obtained for Em& and Estepare intended
and touch potentials (Eq 9 and Eq 10) t o represent the worst case condition for
the ground grid system without provid-
Z
Emesh = Km . (Eq 9) ing the analyst with any information as
to where (or how often) these worst case
conditions exist within the system.
After &esh and Estepof the grid are cal-
culated, they are compared to the calcu-
lated values of the tolerable Etouch and
where Estepas determined from Eq 4 and Eq 5,
p = soil resistivity, ohm meters respectively, in order to establish whether
Z = maximum total fault current, or not the design can be judged to be
amperes (adjusted for the decre- safe. If, in fact, Emeshexceeds EtoWh-
ment factor) t o l e r a e andlor Estep exceeds Estep-tolerable
it is sometimes possible by inspection of
L = total length of grid conductors,
the grid to determine mesh locations
meters
where additional cross-conductors should
Km = mesh coefficient be added in order to achieve a safe de-
Ks = step coefficient sign. The more general approach, how-
Ki = irregularity factor ever, especially when either of the toler-

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

able values is more than only slightly ex- below the earth's surface. The element
ceeded, is to uniformly increase the runs from point (xl, yl, zl) to (xl, y 2 , zl)
number of subdivisions in the original and is radiating current to the surround-
system of grid meshes so as t o result in a ing earth at the linear current density
lower calculated value of either Emeshor U, (the current per unit length). By inte-
Estep (or both). Accordingly, substantial grating U, over the length of the grid
overdesign and unnecessary investment element, the current flux 6 can be found
in buried conductor may result. at any desired point a as follows:
Although this traditional method for
calculating step and mesh potential has
given long and faithful service, grounding
mat analysis computer programs provide
more information about the effectiveness where
of the ground mat design. Greater accu- 6 = current/unit area at any point
racy results because calculation by com- o, = current flowing to ground/unit
puter program does not require as many length of conductor (current den-
simplifying assumptions. sity)
More specifically, the key t o an accur-
ate ground grid analysis is the considera-
tion of each individual grid element, R = J (-i + (j - y ) 2 + ( h - z1)2
rather than the en masse treatment used (i - x l ) i + (j - y ) j + ( h - z l ) h
in [ 6 ] . Fig 103, for example, shows a r=
single grid element located some depth h d(i- x1)2 + 0' - y ) 2 + ( h - Z1)*

Fig 103
Physical Model Used in Calculating Voltage
at Point a Due to a Single Conductor

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Once 6 has been determined, the E-field lady important consideration when find-
at the same point a can be expressed as ing the potential at points near the end
follows for a homogeneous soil: of an element (that is, at the comers of a
ground mat). It can handle grid designs
with large degrees of asymmetry with no
sacrifice of accuracy (symmetry is not
where p is soil resistivity. From this, the presupposed as with the calculating pro-
voltage at point a can be obtained by cedures in [6]).Further, since point a
performing the classical integration: can be located anywhere and examined
as often as required, detailed analysis of
grid design is possible. The most signifi-
cant disadvantage of this and other simi-
lar techniques is the number of tedious
calculations that must be performed t o
accurately model a system. However,
P9 modem digital computers have all but
= --In ci, - y 2 eliminated this concern.
4a

12.4 The Computer in Action. The utility

and accuracy of the new computer pro-
P9 grams can best be appreciated by exam-
+-In di, - y1 ination of some actual test cases. Figure
4a
104 summarizes the result of a computer
+d(i,- x ~ + )ci,~- yl)2 + (ha - z1)2) analysis performed on six different grid
layouts. Measurements recorded during
(Eq 14)
tests on small scale physical models of
where I& is the absolute potential at any these designs provide a convenient set of
point a due t o line 1. This process must benchmark solutions that can be com-
then be repeated for every element in pared t o the calculated results of a
the grid.“ Finally, the individual con- grounding mat analysis computer pro-
tribution of each grid element t o the po-
gram.
tential at point a must be summed t o The calculated voltages (expressed as a
determine the total voltage at every such percentage of the grid voltage) are shown
point of interest. in the center of each mesh in Fig 104.
The advantages of this analytical (For easy reference, the actual measured
method are immediately apparent. This voltages are also shown in parentheses.)
technique automatically accounts for the Each value is the absolute voltage at the
finite length of each element, a particu- point shown relative t o remote ground.
To determine the touch potential hazard,
This process is complicated somewhat by the the calculated point voltages must be
presence of the “current density” factor 0,in subtracted from the calculated grid po-
the equations. Although Eq 11 and Eq 1 2 treat tential. For purposes of design or evalua-
a, as a constant, in actuality it varies continu-
ously along the length of each grid element. In tion the resulting touch potential is
practice, however, very accurate results can be directly compared to the maximum toler-
obtained by using, on a piecewise basis, a con-
stant value for 9 that can be determined by one able value. In the case of step potentials,
of several approximating techniques. the potential difference between any

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

39
136)

GRID A GRID8

GRID C GRID D

8 0 84 85
I 0 84 185 184)
8 4 8 7 8 9 8 6
(85)187) 188 1871

185) 188) I88

86 88 89 86
184H 187) 188) 1871

57
1571

GRID E GRID F

Note: Values shown are center of mesh voltages

expressed as a per cent of total grid voltage
rise above remote ground.
with ( ) = test results
without ( ) = computer calculated

Fig 104
Experimental Grids Showing Various (Mesh) Arrangements

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

two calculated point voltages (taken one needed for each area of the grid through
meter apart) should be compared with the use of the ground mat analysis com-
the maximum allowable step voltage. puter program.
Figure 104 (especially grids E and F)
illustrates the accuracy of the program. 12.5 Input Data Requirements. Like all
Errors are typically on the order of 5 per- other system studies, a grounding mat
cent, and never worse than 1 0 percent. analysis study has specific data require-
Even the results for grids E and F, both ments. The omission of some critical bit
of which are highly irregular, are well of data during a study can significantly
within acceptable design accuracy. affect the validity of the entire study
The most impressive feature of this and its conclusions.
program, however, is its ability t o calcu- Normally, the first step in any ground
late voltages at any point of interest mat study is the determination of the
within or around the mat’s geometric soil resistivity. If the soil resistivity varies
boundaries. By repeated use of the pro- significantly from location to location,
gram throughout the design process, a the calculated point potentials should be
grounding mat layout can be fine-tuned multiplied by an adjustment factor (on
t o achieve the desired protection with- the order of 0.8 to 0.9) to compensate
out the need to overdesign any section for uncertainty about the exact resistiv-
of the mat. ity at any given location. Any extremes in
This process is illustrated in Figs 105- weather conditions that might seriously
108 using the typical ground mat design affect the soil’s resistivity should also
from [Appendix B, 181. Figure 105 be examined. This usually applies to
shows the grid layout and all pertinent droughts that can dry out the soil or
grid information. Figure 106 gives the unusually severe winters that could
results of a computer analysis of the grid freeze the soil below the effective depth
clearly defining the areas of maximum of the grid. If the substation surface is
danger. Figures 107 and 108 show the covered with a layer of crushed rock, its
results of modified grid designs. Note in resistivity must also be determined.
Fig 108 that the amount of additional The next logical step is the determina-
conductor required to safely control tion of the maximum permissible mesh
mesh potentials in the grid has been potential. Many industries have estab-
minimized and that the use of the com- lished a standard value for the maximum
puter program has permitted the loca- mesh potential. Otherwise, the estimated
tion of this conductor t o be optimally fault duration and resistivity of the
determined (that is, the conductor has material at the surface must be used to
been added only where required). calculate the maximum safe mesh poten-
Normally, mesh potentials are greater tial from Eq 5. If a layer of crushed rock
along the outside perimeter of a grid, has been applied to the surface, the cor-
especially at the corner. These potentials rect value of soil resistivity should be
can be controlled by decreasing the dis- used to calculate the maximum safe
tance between grid elements, but if the mesh potential for locations without
same spacing is used throughout the grid surface treatment.
the interior areas of the grid will, in To determine the “total” fault current,
general, be overprotected. Again, the the maximum future value of the avail-
designer can determine the exact spacing able symmetrical ground fault current

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

- rn
psoil= 1316
Psudace = 3 0 0 0
‘fault, = A
’ rn

Clearing Time = .5 sec.

Depth of Burial = .305 rn

K, = 368
K,=.814
Ki = 2.0 (touch), 2.5ktep)

Etouch/worse case = 21
Estep/worse case = 2010

Fig 105
Typical Ground Mat Design Showing
All Pertinent Soil and System Data

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

DANGEROUS
@# MARGINAL
SAFE

Fig 106
Typical Ground Mat Design Showing
Meshes with Hazardous Potentials
as Identified by Computer Analysis

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

DANGEROUS
MARGINAL
0SAFE

Fig 107
Typical Ground Mat Design, First Refinement
Showing Meshes with Hazardous Touch Potentials

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

DANGEROUS
a MARGINAL
0SAFE

I
1

Fig 108
Typical Ground Mat Design, Final Refinement
with no Hazardous Touch Potentials

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

must be calculated first. Next, the sys-

tem frequency, X / R ratio, and fault dur-
ation should be used t o calculate the
decrement factor. The decrement factor
and the symmetrical ground fault current
t-
Perimeter

Grid
Conducterr
can then be multiplied by one another t o d d z 1 mete!

obtain the total fault current used by the

program. The fault current depends on
the grid resistance, which in turn is de-
pendent on grid design, which is con-
stantly being modified. Accordingly,
normal practice is to use one of the sim-
plified formulas t o find a preliminary
value for the grid resistance, then calcu-
late a final value after the grid design has
been fixed.
Finally, a tentative grid design must be Perimeter
Grid -+
laid out showing the diameter, depth Conducters

of burial, and location of each grid con-

ductor. This layout should show any L

special restrictions on the design such as

conductors whose positions have already
been fixed by equipment placement, or
areas where conductors cannot be lo-
cated. Any buried electrically conductive Fig 109
object (a pipe, for example) that crosses Typical Ground Mat Layout Showing
the grid should be marked on the dia- Possible Locations of Critical Step and
gram. The points where the voltage rise Touch Potentials Near Grid Corners
will be calculated must be selected. For
evaluating touch potentials these normal-
ly include the mesh centers, the area and at the level of the grid
underneath the operating switches of all (2) Resistivity of any special soil sur-
major equipment, and the entrances into face dressing material
the substation. In addition, a point should (3) Estimated duration of a ground
be considered one meter away from each fault
grid corner along the line bisecting the (4)System frequency
270" angle formed by the perimeter grid (5) System X / R ratio
conductors (see Fig 109). The potential (6) Maximum symmetrical ground fault
of this point is important for evaluating current, both future and present
either step or touch hazards, depending (7) Grid layout showing the precise lo-
on the location of the perimeter conduc- cation of every conductor
tors relative t o any metallic fencing [ 6 ] . (8) Coordinates where the potential
In summary, a grounding mat study rise must be calculated
requires, as a minimum, the following Consideration of all this information
data: will lead t o a reliable, accurate, and use-
(1)Soil resistivity, both at the surface ful study.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

12.6 Typical Computer Output. Figure 12.8 References

110 shows a typical output report from [l]DALZIEL, C. F. Dangerous Electric
a ground mat analysis computer program. Currents, AIEE Transactions, vol 65, pp
In this particular case the output results 579-585and1123-1124.
apply to grid E of Fig 104. Note that
[2] DALZIEL, C. F. Threshold 60-cycle
both absolute potential and mesh poten-
Fibrillating Currents, AIEE Transactions,
tial are given several different values of
79, pp 667-673,1960.
V O ~
fault current at each point of interest in
the grid. As described earlier, step poten- [3] DALZIEL, C. F. and LEE, W. R. Re-
tial between any two points (one meter evaluation of Lethal Electric Currents,
apart) can be determined simply as the IEEE Transactions Industry General Ap-
difference in the absolute potentials of plications, vol IGA-4, pp 467-476, Sept/
these points. The output report from Oct 1968.
such a program can also include the cal- [4]DALZIEL, C. F. A Study of the Haz-
culated value of grid resistance, the max- ards of Impulse Currents, AIEE Trans-
imum allowable step and touch poten- actions, vol72, pp 1032-1043,1953.
tials, and the total length of conductor
needed to construct the grid. [5] FERRIS, L. P., KING, B. G., SPENCE,
P. W. and WILLIAMS, H. B. Effect of
Electrical Shock on the Heart, AIEE
12.7 Conclusion. The adaptation of clas- Transactions, vol 55, pp 498-515 and
sical analytical techniques and calculat- 1263, May 1936.
ing procedures t o the digital computer
[6] IEEE Std 80-1976, IEEE Guide for
has made grounding mat analysis much
Safety in AC Substation Grounding.
more precise, reliable, and useful. While
all but eliminating unnecessary grid over- [7] DAWALIBI, F. and MUKHEDKAR,
design, a grounding mat analysis by com- D., Optimum Design of Substation
puter program can detect unsafe condi- Grounding in a Two Layer Earth Struc-
tions that might otherwise go undiscov- ture, IEEE Transactions Power Applica-
ered until made apparent by serious mis- tions Systems, vol PAS-94, No 2, pp 252-
hap. 272, Mar/Apr 1975.
Although grounding mat analysis pro-
grams provide an invaluable design tool, [8] SUNDE, E. D. Earth Conduction
they are by no means infallible. If at all Effects in Transmission Systems. New
possible, a follow-up investigation should York: VanNostrand, 1949.
be made of each grid after it has been [9] RUDENBERG, R. Grounding Prin-
installed. This should include a measure- ciples and Practice I-Fundamental Consid-
ment of grid resistance at the very least, erations on Ground Currents, Electrical
and preferably the measurement of the Engineering, vol 64, pp 1-13, Jan 1945.
ac mesh potential at several locations
within the grid. If these measured values [ 101 LAURENT, P. General Fundamentals
differ appreciably from the calculated of Electrical Grounding Techniques, Bulle-
ones, the results of the grid study should tin de la Societe Francaise des Electriciens,
be rechecked and supplemental rods or vol I, series 7, pp 368-402, July 1951.
buried conductors provided as required [ l l ] NIEMANN, J. Changeover from
to establish safe conditions [6]. High-Tension Grounding Installation to

214

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 IEEE
GROUNDING MAT STUDIES Std 399-1980

Operation With a Grounded Star Point, Stations-111, Resistance of Rectangular

Electrotechnische Zeit, vol 73, No 10, pp Grids, AIEE Transactions, vol 75, part 111,
333-337, May 15,1952. pp 926-935,1953.
[I21 SCHWARTZ, s. J- Analytical ExPres- [ 161 GEDDES, L. A. and BAKER, L. E.
sion for Resistance of Grounding System, Response to Passage of Electric Current
AIEE Transactions, VOl73, PP 1011-1016, Through the Body, J. Association Ad-
1954. vancement of Medical Instruction, vol 2,
[13] GROSS, E. T. B., CHITNIS, B. V. and pp 13-189 Feb lg7'.

[14] GROSS, E. T. B. and WISE, R. B. Power Application System, vol PAS-95,

Grounding Grids for High-Voltage Sta- PP 113-1199 Jan/Feb 1976.
tions-11, AZEE Transactions, vol 74, part
[18] KOCH, W. Grounding Methods for
111, pp 801-809, 1955.
High-Voltage Stations With Grounded
[15] GROSS, E. T. B. and HOLLITCH, Neutrals, Elektrotechnische Zeit, vol 71,
R. F. Grounding Grids for High-Voltage No 4, pp 89-91,1950.

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

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 13. Computer Services

13.1 Introduction. The bulk of this book turn-around time, output interpretation,
is concerned with the details of power and with the sources of aid when prob-
system analysis by the use of computers. lems arise.
Very little, t o this point, has been said
about computers, programs, or require- 13.2 Computer Systems. There are basic-
ments for their use. Many readers are ally two types of computer systems avail-
not aware of the wide variety of compu- able t o prospective users
tational aids available, or factors that are (1)In-house company owned or leased
important in choosing the most appro- systems
priate aids for their particular needs. (2) Commerical computing services
This chapter discusses computer systems, available in a wide variety of types
services, their use, and the availability of 13.2.1 In-House Systems. The in-house
such services. Factors impacting the se- system is normally used by firms with a
lection of such things as in-house sys- considerable amount of data processing
tems, commercial services, time sharing, requirements. Most of these systems are
batch systems, and other decisions which general purpose installations with re-
must be made when selecting the most sources shared by several company de-
appropriate computing aids are discussed. partments (for example, Engineering,
The efficiency of these computing tools Accounting, Project Control, etc). Some-
can be increased considerably if the user times a company requires special purpose
has an idea of what to expect and is well computer equipment to support its
prepared before beginning his analysis. engineering operations, and can buy or
This section will strive t o acquaint pro- lease analog or hybrid computer systems.
spective computer users with the prob- These systems are used almost exclusively
lems of data preparation, job submittal, for technical applications. Resources,

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

however, are shared among various t o maintain a group of specialists to

technical disciplines. operate the equipment and to maintain
The decision to select an in-house the software.
system must consider many important 13.2.2 Commercial Computing Ser-
factors. In-house systems are expensive vices. The main advantage of commercial
t o buy or lease and to operate. Whether computing services is that they offer all
bought (and depreciated) or leased, the the capabilities of in-house systems with
costs continue even when not in use. The little or no capital expense. Input and
equipment, which includes not only the output can be by remote terminal or via
computer, but magnetic tape and disk mail. These servicesrange from the simple
drives for bulk data storage, card reader, use of a computer on which the user in-
printer, and other peripherals, must be stalls his own software, t o a total con-
located somewhere. This usually means a sultant service for which the user only
special room, with special environmental supplies the data and receives the answers.
considerations such as temperature and The equipment requirements range from
humidity controls, as well as grounding none t o mini-computer type intelligent
and electro-magnetic interference isola- terminals, the most common equipment
tion. Computers are, for the most part, being teletype or remote batch entry
very sensitive to perturbation in their terminals, any of which can be leased or
power source and can require an uninter- purchased. The programs can be devel-
ruptible power supply t o permit adequate oped by the user or the computing
reliability. Input medium must be pro- service. Also, programs can be obtained
vided (for example, punched cards, from the sources mentioned in the above
paper tape, terminals, etc). This means paragraph for in-house systems.
additional equipment such as keypunch In general the cost of using a commer-
machines or remote terminals. All equip- cial service increases with the amount of
ment must be maintained, and in the service received. It is important to realize
case of hardware failures, highly trained that commercial services must recover all
computer technicians must be called in. costs incurred on an in-house system, as
This is usually provided for through a well as return a profit. Therefore, the
maintenance contract. In most shops, ex- cost per computation is higher with the
cept for very small installations, the services than with a well run, fully u t i -
equipment is operated by specially lized, in-house system. The key here is
trained operators. The software (for the usage requirements. Those firms with
example programs) is developed, and low usage requirements can pay many
maintained by a group of full-time com- times the actual computer costs for
puter programmers. The programs can be services and still save money. Some firms
developed in-house or obtained from out- have computers which are under-utilized.
side sources through lease or purchase. They can be used for other purposes,
Also, they often are obtained from and power systems analysis programs can
government agencies, or from universities be installed on them.
for the cost of reproduction. In sum- 13.3 Types of Computing Service. In this
mary, in-house systems require large section computing services refers t o either
capital investment in equipment, and a commercial computing service or t o an
continued investment in operation and in-house (or captive service) department.
maintenance. Normally there is the need There are two basic operating modes

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 IEEE
COMPUTER SERVICES Std 399-1980

for computer programs, batch and on- sultant comes t o the user and helps find
line. Batch programs are initiated and the necessary data for the analysis. The
executed by submitting a job via card consultant then performs the computer
deck, or terminal input. Once initiated, a study and informs the user of the result.
batch program runs t o completion with- This type of study is quite expensive
out interfacing with the user. On-line, or when compared to studies in which the
time sharing programs, are executed user is more involved. Between these
from terminals. They may require the extremes is a wide variety of services
user to interact by responding t o prompt- which can be piece meal or complete
ing by the computer through the remote analysis reports. In a piece-meal analysis
terminal. the results of initial computer runs must
Batch and on-line programs are avail- be manually transcribed and input to
able either on commercial services or on later runs. For example, load flow analy-
in-house systems. In either case, program sis results are required for short circuit,
initiation is via remote terminal (for motor starting, and stability program in-
example, batch entry card reader, or on- put data. Complete analysis systems
line time sharing terminals). Batch pro- allow results of these initial studies to be
grams are run by the service upon re- stored and reused as input, with only the
ceiving the user data in the mail. On-line additional data necessary for the later
programs are more costly in the use of study required from the user.
computer resources and in general cost Commercial services include user man-
the user more per computation than uals and input data sheets (for batch
batch programs. On-line programs do, on programs) and in most cases some
the other hand, allow more timely amount of consultation for the user.
answers, which means reduced turn- This consultation is very valuable in im-
around time. The user can quickly scan proving the effectiveness of using a
the results and make changes t o the data service. The availability of consultation
if necessary for subsequent runs. Turn- varies between services and should be
around time is defined as the elapsed considered when selecting a commercial
time between submittal of a problem service. This consultation should be
and receiving the output results. sought early in the analysis to avoid
As mentioned previously, the amount problems and wasted man-hours and
of service varies greatly in the amount of computer runs.
consultation available between comput-
ing services. A greater amount of service 13.4 Use of Computing Services. After
implies a higher cost. At one extreme, deciding which type of computing
programs obtained from free sources service is most appropriate for the user’s
might not have enough documentation. present needs, several service representa-
In these cases input and output format tives should be contacted by mail or
can be determined from analyzing the phone. The larger national computing
program code and the usability of the services have representatives in most
output format may be questionable. On large cities and will gladly send informa-
the other end of the spectrum is the tion or a representative on request. A
total hands-off analysis by a consultant user should study available user manuals
type computer based on the user’s speci- and company literature to determine if
fications and data. In this case, the con- the computing service in question has

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 IEEE
Std 399-1980 INDUSTRLAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

clear and complete instructions for data manuals normally have a section explain-
entry. They should also give some ex- ing output reports. What is lacking in
planation on how t o interpret the out- many user manuals is trouble-shooting
put, or results. advice if the results appear to be not as
In general, input data is the same as expected. All results of computer pro-
that needed for hand calculations. It grams should be scrutinized for answers
may, however, be required in a different which are contrary t o what the user’s
form than is immediately available t o the experience would predict. If the cause of
user. Some programs require data in per- the discrepancy is not obvious from the
cent or per unit on a defined base, while printout or cannot be discerned from the
others can be on the specific base of the user manual, the computing service’s
piece of equipment. The user must con- consultant should be contacted. Reports
sult the user manual and give the input can be mailed to the user or printed di-
data as required. It should be noted that rectly at his location, depending on the
most problems encountered through a amount of hardware the user has.
computer program are caused by errors
in input data. One should be extremely 13.5 Availability of Computing Services.
careful when converting data to the form Computing services are available to any-
required by the program. Data should be one who has access to a telephone. Tele-
as complete as possible whether sub- phone lines are the normal means of
mitted via mailed input data sheets, time communication when remote terminals
sharing terminal, or card deck to a batch are used. These lines can be leased or
card reader. The results will be only as paid for on a usage basis. In many cases
good as the input data. The computer additional transmission hardware is re-
has no intelligence and can only work quired which is usually available from
with the data given, in exactly the man- the telephone company.
ner prescribed by the program. Most Depending on the size of the comput-
computing services have a consultation ing service being used, a large library of
service t o aid the user in defining input analysis programs is available. Most
data requirements and t o help him debug power system analysis programs contain
the input data in case of program failure. short circuit, load flow, stability, and
The user should take full advantage of all motor starting programs. The complexity
consultation available from the comput- and sophistication of these programs or
ing service. program systems vary widely. The user
Once the input has been entered the must be careful to select a service whose
time required for a response (turn- programs meet his needs. For example
around time) will be a function of not a load flow program which can only
only the type of program (batch or on- handle 50 buses may be of no use t o a
line) but the time of day. Computing large utility , while being perfectly suited
services have busy hours (prime time) for a small industrial application. In gen-
which are normally described in their eral, the larger the computing service,
literature. Turn-around is usually better the wider the selection of available pro-
during non-prime time hours. grams. Large services normally have pro-
Output reports from most commercial grams of varying complexity and sophis-
computing services are complete and tication to satisfy more customers.
well labeled to aid interpretation. User For some users the best decision is to

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 IEEE
INDEX Std 399-1980

contract with a general service agency pensive than performing the analysis in-
which can perform most of the analysis. house, but is desirable if time or man-
These services are available from engi- power constraints dictate so.
neering consultants or some of the large Much of the information used in the
equipment manufacturers. They permit preparation of this section was obtained
an analysis as complete as the user re- from literature published by companies
quests and can give advice or opinions if interested in data processing equipment
desired. This type of service is more ex- and computing services.

A regulated, 98
slack or swing, 22, 52, 95, 105
ac control devices, 1 4 1 unregulated active, 101
ac fault potentials, 22 var limited, 101
ac generator, 25 voltages, 105, 149,153, 156
ac mesh potential, 214
ac network analyzer, 21 C
Acceleration factors, 101
Accelerating time study, 144, 150, 161 Cables, 58, 60, 175, 182, 189
Active elements, 44 Capacitor starting system, 142
Air-gap flux, 127 Capacitors, 1 4 2 , 1 4 3 , 1 6 6 , 1 6 7 , 1 6 9 , 1 7 5 ,
Analog computers, 21, 24 179,181,185,188
Analysis Case studies, 101, 188
grounding mat, 206, 208, 214 Cathode ray tube (CRT), 189
interruptions, 26 Circuit breakers, 25,105, 185, 192, 194
load flow, 217 Commutating reactance fact (CRF), 168
power system, 216, 217;219 Component, 191-195
reliability, 26 Computer services
Analytical solution methods availability of, 219
Fourier representation, 37 commercial, 22, 217-219
linearity, 29 systems, 216, 217
per unit method, 42 types of, 217
phasor representation, 35 use of, 218
single-phase equivalent circuit, 37 Connected load, 8 3
sinusoidal forcing function, 34 Contactors, 141, 161
superposition, 30 Control devices
symmetrical component analysis, 39 ac, 141
Thevenin equivalent circuit, 31 dc, 141
Applied loads, 25 Current
Automatic load shedding, 134 harmonic, 165, 167
Auto-transformer starter, 143,144, 149 inrush, 1 4 1 , 1 4 2 , 1 4 9
Availability, 191, 193 locked rotor, 71
Available fault current, 198 Current method, 148

D
B
Dalziel, Charles, 197
Batch programs, 217, 218, 219 Data
Brake horsepower, 80 load, 146
Bus (buses) machine, 146
floating, 98 Data references, 8 3
infinite, 23, 49 dc control devices, 143
lighting, 140 dc motor drives, 164
motor, 142 Demand
passive, 98 instantaneous, 8 3
power circuit, 182 maximum, 8 3

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Demand factor, 8 3 Ground

Demand interval, 8 3 fault current, 201, 213
Diagram resistivity, 197, 201, 203, 208
impedance, 22, 46, 55, 56, 114, 119, Grounding mat, 197, 201, 202, 203
151,153 studies, 197, 203
one-line, 37, 38, 9 1 , 9 2 , 1 0 9 , 1 1 4 , 1 6 8 ,
172,180,185
resistance, 198 H
single-line, 22, 91, 92, 109
Digital computer study, 142, 162, 178, Harmonic analysis study, 164, 167, 169,
179,180 171,172
Digital Computers, 21, 22, 24, 25, 26, 28, Harmonic current, 167, 168, 169
34,162,206,214 Harmonic filters, 1 0 5
Dropout voltages, 1 4 1 Harmonic frequency, 170
Dynamic programs, 91 Harmonic resonance, 169, 170,182

E I
Electromagnetic models, 181 Impact loads, 24
Expected interruption duration, 192,193, Impedance amplifier, 182
195,196 Impedance diagram, 22, 44, 46, 49, 55,
Exposure time, 191 56,114,119,150,151
Impedance method, 1 4 7 , 1 4 8
Impedances
F circuit, 34, 147
generator, 145
Failure, 191, 192, 194 locked rotor, 147
Failure modes and effects analysis (FMEA), parallel, 167
193,194,195 system, 168
Failure rate, 191, 1 9 3 transfer, 181
Fault transient, 140, 141, 149
line-to-ground, 25 utility, 145
local contributions, 118 Induction motors, 26, 148, 153
remote contributions, 118 Infinite bus, 22, 49
switching, 190 In-house computer systems, 23, 216, 217,
Fault current, 201 218. 219
multiplier, 114, 201 Inrush current, 1 4 1 , 1 5 2 , 1 4 9
Fault studies, 25 Interrupting calculations, 114
Floating bus, 98 Interruption frequency, 192, 193, 196
Forced outages Interruptions, 21, 25,191, 192, 194,195,
permanent, 194 201
transient, 194 Iteration, 100, 101
Forced unavailability, 1 9 2
Fourier representation, 22,29,41,42,165
Frequency reliability studies, 194
Frolich’s approximation, 159
Kirchoff’s laws, 91, 178
G
Galvanometers, 189, 190
Gauss-Side1 iteration method, 101 Lighting buses, 140
Generator voltage regulator, 147,149,150 Line drops, 105
Generators, 44, 55, 66, 79, 118,144,149, Line-to-ground faults, 25
156.179.181 Linearity, 29, 30, 31, 34, 37, 42
impedances, 145 Load bus, 105
ratings, 8 5 Load data, 145
Grid Load diversity, 80
geometry, 197, 198 Load flow
resistance, 201, 203, 208, 213 analysis, 105, 218
voltages, 197 harmonic, 167

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 IEEE
INDEX Std 399-1980

output presentation, 106 P

program, 21,102, 219
real time, 92 Parallel impedance, 167
results, 102 Parallel resonance, 167
solution method, 148, 156 Passive bus, 101
system data organization, 105 Passive elements, 44
system representation, 92 Passive system, 110
Load flow studies, 21, 24, 25, 91, 92 Per unit method, 2 9 , 4 2
Load shedding, 1 3 4 , 1 3 5 Phase angle, 36, 45, 52, 105
Loads Phasor representation, 29, 36, 37
applied, 24 Power circuit bus, 193
impact, 24 Power factor, 83, 146, 164, 169,175,188
Locked rotor current, 71, 147 Power flow
reactive, 153
M real, 1 5 3
Power generation planning, 26
Machine data, 146 Power system
Magnetizing reactance, 185 analysis, 21, 24, 28, 216, 217, 219
Maintenance outage, 196 studies, 21, 22, 24, 28
Mathematical models, 44, 180 Programs
Mechanical models, 129 batch, 218, 219
Modeling, 22, 46, 49, 167, 177, 179, 180, on-line, 218, 219
182,188,197 Protective relaying, 134
Models
electromagnetic, 180
mathematical, 44, 180 R
mechanical, 130
scaled down, 44 Reactance, 55, 60,175
Momentary calculations, 114 magnetizing, 188
Motor bus, 141 subtransient, 72, 181
Motor impedances, 113 transient, 149, 150, 153, 181
Motor starting studies, 21, 25, 140, 141, Reactive power, 64, 154
162 Reactor, 25, 182
Motors, 140, 179 Real power flow, 141
induction, 26, 146, 150 Real time load flows, 91
synchronous, 25, 26,146,150 Rectifiers, 164, 165, 167, 181
Multimachine system, 128 Reduced voltage, 161
Mutual inductance, 60 Regulated bus, 98
Reliability, 21, 24,25,191,193,195,201,
21 7
N Reliability studies, 191, 1 9 3
Repair time, 192
Networks, 37, 101 Resistance, 55,59,60,175,178,183,197,
203
Resistance diagram, 197
0 Resistor switching contactors, 161
Resonance, 166, 167,168
On-line programs, 217, 218, 219 Rotating components, 110
One-line diagram (Single-line diagram), 42, Rotor angle, 125
43, 91,92,109,113,169,172,180,
185 S
Oscillogram, 186
Oscillograph, 189, 190 Scheduled outage, 191, 1 9 3
Oscilloscope, 185, 188, 190 Scheduled outage duration, 192, 193
Outage Scheduled outage rate, 192, 1 9 3
forced, 191 Short circuit analysis, 109
maintenance, 196 Short circuit possibilities
scheduled, 191 double line-to-ground, 109
Overhead lines, 60 line-to-line, 109
Overload capacity, 84 single line-to-ground, 109
Overvoltage, 185, 187 three-phase, 109

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 IEEE
Std 399-1980 INDUSTRIAL AND COMMERCIAL POWER SYSTEMS ANALYSIS

Short circuit ratings, 84

Short circuit studies, 21, 25
Shunt capacitance, 60, 181, 182
Shunt conductance, 61
Single-line diagram (one-line diagram), 22, T
91,92,109
Single-phase equivalent circuit, 22, 29,37, Tag number, 98
38, 39 Tap settings, 142
Sinusoidal forcing function, 29,34,36, 37 Thevenin equivalent circuit, 29,31,32, 34
Slack or swing bus, 21, 52,101, 105 Thyristor drive, 168
Soil resistivities, 201, 205, 208 Time share basis, 92, 113, 114
Speed-torque analysis, 144,146,153,160, Time share programs, 92
162 Touch contact, 197
Stability, 125 Touch potential, 197, 198, 200
steady-state, 21, 25, 125, 162 Transfer impedances, 183
transient, 125 Transformer, 24,44,62, 72, 94, 145,170,
Stability studies, 22, 25, 26 172, 175, 176, 178, 180, 181, 183,
Static programs, 92 185,186,187
Steadystate probability, 192 Transformer inrush, 84
Steady-state stability, 21, 25, 124, 162 Transient impedances 142,150, 153
Step contact, 197, 198 Transient network analyzer (TNA), 177-
Step potential, 197, 198, 199, 214 185
Studies Transient reactance, 149, 150, 151, 183
fault, 25 Transient stability, 21, 25, 125, 162
grounding mat, 29, 197, 213 Transmission lines, 82
harmonic analysis, 29, 164, 167, 169,
171,172
load flow, 21, 24, 25,29,92
motor starting, 21, 25, 29, 140, 141,
142,161,162 U
power system, 21, 22, 24, 28
reliability, 29 Unavailability, 192
short circuit, 22, 25, 29 Unfaulted buses, 111
stability, 22, 25, 29 Unregulated active bus, 5-12, 95
switching transients, 29, 177, 178, 179, Utility impedances, 149
180,181,187,190
voltage drop, 144, 145, 146, 147, 149,
152,153,162
Subtransient reactance, 72, 183
Superposition, 29, 30, 35 V
Supply transformers, 79
Swing curve, 134 var limited bus, 98
Swing equation, 130 Ventricular fibrillation, 197
Switchgear, 25, 134 Voltage
Switching time, 192 bus, 149, 153, 156
Switching transients, 25, 177, 178, 179, dropout, 141
180,181,182,189, 190, 191 nominal system, 39
Symmetrical component analysis, 25, 39, recovery, 156
40,41 reduced, 162
Symmetrical current, 119 regulator, 156
Synchronizing power, 129 tap, 142
Synchronous machines, 125 terminal, 142
Synchronous motors, 24, 25, 145, 153 Voltage dip, 25, 140, 142, 143, 144, 148,
System, 192, 193, 195 156,162
System impedance, 168 Voltage drop snapshot study, 143, 145,
System power flow, 105 146,147,149,152.153, 162
System reliability, 192 Voltage rating, 39, 175
System studies, 21, 22 Voltmeter, 190, 191

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