Computer-Aided Power Systems Analysis, Second Edition

392 Pages·2008·6.42 MB·English

by  George Kusic

Computer-Aided
Power Systems Analysis
Second Edition
Computer-Aided
Power Systems Analysis
Second Edition
Dr. George Kusic
University of Pittsburgh
Pittsburgh, Pennsylvania, U.S.A.

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Dedication
To the Serbian father
of power engineering—Nikola Tesla
Contents
Contents ...........................................................................................................................vii
Preface ...............................................................................................................................xi
1 Central Operation and Control of Power Systems ...........................................................1
1.1 General .....................................................................................................................................1
1.2 Control Center of a Power System ........................................................................................2
1.3 Digital Computer Configuration ..........................................................................................5
1.4 Automatic Generation Control for a Power System ...........................................................7
1.4.1 Area Control Error ......................................................................................................9
1.4.1.1 CPS1, 1 Minute Average ..............................................................................12
1.4.1.2 CPS2, 10 Minute Average ............................................................................12
1.4.1.3 Disturbance Conditions ..............................................................................14
1.5 Operation without Central Computers or AGC ...............................................................14
1.6 Parallel Operation of Generators ........................................................................................19
1.7 Network Power Flows ..........................................................................................................24
1.7.1 Oversimplified Power Flow (dc Power Flow) ........................................................25
1.8 Area Lumped Dynamic Model...........................................................................................30
Problems .........................................................................................................................................34
References ......................................................................................................................................38
2 Elements of Transmission Networks .................................................................................39
2.1 Phasor Notation ....................................................................................................................40
2.2 Symmetrical Component Transformation ........................................................................44
2.2.1 Floating Voltage Base Per-Unit Systems .................................................................52
2.3 Overhead Transmission Line Representation ..................................................................56
2.3.1 Inductance of Long Parallel Conductors ................................................................59
2.3.2 Balanced Three-Phase Lines ....................................................................................65
2.3.3 Unbalanced Lines ......................................................................................................74
2.3.4 Capacitance of Transmission Lines .........................................................................76
2.3.5 General Method to Determine Aerial Transmission Line Parameters ..............87
2.4 Transformer Representation ...............................................................................................97
2.4.1 Wye–Delta and Phase-Shift Transformers...........................................................100
2.4.2 Multiple-Winding Transformers ...........................................................................105
2.5 Synchronous Machine Representation ............................................................................108
2.5.1 Steady-State Synchronous Machine Equivalent .................................................114
2.5.1.1 Short-Circuit Characteristics ....................................................................120
2.5.2 Transient Time-Frame Synchronous Machine Equivalent ................................120
2.5.3 Subtransient Time-Frame Synchronous Machine Equivalent ..........................122
Problems .......................................................................................................................................131
References ....................................................................................................................................139
3 Bus Reference Frame ..........................................................................................................141
3.1 Linear Network Injections and Loads .............................................................................142
3.2 Bus Impedance Matrix for Elements without Mutual Coupling .................................151
3.2.1 Adding a Tree Branch to Bus p ..............................................................................153
3.2.2 Adding a Tree Branch to the Reference ................................................................155
3.2.3 Adding a Cotree Link between Buses p and q ....................................................156
3.2.4 Adding a Cotree Link from Bus p to Reference ..................................................158
3.3 The Bus Admittance Matrix ..............................................................................................160
3.3.1 Bus Impedance Matrix for Elements with Mutual Coupling ...........................165
3.4 Inversion of the Y Matrix for Large Systems..............................................................169
BUS
3.4.1 Tinney’s Optimally Ordered Triangular Factorization [3] ................................169
3.4.1.1 Tinney’s Schemes for Near-Optimal Ordering .....................................176
3.4.2 Several Iterative Methods for Linear Matrices ....................................................180
3.4.2.1 Gaussian Iteration ......................................................................................181
3.4.2.2 Gauss-Seidel Iteration ................................................................................182
Problems .......................................................................................................................................185
References .....................................................................................................................................191
4 Network Fault and Contingency Calculations ..............................................................193
4.1 Fault Calculations Using Z ...........................................................................................193
BUS
4.1.1 Approximations Common to Short-Circuit Studies ...........................................204
4.2 Fault Calculations Using the Y Table of Factors ........................................................209
BUS
4.3 Contingency Analysis for Power Systems ......................................................................212
4.3.1 Contingency Analysis for Power Systems ...........................................................213
4.3.2 Contingencies Using Z in a Superposition Method ......................................213
BUS
4.3.3 Z Line Contingency Method .............................................................................214
BUS
4.4 Using the Y Table of Factors for Contingencies .........................................................215
BUS
4.4.1 Double Contingencies Using Y Table of Factors (Balanced Case)................219
BUS
Problems .......................................................................................................................................223
References ....................................................................................................................................229
5 Power Flow on Transmission Networks .........................................................................231
5.1 Slack Bus ..............................................................................................................................233
5.2 Z Formulation for Load-Flow Equations ....................................................................234
BUS
5.3 Gauss or Gauss-Seidel Iteration Using Y ....................................................................240
BUS
5.4 Newton-Raphson Iterative Scheme Using Y ..............................................................243
BUS
5.4.1 Approximations to the Jacobian in the Newton-Raphson Method .................257
5.5 Adjustment of Network Operating Conditions .............................................................262
5.6 Operational Power Flow Programs ..................................................................................275
Problems .......................................................................................................................................278
References ....................................................................................................................................284
6 Generator Base Power Setting ..........................................................................................285
6.1 Economic Dispatch of Generation without Transmission Line Losses ......................286
6.2 Economic Dispatch of Generation with Line Losses .....................................................290
6.3 On-Line Execution of the Economic Dispatch ................................................................295
6.4 Day-Ahead Economic Dispatch with a Variable Number of Units On-Line .............299
6.5 Power Transmission Line Losses for Economic Dispatch ............................................307
6.6 Utilizing the Load-Flow Jacobian for Economic Dispatch ...........................................314
6.7 Economic Exchange of Power between Areas ................................................................320
6.7.1 Economy A Program ...............................................................................................322
Problems .......................................................................................................................................326
References ....................................................................................................................................333
7 State Estimation from Real-Time Measurements .........................................................335
7.1 The Line Power Flow State Estimator ..............................................................................336
7.2 State Estimation and Noisy Measurements ....................................................................344
7.3 Monitoring the Power System ...........................................................................................354
7.4 Determination of Variance (cid:51)2 to Normalize Measurements .......................................357
Problems .......................................................................................................................................364
References ....................................................................................................................................367
Appendix A: Conductor Resistance and Rating ..................................................................369
Index ................................................................................................................................377
Preface
This textbook presents basic principles of power systems from the point of view of the cen-
tral control facility. Each chapter of the book has accompanying computer software that is
integrated with power system concepts and extends the student’s understanding beyond
hand calculations. The software is representative of computer programs used to control
and monitor large scale interconnections of power systems.
Chapter 1 discusses central digital computers used to process real time power system
data, present select data to an operator, and allow the operator to implement commands to
equipment in the field. All electric utilities, from the largest to the smallest rural electrifica-
tion cooperatives, have progressively increased the amount of instrumentation delivering
information to the central computer and the control authority of the central facility. The
central point of view emphasizes emergency power to/from interconnection neighbors
and the economic exchange of power. This chapter also demonstrates the droop property
of generation that allows power systems to operate without a central control facility.
Chapter 2 develops the analytical characteristics of the major equipment used in power
systems. These characteristics are transformed into the symmetrical component frame to
simplify system analysis. Software performs the transformation for unbalanced networks
and for transmission lines with specified dimensions and conductor type. This chapter,
except for symmetrical components and the per unit system, can be covered cursorily by a
reader with a prior course in power equipment.
Chapter 3 introduces computer-aided methods to construct and invert the important
bus impedance and bus admittance matrices. Software programs are used by the students
for networks consisting of more than several busses and lines. The matrices are used for
short circuit calculations and to describe networks for power flow. Sparse matrix tech-
niques are introduced since they are essential to programs used for huge interconnections
such as the eastern United States. Several matrix iterative methods are presented in the
chapter because they remain in use for special applications in large-scale power systems.
Chapter 4 is devoted to linearized network equations to calculate short circuit currents
for balanced and unbalanced faults, and contingency cases. Contingency cases are modi-

fications of network flow conditions due to line switching, generation changes, or load
demand changes. Several basic contingency methods which employ sparse matrix tech-
niques are presented.
Chapter 5 contains the Gauss-Seidel, Newton-Raphson, and Fast-Decoupled methods
to iteratively solve the non-linear equations that describe network power flow. Network
reactive compensation and adjustment of operating conditions are discussed. A software
program is provided that uses a Newton-Raphson method and has a common input data
format for other programs.
Chapter 6 calculates the minimum cost base power setting for generators on the net-
work. A unit commitment program shows economic dispatch over a time interval with
a constrained variable number of units on-line. The B coefficients used to approximate
transmission line power losses are derived by a network reduction program. Congestion
on networks is discussed. The Jacobian from a power flow program is used to adjust
generator power setting as modified by transmission line losses. Economic exchange of
power between areas is discussed.
Chapter 7 has state estimation to calculate the voltage and phase angle of all busses on
the system from real-time measurements on the system. Both the line flow and general
method for state estimation are presented. The chapter demonstrates selection of measure-
ments required to determine the state of the power system. Normalized residuals are used
to detect the most probable error among measurements. The accompanying state estimator
software program is flexible for the user to select bus injections, line flows, a “bad data”
threshold, and set the measurement data weighting factors. An accompanying program
allows the user to corrupt measurements with Gaussian white noise.
A fundamental concept in the book is that computer applications yield more insight
into system behavior than is possible from hand calculations on system elements. The
book develops methods which are used for full-scale networks, so that the student can
understand and expand computer control of systems. The problems at the end of each
chapter apply the methods and generally require the accompanying computer software to
calculate the solutions.
The format of the accompanying software is such that a student can save files of all
problems he runs, along with their own documentation. For example, a common network
file of bus interconnections, bus injections, and line flows can be used in five different
chapters of the book, with minor modifications for particular cases.
All textbook software is in the form of self-contained executable programs which are
independent of the computer operating system. Input data file formats and names are
carefully defined. All programs run with or without the Powerpoint presentation. The
only program dependent upon other software is the use of MATLAB to compute dynamic
response for several problems in Chapter 1. These Chapter 1 problems can be run on any
dynamic simulation software.
The author has selected the material in this textbook based upon interaction with util-
ity and industrial colleagues, teaching power systems for a number of years, and many
publications in the power field. The references at the end of each chapter are often the
first of publications on the subject and serve as an introduction to extensive literature in
the power field. There are many contributors to our present state of technology in power
systems.
The author expresses my appreciation to my wife, Alexandra, and the University of
Pittsburgh Department of Electrical and Computer Engineering that encouraged me to
write this book.