Lecture 1

Course Road Map

 System Representation

 Modeling of power system components for stability

analysis

 Excitation systems modeling

 Transients Stability

 Voltage stability

 Power control

 Power system stabilizer (PSS)

Reference Books
1. J. Machowski, Z. Lubosny, J. W. Bialek, J. Bumby, (2020), Power System
Dynamics: Stability and Control, 3rd Ed., Wiley, ISBN-13: 978-
1119526346.
2. V. Vittal, J. McCalley, A. Fouad and P. Anderson, (2020), Power System
Control and Stability. Hoboken, New Jersey: Wiley.
3. P. Kundur, (1994), Power System stability and Control. Estados Unidos
de America: McGraw Hill.
4. Leonard L. Grigsby, (2016), Power System Stability and Control, 3rd Ed.,
CRC Press; ISBN-13: 978-1439883204.
5. Modern Power Systems Analysis by D. P. Kothari
 Introduction
• All over the world, more and more power systems are being
interconnected due to growth in population and industrialization.
• Result - large, complex systems that cover very large geographical
areas.
• The interconnected power system is often referred to as the largest and
most complex mechanism/system ever built by humankind
• The interconnections have been made to realize benefits such as:
✓ shared generation reserves
✓ diversity in sources of power
✓ improved security of supply
✓ ensures economic operation
✓ smaller frequency deviations for higher load changes 4
 Introduction

 There is complex interdependency of different parts of the

system

 Events in geographically distant parts of the system may

interact strongly and in unexpected ways

 Power system analysis is concerned with understanding the

operation of the system as a whole.

 Generally, the system is analyzed either under steady-state

operating conditions or under dynamic conditions during
disturbances.

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 Structure of the Power System
 Electrical power systems vary in size and structural components. However, they
all have the same basic characteristics.
 Generation: use of synchronous machines (generators) 11-35kV

 Transmission systems:
 main transmission – interconnects all main generating stations and main load
centers at highest voltage ranges
 sub transmission- transmission substation to distribution substations

 Distribution systems: primary (4-33kV) and secondary (residential and

commercial customers).
 Electric power is produced at generating stations (GS) and transmitted to
consumers through a complex network of individual components, including
transmission lines, transformers and switching devices.

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Basic components of PS

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Power System Control
 Energy is seldom consumed in the electrical form but is
rather converted to other forms such as heat, light and
mechanical energy.

 The merit of the electrical form of energy is that it can be

transformed and controlled with relative ease.

 The PS must be able to meet the continually changing

load demand for active and reactive power.

 Power quality : constancy of frequency; constancy of

voltage and level of reliability.
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 PS associated controls

• Control of load following

system

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 Stability Analysis

 Power system stability is one of the main challenges in large

interconnected power systems.

 The full effect of a disturbance in some parts of the system far

from the location of the disturbance is felt some time after the
occurrence.

 This causes different parts of the system to respond to the same

disturbance at different times (i.e. there is a time lag)

 The initial disturbance may sometimes cause other disturbances

in neighbouring areas, which may result in widespread system
instability; may eventually culminate in a blackout.

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 Stability Analysis
 Under steady-state conditions, the mechanical torque input and the
electromagnetic torque output of each generator connected in the
power system are balanced.

 The change in electrical torque following a disturbance has two

components:

◼ synchronising torque component; in phase with a rotor angle

perturbation

◼ damping torque components; in phase with the speed deviation.

 Both components must exist and be positive for stability to be

maintained.
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Power System Stability

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Classification of power system stability

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Rotor Angle Stability

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Stability Phenomena

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Voltage Stability

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❑ For planning and operating studies, the most significant large disturbances
include:

✓ Stability of one or more generating stations following a severe fault in

its vicinity

✓ Excitation system control behaviour under all types of disturbances

✓ Determination of inter-area power transfer limit after a disturbance

✓ Sudden loss of one or more large unit(s)

✓ Generator and power system performance with delayed fault clearing

and associated relay performance

✓ Effects of large industrial loads and load shedding

✓ Inter-area tie line oscillations of a pronounced magnitude

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 For generators in the vicinity of a disturbance, the following are important
issues:

◼ Pre-disturbance generator power or torque

◼ Post-disturbance generator power, angle, and voltage several seconds

after the fault

Timescale of power system dynamic phenomena 23

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Per Unit Values

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Per Unit Values

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 Per Unit Values
• Change of base: Sometimes it is necessary to convert pu quantities from one
base to another e.g. if the impedances in a power system have been given in
p.u. and the bases chosen are different from those used to determine the p.u.
quantities.
• The new p.u. values are determined as follows:

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• NB: Unless otherwise specified, base voltage in a 3-ϕ system is the line-to-line
voltage and base VA is the total 3-ϕ base VA.

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 Choice of Base Values

• We need base values for all quantities: Power, Voltage,

• Current, Impedance, Admittance

• Base values do not have to be the same for all equipment inthe system. However,
a wise choice helps simplify the analysis

Rules for choosing base values

• Choose ONE base power for the entire system e.g. total system MVA, largest
MVA or any round figure

• Choose ONE base voltage for one voltage level e.g. rated voltage for a section.
Base voltages for other sections assigned as per transformer turns ratio.

• Other base values are chosen to get the same relations between per unit quantities
as between actual quantities.
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 Advantages of p.u. system

1. If the base quantities are properly specified the ideal transformer winding
can be eliminated as the electrical parameters are the same when referred on
either side of the transformer.

2. Device parameters tend to lie within a relatively narrow range hence it is

easy to detect errors.

3. Per unit phase quantities are the same as per unit line quantities regardless
of connection. Minimises confusion.

4. There is a significantly reduced computational effort.

5. Manufacturers normally include the necessary information in the nameplate as
per unit values.

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 Practice Question
1. An impedance of 4 + j8 Ω is connected in series with a voltage source of
220 V, 50 Hz source. Calculate the per unit values of resistance, reactance,
and impedance by considering the base values of 100 V and 100 VA.

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Practice Question

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 PS component Representation
• A complete diagram of a power system representing all the three phases
becomes too complicated for a system of practical size, such that it may no
longer convey the information it is intended to convey.

• It is much more practical to represent a power system by means of simple

symbols for each component resulting in what is called a one-line diagram.

• Per unit system leads to great simplification of three-phase networks involving

transformers. An impedance diagram drawn on a per unit basis does not
require ideal transformers to be included in it.

• An important element of a power system is the synchronous machine, which

greatly influences the system behaviour during both steady state and transient
conditions.
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The One Line Diagram

• A one-line diagram of a power system

shows the main connections and
arrangements of components.
• The one-line diagram (also know as
single-line diagram) shows the inter-
connections of basic power system
components.
• These include generators, transformers,
CBs, VTs & CTs, rotating loads,
transmission lines etc.
• Generator & transformer connections -
star, delta, and neutral grounding are
indicated by symbols drawn by the side
of the representation of these elements.
• Some of the standard symbols used to
represent these components are shown
below.

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 Per Unit Impedance Diagram of a Power System

• From a one-line diagram of a power system one can directly draw the
impedance diagram by following the steps given below:

1. Choose an appropriate common MVA (or kVA) base for the system.

2. Consider the system to be divided into a number of sections by the

transformers. Choose an appropriate kV base in one of the sections.
Calculate kV bases of other sections in the ratio of transformation.

3. Calculate per unit values of voltages and impedances in each section and
connect them up as per the topology of the one-line diagram. The result is
the single-phase per unit impedance diagram

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Practice Question

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