SEEA1501- Power System

Analysis
Dr. D. Godwin Immanuel
Associate Professor
Department of EEE
Sathyabama Institute of Science and Technology

1
Prerequisite

• Transmission and Distribution

• Circuit Theory
• Electrical Machines – AC Generator, transformer, induction motor,
synchronous motor

2
Course Objectives
• To impart knowledge in modelling of power system elements.
• To implement Numerical methods in power flow problem.
• To analyze the system in various fault conditions.
• To have a knowledge in stability of power systems.

3
Course Contents
Unit Description Hours
1 POWER SYSTEM MODELING 9 Hrs
Need for system analysis in planning and operation of power system - per phase
analysis of symmetrical three-phase system. General aspects relating to power
flow, short circuit and stability analysis - Modeling of generator, load, shunt
capacitor, transmission line, shunt reactor for short circuit, power flow and
stability studies -per unit representation - bus admittance by analytical method
and direct inspection method.
2 POWER FLOW ANALYSIS 9 Hrs
Problem definition - bus classification - derivation of power flow equation -
solution by Gauss Seidel and Newton Raphson methods by polar form - P V bus
adjustments for both methods - computation of slack bus power, line flow and
transmission loss.
3 SYMMETRICAL SHORT CIRCUIT ANALYSIS 9 Hrs
Need for short circuit study - Bus impedance matrix formation - Symmetrical short
circuit analysis using Z-bus. - computations of short circuit capacity, post fault
voltage and current.

4
Course Contents
Unit Description Hours
4 UNSYMMETRICAL SHORT CIRCUIT ANALYSIS 9 Hrs
Symmetrical component transformation - sequence impedances.- Sequence
Networks - unsymmetrical short circuit analysis for single line fault, line to line
fault and double line to ground fault using Z-bus - computations of short circuit
capacity, post fault voltage and current.

5 STABILITY & SECURITY ANALYSIS 9 Hrs

Distinction between steady state and transient state - Concepts of Stability &
Security - Swing equation-solution to swing equation - step by step method -
power angle equation - equal area criterion - critical clearing angle and time.
Stability analysis of single machine connected to infinite bus by modified Euler's
method - Multi-machine stability analysis using Runge Kutta method

5
Course Outcomes

• On completion of the course, student will be able to

• CO1 - Model Impedance and Reactance networks for the given power
system Network and formulate bus admittance matrix.
• CO2 - Apply Y Bus in load flow analysis and examine the power flows and
voltages in a power grid.
• CO3 - Formulate bus impedance matrix and apply Z Bus in symmetrical
short circuit analysis and evaluate the fault currents and post fault
voltages.
• CO4 - Model sequence networks and apply Z Bus in unsymmetrical short
circuit analysis and evaluate the fault currents and post fault voltages.
• CO5 - Analyze the transient and steady state stability conditions.
• CO6 - Solve transient stability problems.
6
Text / Reference Books
• 1.John J. Grainger and Stevenson Jr. W.D., "Power System Analysis",
Tata McGraw Hill, 2017.
• 2. Kothari .D.P and Nagarath.I.J., "Power system Engineering", 2nd
Edition, Tata McGraw Hill, 2011.
• 3. Pai. M.A,” Computer Techniques in Power System Analysis”, Tata
McGraw-Hill Publishing Company Limited, New Delhi, 2006.
• 4. Nagarath, I.J. and Kothari, D.P., "Modern Power System Analysis",
4th Edition, Tata McGraw Hill Publishing Company, 2011.
• 5. Hadi Saadat, "Power system Analysis", Tata McGraw Hill Publishing
Company, 3rd Edition, 2011.

7
Text / Reference Books
• A.Nagoor Kani, “Power System Analysis”, RBA Publications
• M. Jeraldin Ahila, “ Power System Analysis”, Lakshmi Publications.

8
 Unit 1-POWER SYSTEM MODELING

Need for system analysis in planning and operation of power system - per
phase analysis of symmetrical three-phase system. General aspects relating
to power flow, short circuit and stability analysis - Modeling of generator,
load, shunt capacitor, transmission line, shunt reactor for short circuit, power
flow and stability studies -per unit representation - bus admittance by
analytical method and direct inspection method.

9
Single line Diagram -
Structure of Power system

10
Components of Power System

• Generators
• Power Transformers
• Transmission lines
• Substation Transformers
• Distribution Transformers
• Loads

11
Single line Diagram
Components of single line diagram

Generating Station
Primary Transmission
Secondary Transmission
Primary Distribution
Secondary Distribution

12
13
14
Symbols used in Single line diagram

15
Single line Diagram

• The various components of power system components of Power

system like alternators, motors, transformers etc., have their voltage,
power, current and impedance ratings in KV,KVA,KA and 
• The components or various sections of power system may operate at
different voltage and power levels
• It will be convenient for analysis of power system if the voltage,
power, current and impedance ratings of components of power
system are expressed with reference to a common value called base
value

16
Single line Diagram Contd..
• Hence the analysis purpose a base value is chosen for voltage, power,
current and impedance
• The power system requires the base values of four quantities and they
are Voltage, Power, Current and Impedance.
• Selection of base values for any two of them determines the base
values of the remaining two

17
 Per Unit Value

Formula for finding base Value

The same formula holds good for Three phase
Single Phase System
system also both for star connected and Delta
Let KVAb = Base KVA connected
KVb=Base voltage in KV In 3 phase system, the KVb is a line value and MVAb
Ib=Base current in A is a 3 phase MVA. The Impedance value is always
expressed as Phase Value
Zb=Base impedance in W
18
Problem 1.1
A three Phase generator with rating 1000KVA,
33KV has its armature resistance and
synchronous reactance as 20/Phase and
70/Phase. Calculate P.U. impedance of the
generator

19
Problem 1.2
• If the reactance in ohms is 15 ohms, find the p.u value for a base of
15kVA and 10kV.
•

20
Problem 1.3

• A Y-connected generator rated at 300MVA,33kV has a reactance of

1.24 p.u. Find the ohmic value of reactance.
•

21
Problem 1.4

• The base kV and base MVA of a three phase transmission line is 33kV
and 10MVA respectively. Calculate the base current and base
impedance.

22
Problem 1.5
A three phase, /Y transformer with rating 100KVA,
11KV/400V has its primary and secondary leakage
reactance as 12 /Phase and 0.05  /Phase respectively.
Calculate the p.u reactance of the transformer

23
• Case ii

Note:
1. It is observed that P.U. reactance
of a transformer referred to
primary and secondary are same.
2. In three phase transformer if the
voltage ratio K is obtained using
line values then using this value
of K , The phase impedance per
phase of star side can be directly
transferred to delta side or vice
versa

24
Advantages of Per Unit
Computations
 Manufactures usually specify the impedance of a device or machine in
percent or per unit on the base of the name plate rating
The Per Unit impedances of a machines of the same type and widely
different rating usually lie within a narrow range, although the ohmic
Values differ widely for machines of different ratings
 The Per Unit impedance of circuit element connected by transformers
expressed on a proper base will be same if it is referred to either side of
a transformer
 The way in which the transformers are connected in a 3 phase circuits (Y
/) does not affect the per unit impedances of the equivalent circuit,
although the transformer connection does determine the relation
between the voltage bases on the two sides of the transformer
25
Equivalent Circuits of Components of Power
System
• Equivalent Circuit of Generator

3 – Phase Equivalent Circuit Single Phase Equivalent Circuit

26
Equivalent Circuits of Components of Power
System
• Equivalent Circuit of Synchronous motor

3 – Phase Equivalent Circuit Single Phase Equivalent Circuit

27
Equivalent Circuits of Components of Power
System
• Equivalent Circuit of Transformer

28
Equivalent Circuits of Components of Power
System
• Equivalent Circuit of Induction Motor

29
Equivalent Circuits of Components of Power
System
• Equivalent Circuit of Transmission line

30
Representation of resistive and reactive loads
• Single Phase Load
Constant Impedance representation
Constant Power representation
S=P+jQ

Constant Current representation

31
Three Phase Load (Balanced Star Connected
load)
Constant Power representation • P= Three Phase active Power of star connected load in
watts
S=P+jQ
• Q= Three Phase reactive Power of star connected load in
VARS
Constant Current representation
• V,VL = Phase & line voltage of load respectively
• I,IL= Phase & line current of load respectively
Constant Impedance representation

32
Three Phase Load (Balanced Delta Connected
load)
Constant Power representation

S=P+jQ
Constant Impedance representation
Constant Current representation

33
Impedance Diagram
• The impedance diagram is the equivalent circuit of Power system in
which the various components of power system are represented by
their approximate or simplified equivalent circuits •
• It is used for load flow studies

Approximations made in Impedance Diagram

• The neutral reactances are neglected •
• The shunt branches in equivalent circuit of Transformers & induction
motor are neglected

34
Reactance Diagram
• It is a simplified equivalent circuit of power system in which the various
components are represented by their reactance
• It can be obtained from impedance diagram if all the resistive components are
neglected
• • It is used for fault calculations
Approximations made in Reactance Diagram
• The neutral reactance are neglected
• Shunt branches in the equivalent circuits of transformer are neglected .
• The resistances are neglected
• All static loads and induction motors are neglected
• The capacitance of the transmission lines are neglected
35
Single Line Diagram

36
Equations

37
1.Single Line
2. Impedance Diagram
Diagram

3. Reactance Diagram

38
 Problem 1.6
• A 300 MVA, 20KV, 3 phase generator has a subtransient reactance of 20%. The
generator supplies 2 synchronous motors through a 64Km transmission line having
transformers at both ends as as shown in Fig. In this, T1 is a 3 phase transformer and
T2 is made of 3 single phase transformer of rating 100 MVA, 127/13.2KV, 10%
reactance. Series reactance of the transmission line is 0.5 ohm/Km. Draw the
reactance diagram with all the reactances marked in p.u. Select the generator ratings
as base values.

39
Solution

40
41
Problem 1.7
• Draw the reactance diagram for the power system shown in fig.
Neglect resistance and use a base of 100 MVA, 220KV in 50 ohm line.
The ratings of the generator, motor and transformer are given below.

Generator: 40MVA,25KV,X’’=20%
Synchronous motor: 50MVA,11KV,X’’=30%
Y-Y Transformer : 40MVA,33/220KV,X=15%
Y- Transformer : 30MVA,11/220KV( /Y), X=15%

42
Solution

Generator: 40MVA,25KV,X’’=20%
Synchronous motor: 50MVA,11KV,X’’=30%
Y-Y Transformer : 40MVA,33/220KV,X=15%
Y- Transformer : 30MVA,11/220KV( /Y),
X=15%

43
• Generator: 40MVA,25KV,X’’=20%
• Synchronous motor:
50MVA,11KV,X’’=30%
• Y-Y Transformer :
40MVA,33/220KV,X=15%
• Y- Transformer : 30MVA,11/220KV(
/Y), X=15%

44
Solution

Reactance Diagram

Generator: 40MVA,25KV,X’’=20%
Synchronous motor: 50MVA,11KV,X’’=30%
Y-Y Transformer : 40MVA,33/220KV,X=15%
Y- Transformer : 30MVA,11/220KV( /Y),
X=15%

45
 Problem 1.8
• A 15MVA, 8.5KV, 3- Phase generator has a substransient reactance of 20%. It is
connected through a  - Y transformer to a high voltage transmission line having
a total series reactance of 70.The load end of the line has Y-Y step down
transformer. Both transformer banks are composed of single Phase transformers
connected for 3-Phase operation. Each of three transformers composing three
phase bank is rated 6667KVA, 10/100KV, with a reactance of 10%. The load
represented as impedance, is drawing 10MVA at 12.5KV and 0.8pf lagging. Draw
the single line diagram of the power network. Choose a base of 10MVA,12.5KV in
the load circuit and determine the reactance diagram. Determine also the voltage
at the terminals of the generator.

46
• MVAb,new=10MVA
• KVb,new=12.5KV

47
48
49
50
Problem 1.9

51
52
53
54
55
BUS ADMITTANCE MATRIX
• Bus
• The meeting point of various components in a power system is called a
bus
• The bus is a conductor made of copper or aluminum having negligible
resistance
• The buses are considered as points of constant voltage in a power
system
• Bus admittance matrix
• The matrix consisting of the self and mutual admittance of the network
of a power system is called Bus admittance matrix
• It is given by the admittance matrix Y in the node basis matrix equation
of a power system. Denoted as Ybus
56
To Bus Admittance Matrix

• Direct Inspection Method

• Singular Transformation (or) Analytical Method

• Reducing Admittance Matrix

57
58
 Y bus formation using
Direct Inspection Method

59
Direction Inspection Method

• The Guidelines to form bus admittance matrix by Indirect Inspection

method are:
• The diagonal element Yjj is given by sum of all the admittances
connected to node j.
• The off diagonal elements Yjk is given by negative of the sum of all
the admittances connected between node j and node k.

60
 Problem 1.10
• For the given system form the admittance matrix by direct inspection
method.

61
 Final Answer :

• Ybus(1,1) = 1/(0.02+j0.04) + 1/(0.01+j0.03) = 20 – j50

• Ybus(2,2) = 1/(0.02+j0.04) + 1/(0.0125+j0.025) = 10.1995 –j23.99
• Ybus(2,2) = 1/(0.01+j0.03) + 1/(0.0125+j0.025) = 26 –j62
• Ybus(1,2) = Ybus(2,1) = -1/(0.02+j0.04) = -10+j20
• Ybus(1,3) = Ybus(3,1) = -1/(0.01+j0.03) = -10+j30
• Ybus(2,3) = Ybus(3,2) = -1/(0.0125+j0.025) = -16+j32
62
CALCULATOR USAGE

63
991MS CALCULATOR
• PRESS MODE
• SELECT MODE 2 COMPLX – PRESS 2
• NOW TYPE THE OPERAND , FOR EXAMPLE
• 1/(0.2+0.4i) press shift – (minus) for getting answer in Rectangular
form
• In the screen , u will get 1/(0.2+0.4i)>a+bi
• Now press = for getting real part value = 1
• Press shift = for getting imaginary value =-2i
• Final answer write as 1-2i

64
Problem 1.11

• For the given 4-bus system form the admittance matrix by direct
inspection method.
Line Resistance, R (pu) Reactance, X (pu)

1-2 0.05 0.15

1-3 0.1 0.3

1-4 0.2 0.4

2-4 0.1 0.3

3-4 0.05 0.15

65
• Ybus(1,1) = 1/(0.05+j0.15) + 1/(0.1+j0.3) + 1/(0.2+j0.4) = 4-j11
• Ybus(2,2) = 1/(0.05+j0.15) + 1/(0.1+j0.3) = 3-j9
• Ybus(3,3) = 1/(0.1+j0.3) + 1/(0.05+j0.15) = 3-j9 Line
Resistance, R Reactance, X
(pu) (pu)
• Ybus(4,4) = 1/(0.2+j0.4) + 1/(0.1+j0.3) + 1/(0.05+j0.15) = 4-j11
1-2 0.05 0.15
• Ybus(1,2) = Ybus(2,1) = -1/(0.05+j0.15) = -2+j6
1-3 0.1 0.3
• Ybus(1,3) = Ybus(3,1) = -1/(0.1+j0.3) = -1+j3
1-4 0.2 0.4
• Ybus(1,4) = Ybus(4,1) = -1/(0.2+j0.4) = -1+j2
2-4 0.1 0.3
• Ybus(2,4) = Ybus(4,2) = -1/(0.1+j0.3) = -1+j3
3-4 0.05 0.15
• Ybus(3,4) = Ybus(4,3) = -1/(0.05+j0.15) = -2+j6

Final Answer :

66
 Problem 1.12
• For the given 5-bus system form the admittance matrix by direct
inspection method.

67
68
69
 Y bus Formation Using
Analytical method or
Singular transformation
Method

70
Analytical method or Singular
transformation Method

71
 Problem 1.13
• For the given system form the admittance matrix by analytical method.

1 0.02 + j0.04 2

0.01 + j0.03 0.0125 + j0.025

72
1 0.02 + 2
j0.04

0.01 + 0.0125 +
j0.03 j0.025

73
Problem 1.14
• For the given 4-bus system form the admittance matrix by analytical
method.
Line Resistance, R (pu) Reactance, X (pu)
1-2 0.05 0.15
1-3 0.1 0.3
1-4 0.2 0.4
2-4 0.1 0.3
3-4 0.05 0.15

74
Line Resistance, R (pu) Reactance, X (pu)
1-2 0.05 0.15
1-3 0.1 0.3
1-4 0.2 0.4
2-4 0.1 0.3
3-4 0.05 0.15

75
76
Problem 1.15

• For the given system form the admittance matrix by analytical

method

77
78
Eliminating a node in a
Y bus

79
 Problem 1.16
• For the network shown in Fig, form the bus admittance matrix.
Determine the reduced admittance by eliminating node 4. The values
are marked in p.u

80
81
82
 Problem 1.17

• Determine the bus admittance matrix of the system whose reactance

diagram is shown in fig. the currents and admittances are given in p.u.
Determine the reduced bus admittance matrix after eliminating node-3

83
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Need of System analysis in planning and
operation of power System

• Load Flow Studies:

• It is a steady state behavior of the power system under normal conditions & its dynamic
behavior under small scale disturbances
• In Load flow studies, the main concentration is on transmission with generators & loads
modeled by the complex powers. The transmission system may be a primary or sub
transmission system
• The transmission system is to be designed in such a manner that power system operation
is reliable and economical & no difficulties arise during its operation
• But these two objectives are conflicting, so more concentration is needed in load flow
studies
• Now power system is highly complicated consisting of hundreds of buses & transmission
lines
• So load flow involves extensive calculations
86
• Short Circuit Analysis:
• It is the abnormal system behavior under conditions of fault during
operation
• In a large interconnected power system, heavy currents flowing
during short circuits must be interrupted through a circuit breaker.
• So maximum current that circuit breaker can withstand momentarily
has to be determined
• For selection of circuit breakers, the initial current that flows on
occurrence of a short circuit & the transient current that flows at the
time of circuit interruption has to be calculated from short circuit
studies

87
• Stability Studies:
• The stability of an interconnected power system is its ability to return to its
normal or stable operation after having been subjected to some form of
disturbances
• Stability is considered as an essential part of power system planning for a long
time
• During a fault, electrical power from nearby generators is reduced drastically,
while power from remote generators is scarcely affected
• In some cases, the system will be stable even with a sustained fault, whereas
other system will be stable only if the fault is cleared rapidly
• Whether the system is stable on occurrence of a fault depends not only on the
system itself, but also on the type of the fault, location of the fault, rapidity on
clearing the fault and method used in clearing the fault
• Thus for a reliable, economical operation of power system, the need of system
analysis like load flow analysis, short circuit analysis, stability analysis is essential
to have effective planning & operation of power system
88