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Copyright © 2006, New Age International (P) Ltd., Publishers
Published by New Age International (P) Ltd., Publishers
All rights reserved.
No part of this ebook may be reproduced in any form, by photostat, microfilm,
xerography, or any other means, or incorporated into any information retrieval
system, electronic or mechanical, without the written permission of the publisher.
All inquiries should be emailed to
ISBN (13) : 978-81-224-2515-4
PUBLISHING FOR ONE WORLD
NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS
4835/24, Ansari Road, Daryaganj, New Delhi - 110002
Visit us at www.newagepublishers.com
To
My Wife Shanta
Son Debojyoti
and
Daughter Deboleena
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Preface
During the last fifty years, the field of Electrical Engineering has become very diversified and
is much broader in scope now than ever before. With emerging new topic areas, ranging from
microelectro-mechanics to light-wave technology, the number of Electrical Engineering courses
available to students has considerably increased. In order to keep pace with the progress in

governor and turbine models are presented. Both steady-state and dynamic analysis are
presented. Treatment of generation rate constraint in mathematical model is also discussed.
Multiunit AGC system is discussed.
Chapter 13 discusses the AGC in restructured environment. Block diagram representation
of AGC system in restructured enviornment is discussed and equivalent block diagram is
presented for easy understanding. Different case studies are presented.
Chapter 14 deals with corona loss of transmission lines. All mathematical derivations are
presented in detail and the factors affecting the corona are discussed.
Chapter 15 deals with sag and tension analysis of transmission lines. Catenary and Parabolic
representation are presented. Effect of wind pressure and ice coating on conductors are considered
and mathematical derivations are presented.
Chapter 16 deals with optimal system operation. A rigorous treatment for thermal system
is presented. Gradient method for optimal dispatch solution is presented. Derivation of loss
formula is also presented.
Every concept and technique presented in each chapter is supported through several
examples. At the end of each chapter, unsolved problems with answers are given for further
practice. At the end a large number of objective type questions are added to help the students
to test himself/herself. As listed in the bibliography at the end of this book, several excellent text
are available which will help the reader to locate detailed information on various topic of his/
her interest. After reading the book, students should have a good perspective of power system
analysis.
The author wishes to thank his colleagues at I.I.T., Kharagpur, for their encouragement
and various useful suggestions.
My thanks are also due to New Age International (P) Limited, especially its editorial
and production teams for their utmost cooperation in bringing out the book on time.
Last, but not least, I thank my wife Shanta for her support, patience, and understanding
through the endeavour.
I welcome any constructive criticism and will be very grateful for any appraisal by the
reader.
DEBAPRIYA DAS

3.2 Electric Field and Potential Difference 53
3.2 Potential Difference in an Array of Solid Cylindrical Conductors 54
3.3 Capacitance of a Single Phase Line 55
3.4 Capacitance of Three Phase Transmission Lines 56
3.5 Bundled Conductors 58
3.6 Capacitance of Three Phase Double Circuit Lines 59
3.7 Effect of Earth on the Capacitance 61
3.8 Capacitance of a Single Phase Line Considering the Effect of Earth 61
4. Synchronous Machine: Steady State and Transient Operations 79
4.1 Introduction 79
4.2 Synchronous Generator 79
4.3 Model of Generator 80
x Electrical Power Systems
4.4 Power Angle Characteristics 84
4.5 Salient Pole Synchronous Generators 86
4.6 Transients of Synchronous Machine 89
4.7 Simplified Representation of Synchronous Machine for Transient Analysis 90
4.8 DC Components of Stator Currents 92
4.9 Effect of Load Current 93
5. Power System Components and Per Unit System 96
5.1 Introduction 96
5.2 Single Phase Representation of a Balanced Three Phase System 96
5.3 The Per-Unit (pu) System 99
5.4 Per-Unit Representation of Transformer 101
5.5 Methods of Voltage Control 115
6. Characteristics and Performance of Transmission Lines 124
6.1 Introduction 124
6.2 Short Transmission Line 124
6.3 Voltage Regulation 125
6.4 Medium Transmission Line 126

8.6 Algorithm for Building Z
BUS
Matrix 217
Contents xi
9. Symmetrical Components 226
9.1 Introduction 226
9.2 Symmetrical Components of an Unbalanced Three Phase System 226
9.3 Power Invariance 229
9.4 Sequence Impedances of Transmission Lines 230
9.5 Sequence Impedances of Synchronous Machine 231
9.6 Sequence Networks of a Loaded Synchronous Machine 232
9.7 Sequence Impedances of Transformers 235
10. Unbalanced Fault Analysis 250
10.1 Introduction 250
10.2 Single Line to Ground Fault 250
10.3 Line-to-Line Fault 252
10.4 Double-Line-to-Ground (L-L-G) Fault 254
10.5 Open Conductor Faults 256
11. Power System Stability 276
11.1 Introduction 276
11.2 Inertia Constant and the Swing Equation 276
11.3 Multi-Machine System 279
11.4 Machines Swinging in Unison (Coherently) 280
11.5 Power Flow Under Steady-State 282
11.6 Equal-Area Criterion 286
11.7 Critical Clearing Angle and Critical Clearing Time 290
11.8 Step-by-Step Solution 299
11.9 Evaluation of P
a
and W

13.5 State Space Representation of the Two-Area System in
Deregulated Environment 345
14. Corona 356
14.1 Introduction 356
14.2 The Phenomenon of Corona 356
14.3 Potential Gradient for Single-Phase Line 357
14.4 Potential Gradient for Three-Phase Line 359
14.5 Disruptive Critical Voltage for a Single Phase Transmission Line 361
14.6 Disruptive Critical Voltage for a Three Phase Transmission Line 362
14.7 Formula for Disruptive Critical Voltage Suggested by F.W. Peek 362
14.8 Visual Critical Voltage 363
14.9 Corona Power Loss 364
14.9 Factors Affecting Corona Loss 365
14.10 Effect of Corona on Line Design 366
15. Analysis of Sag and Tension 373
15.1 Introduction 373
15.2 Effect of Temperature Change 374
15.3 Calculations of Line Sag and Tension 375
15.4 Unsymmetrical Spans (Supports at Different Levels) 385
15.5 Ruling Span or Equivalent Span (Spans of Unequal Length) 387
15.6 Effect of Ice 388
15.7 Effect of Wind 389
15.8 Location of Line 393
15.9 Sag Template 393
15.10 Aeolian Vibration (Resonant Vibration) 402
15.11 Galloping or Dancing of Conductors 402
16. Optimal System Operation 405
16.1 Introduction 405
16.2 Formulation of the Economic Dispatch Problem 405
16.3 General Problem Formulation 408

at 132 kV, 66 kV, 33 kV, 11 kV or 6.6 kV and supply the final consumer feeders at 400 volt three
phase, giving 230 volt per phase.
Figure 1.1 shows the schematic diagram of a power supply network. The power supply
network can be divided into two parts, i.e., transmission and distribution systems. The
transmission system may be divided into primary and secondary (sub-transmission) transmission
system. Distribution system can be divided into primary and secondary distribution system.
Most of the distribution networks operate radially for less short circuit current and better
protective coordination.
Distribution networks are different than transmission networks in many ways, quite apart
from voltage magnitude. The general structure or topology of the distribution system is different
and the number of branches and sources is much higher. A typical distribution system
consists of a step-down transformer (e.g., 132/11 kV or 66/11 kV or 33/11 kV) at a bulk supply
point feeding a number of lines with varying length from a few hundred meters to several
kilometers. Several three-phase step-down transformers, e.g., 11 kV/400 V are spaced along the
feeders and from these, three-phase four-wire networks of consumers are supplied which give
230 volt single-phase supply to houses and similar loads. Figure 1.3 shows a typical distribution
system.
2 Electrical Power Systems
Fig. 1.2: Part of a power system.
Fig. 1.1: Schematic diagram of a power supply system.
Figure 1.2 shows part of a typical power system.
Structure of Power Systems and Few Other Aspects 3
1.2 REASONS FOR INTERCONNECTION
Generating stations and distribution systems are connected through transmission lines. The
transmission system of a particular area (e.g., state) is known as a grid. Different grids are
interconnected through tie-lines to form a regional grid (also called power pools). Different
regional grids are further connected to form a national grid. Cooperative assistance is one of the
planned benefits of interconnected operation. Interconnected operation is always economical
and reliable. Generating stations having large MW capacity are available to provide base or
intermediate load. These generating stations must be interconnected so that they feed into the

Induction motors : 0.6 0.85
Fractional HP motors : 0.50.80
Fluorescent lamps : 0.550.90
Neon signs : 0.400.50
Fans : 0.550.85
Induction furnaces : 0.700.85
Arc welders : 0.35 0.55
1.5 BASIC DEFINITIONS OF COMMONLY USED TERMS
Connected Load: Each electrical device has its rated capacity. The sum of the continuous
ratings of all the electrical devices connected to the supply system is known as connected load.
Demand: The demand of an installation or system is the load at the receiving terminals
averaged over a specified interval of time. Here, the load may be given in kW, kVA, kiloamperes,
or amperes.
Demand Interval: It is the time period over which the average load is computed. The time
period may be 30 minute, 60 minute or even longer.
Maximum Demand: The maximum demand of an installation or system is the greatest of
all demands which have occurred during the specified period of time. Maximum demand
statement must express the demand interval used to measure it. For example, the specific
demand might be the maximum of all demands such as daily, weekly, monthly or annual.
Coincident Demand (or Diversified Demand): It is the demand of composite group, as
a whole, of somewhat unrelated loads over a specified period of time. It is the maximum sum of
the contributions of the individual demands to the diversified demand over a specific time
interval.
Noncoincident Demand: It is the sum of the demands of a group of loads with no
restrictions on the interval to which each demand is applicable.
Demand Factor: It is the ratio of the maximum demand of a system to the total connected
load of the system. Thus, the demand factor (DF) is given as:
DF =
Maximum demand
Total connected load

Diversity Factor: It is the ratio of the sum of the individual maximum demands of the
various subdivisions or groups or consumers to the maximum demand of the whole system.
Therefore, the diversity factor (FD) is given as
FD =
Sum of individual maximum demand
Coincident maximum demand
(1.6)
or FD =
P
P
i
i=1
n
c
å
(1.7)
where
P
i
= maximum demand of load i
P
c
= coincident maximum demand of group of n loads.
The diversity factor can be equal or greater than unity. From eqn. (1.1), the demand
factor is
DF =
Maximum demand
Total connected load
\
Maximum demand = Total connected load × DF (1.8)

Sum of individual maximum demands
(1.11)
or CF =
P
P
c
i
i=1
n
å
(1.12)
From eqns. (1.12) and (1.7), we get
CF =
1
FD
(1.13)
Thus, the coincidence factor is the reciprocal of the diversity factor.
Load Diversity: It is the difference between the sum of the peaks of two or more individual
loads and the peak of the combined load. Therefore load diversity (LD) is defined as
LD =
P
i
i=1
n
å
F
H
G
I
K

n
å
(1.15)
From eqns. (1.12) and (1.15), we get,
CF =
CP
P
ii
i=1
n
i
i=1
n
å
å
(1.16)
Structure of Power Systems and Few Other Aspects 7
Case-1:
If P
1
= P
2
= P
3
= = P
n
= P
Then
CF =
PC

´
å
å
i
i=1
n
i
i=1
n
= C (1.18)
That is, coincidence factor is equal to the contribution factor.
Load Factor: It is the ratio of the average load over a designated period of time to the peak
load occurring on that period.
Therefore, the load factor (LF) is defined as:
LF =
Average load
Peak load
(1.19)
or
LF =
Average load
Peak load
´
´
T
T
\
LF =
Energy served
Peak load ´ T

(a) Plot the load curve and find out the load factor.
(b) Determine the proper number and size of generating units to supply this load.
(c) Find the reserve capacity of the plant and plant factor.
(d) Find out the operating schedule of the generating units selected.
Solution:
(a) Figure 1.4 show the plot of load curve
Fig. 1.4: Load curve of Ex1.1.
Units generated during 24 hours
= (2 × 1.2 + 1 × 2 + 3 × 3 + 2 × 1.5 + 4 × 2.5 + 2 × 1.8 + 1 × 2
+ 2 × 1 + 6 × 0.5 + 1 × 0.8) MWhr.
= 37.80 MWhr
Average load =
Units generated
Time in hours
\
Average load =
37 80
24
.
= 1.575 MW.
Structure of Power Systems and Few Other Aspects 9
Load factor,
LF =
Average load
Maximum load
Maximum load = 3 MW
\
LF =
1575
3

, calculate (a) load factor (b) demand factor.
Solution:
Maximum demand = 80 MW
Connected load = 150 MW
Units generated in one year = 400 ×10
3
MWhr
Total number of hours in a year T = 8760
\
Average load =
400 10
8760
3
´
= 45.662 MW
Load factor, LF =
Average load
Maximum load
\
LF =
45 662
80
.
= 0.57
10 Electrical Power Systems
Demand factor,
DF =
Maximum demand
Connected load
\

P
1
c
+
2
P
1
= 2 MW, P
2
= 2 MW and P
c
= 3 MW
\
FD =
()22
3
+
= 1.33
(b) From eqn. (1.14), load diversity is,
LD =
P
i
i=1
n
å
F
H
G
I
K

1.6 RELATIONSHIP BETWEEN LOAD FACTOR (LF) AND
LOSS FACTOR (LLF)
In general, loss factor can not be determined from load factor. However, the limiting values of
the relationship can be established. Fig. 1.6 shows an arbitrary and idealized load curve and it
does not represent a daily load curve.
Fig.1.6: Idealized load curve.
Assume that at peak load P
2
, loss is L
2
and at off-peak load P
1
, loss is L
1
.
The load factor is,
LF =
P
P
avg
max
=
P
P
avg
2
(1.23)
From Fig.1.6,
P
avg

T
-
F
H
G
I
K
J
(1.25)
The loss factor is
LLF =
L
L
avg
max
=
L
L
avg
2
(1.26)
where
L
max
= maximum power loss = L
2
L
avg
= average power loss.
From Fig. 1.6, we obtain

1
2
(1.29)
L
2
= K ×
P
2
2
(1.30)
From eqns. (1.28), (1.29) and (1.30), we get,
LLF =
t
T
+
P
P
1
2
2
F
H
G
I
K
J
Tt
T
-
F