123,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press Series on Power Engineering
- Sprache: Englisch
Optimization of Power System Operation, 2nd Edition, offers a practical, hands-on guide to theoretical developments and to the application of advanced optimization methods to realistic electric power engineering problems. The book includes: * New chapter on Application of Renewable Energy, and a new chapter on Operation of Smart Grid * New topics include wheeling model, multi-area wheeling, and the total transfer capability computation in multiple areas * Continues to provide engineers and academics with a complete picture of the optimization of techniques used in modern power system operation
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 864
Veröffentlichungsjahr: 2016
Ähnliche
Table of Contents
Cover
IEEE Press
Title Page
Copyright
Dedication
PREFACE
PREFACE TO THE FIRST EDITION
ACKNOWLEDGMENTS
AUTHOR BIOGRAPHY
CHAPTER 1: INTRODUCTION
1.1 POWER SYSTEM BASICS
1.2 CONVENTIONAL METHODS
1.3 INTELLIGENT SEARCH METHODS
1.4 APPLICATION OF THE FUZZY SET THEORY
REFERENCES
CHAPTER 2: POWER FLOW ANALYSIS
2.1 MATHEMATICAL MODEL OF POWER FLOW
2.2 NEWTON-RAPHSON METHOD
2.3 GAUSS-SEIDEL METHOD
2.4 P-Q DECOUPLING METHOD
2.5 DC POWER FLOW
2.6 STATE ESTIMATION
REFERENCES
CHAPTER 3: SENSITIVITY CALCULATION
3.1 INTRODUCTION
3.2 LOSS SENSITIVITY CALCULATION
3.3 CALCULATION OF CONSTRAINED SHIFT SENSITIVITY FACTORS
3.4 PERTURBATION METHOD FOR SENSITIVITY ANALYSIS
3.5 VOLTAGE SENSITIVITY ANALYSIS
3.6 REAL-TIME APPLICATION OF THE SENSITIVITY FACTORS
3.7 SIMULATION RESULTS
3.8 CONCLUSION
REFERENCES
CHAPTER 4: CLASSIC ECONOMIC DISPATCH
4.1 INTRODUCTION
4.2 INPUT–OUTPUT CHARACTERISTICS OF GENERATOR UNITS
4.3 THERMAL SYSTEM ECONOMIC DISPATCH NEGLECTING NETWORK LOSSES
4.4 CALCULATION OF INCREMENTAL POWER LOSSES
4.5 THERMAL SYSTEM ECONOMIC DISPATCH WITH NETWORK LOSSES
4.6 HYDROTHERMAL SYSTEM ECONOMIC DISPATCH
4.7 ECONOMIC DISPATCH BY GRADIENT METHOD
4.8 CLASSIC ECONOMIC DISPATCH BY GENETIC ALGORITHM
4.9 CLASSIC ECONOMIC DISPATCH BY HOPFIELD NEURAL NETWORK
APPENDIX A: OPTIMIZATION METHODS USED IN ECONOMIC OPERATION
REFERENCES
CHAPTER 5: SECURITY-CONSTRAINED ECONOMIC DISPATCH
5.1 INTRODUCTION
5.2 LINEAR PROGRAMMING METHOD
5.3 QUADRATIC PROGRAMMING METHOD
5.4 NETWORK FLOW PROGRAMMING METHOD
5.5 NONLINEAR CONVEX NETWORK FLOW PROGRAMMING METHOD
5.6 TWO-STAGE ECONOMIC DISPATCH APPROACH
5.7 SECURITY CONSTRAINED ECONOMIC DISPATCH BY GENETIC ALGORITHMS
APPENDIX A: NETWORK FLOW PROGRAMMING
REFERENCES
CHAPTER 6: MULTIAREAS SYSTEM ECONOMIC DISPATCH
6.1 INTRODUCTION
6.2 ECONOMY OF MULTIAREAS INTERCONNECTION
6.3 WHEELING
6.4 MULTIAREA WHEELING
6.5 MAED SOLVED BY NONLINEAR CONVEX NETWORK FLOW PROGRAMMING
6.6 NONLINEAR OPTIMIZATION NEURAL NETWORK APPROACH
6.7 TOTAL TRANSFER CAPABILITY COMPUTATION IN MULTIAREAS
APPENDIX A: COMPARISON OF TWO OPTIMIZATION NEURAL NETWORK MODELS
REFERENCES
CHAPTER 7: UNIT COMMITMENT
7.1 INTRODUCTION
7.2 PRIORITY METHOD
7.3 DYNAMIC PROGRAMMING METHOD
7.4 LAGRANGE RELAXATION METHOD
7.5 EVOLUTIONARY PROGRAMMING-BASED TABU SEARCH METHOD
7.6 PARTICLE SWARM OPTIMIZATION FOR UNIT COMMITMENT
7.7 ANALYTIC HIERARCHY PROCESS
REFERENCES
CHAPTER 8: OPTIMAL POWER FLOW
8.1 INTRODUCTION
8.2 NEWTON METHOD
8.3 GRADIENT METHOD
8.4 LINEAR PROGRAMMING OPF
8.5 MODIFIED INTERIOR POINT OPF
8.6 OPF WITH PHASE SHIFTER
8.7 MULTIPLE OBJECTIVES OPF
8.8 PARTICLE SWARM OPTIMIZATION FOR OPF
REFERENCES
CHAPTER 9: STEADY-STATE SECURITY REGIONS
9.1 INTRODUCTION
9.2 SECURITY CORRIDORS
9.3 TRADITIONAL EXPANSION METHOD
9.4 ENHANCED EXPANSION METHOD
9.5 FUZZY SET AND LINEAR PROGRAMMING
APPENDIX A: LINEAR PROGRAMMING
REFERENCES
CHAPTER 10: APPLICATION OF RENEWABLE ENERGY
10.1 INTRODUCTION
10.2 RENEWABLE ENERGY RESOURCES
10.3 OPERATION OF GRID-CONNECTED PV SYSTEM
10.4 VOLTAGE CALCULATION OF DISTRIBUTION NETWORK
10.5 FREQUENCY IMPACT OF PV PLANT IN DISTRIBUTION NETWORK
10.6 OPERATION OF WIND ENERGY [1, 10–16]
10.7 VOLTAGE ANALYSIS IN POWER SYSTEM WITH WIND ENERGY
REFERENCES
CHAPTER 11: OPTIMAL LOAD SHEDDING
11.1 INTRODUCTION
11.2 CONVENTIONAL LOAD SHEDDING
11.3 INTELLIGENT LOAD SHEDDING
11.4 FORMULATION OF OPTIMAL LOAD SHEDDING
11.5 OPTIMAL LOAD SHEDDING WITH NETWORK CONSTRAINTS
11.6 OPTIMAL LOAD SHEDDING WITHOUT NETWORK CONSTRAINTS
11.7 DISTRIBUTED INTERRUPTIBLE LOAD SHEDDING (DILS)
11.8 UNDERVOLTAGE LOAD SHEDDING
11.9 CONGESTION MANAGEMENT
REFERENCES
CHAPTER 12: OPTIMAL RECONFIGURATION OF ELECTRICAL DISTRIBUTION NETWORK
12.1 INTRODUCTION
12.2 MATHEMATICAL MODEL OF DNRC
12.3 HEURISTIC METHODS
12.4 RULE-BASED COMPREHENSIVE APPROACH
12.5 MIXED-INTEGER LINEAR-PROGRAMMING APPROACH
12.6 APPLICATION OF GA TO DNRC
12.7 MULTIOBJECTIVE EVOLUTION PROGRAMMING TO DNRC
12.8 GENETIC ALGORITHM BASED ON MATROID THEORY
APPENDIX A: EVOLUTIONARY ALGORITHM OF MULTIOBJECTIVE OPTIMIZATION
REFERENCES
CHAPTER 13: UNCERTAINTY ANALYSIS IN POWER SYSTEMS
13.1 INTRODUCTION
13.2 DEFINITION OF UNCERTAINTY
13.3 UNCERTAINTY LOAD ANALYSIS
13.4 UNCERTAINTY POWER FLOW ANALYSIS
13.5 ECONOMIC DISPATCH WITH UNCERTAINTIES
13.6 HYDROTHERMAL SYSTEM OPERATION WITH UNCERTAINTY
13.7 UNIT COMMITMENT WITH UNCERTAINTIES
13.8 VAR OPTIMIZATION WITH UNCERTAIN REACTIVE LOAD
13.9 PROBABILISTIC OPTIMAL POWER FLOW
13.10 COMPARISON OF DETERMINISTIC AND PROBABILISTIC METHODS
REFERENCES
CHAPTER 14: OPERATION OF SMART GRID
14.1 INTRODUCTION
14.2 DEFINITION OF SMART GRID
14.3 SMART GRID TECHNOLOGIES
14.4 SMART GRID OPERATION
14.5 TWO-STAGE APPROACH FOR SMART GRID DISPATCH
14.6 OPERATION OF VIRTUAL POWER PLANTS
14.7 SMART DISTRIBUTION GRID
14.8 MICROGRID OPERATION
14.9 A NEW PHASE ANGLE MEASUREMENT ALGORITHM
REFERENCES
Index
Series Page
End User License Agreement
Pages
xvii
xviii
xix
xx
xxi
xxiii
1
2
3
4
5
6
7
8
9
10
11
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
529
530
531
537
532
533
534
535
536
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
574
573
575
576
577
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
629
630
631
631
633
Guide
Cover
Table of Contents
Preface
Begin Reading
OPTIMIZATION OF POWER SYSTEM OPERATION
Second Edition
JIZHONG ZHU
Copyright © 2015 by The Institute of Electrical and Electronics Engineers, Inc.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.
Library of Congress Cataloging-in-Publication Data is available.
Zhu, Jizhong, 1961
Optimization of power system operation / Jizhong Zhu. Second edition.
pages cm (IEEE Press series on power engineering)
Summary: “Addresses advanced methods and optimization technologies and their applications in power systems”-- Provided by publisher.
ISBN: 978-1-118-85415-0(hardback)
1. Electric power systems--Mathematical models. 2. Mathematical optimization. I. Title.
TK1005.Z46 2015
621.3101′5196-dc23
To My Wife and Son
PREFACE
It has been five years since the first edition was published. Some developments have taken place in the power industry. The renewable energy and smart grid include many fresh and vital technologies that are needed to make enormous progress in power grid development. With the development of information technology and computer-based remote control and automation, the systems and technologies for the smart grid are made possible by two-way communication technology and computer processing. This modernized electricity network, which sends electricity from power suppliers to consumers using digital technology to save energy, reduce cost, and increase reliability and transparency, is being promoted by many governments as a way of addressing energy independence, global warming, environment protection, and emergency resilience issues.
In this new edition, Optimization of Power System Operation, continues to provide engineers and academics with a complete picture of the optimization techniques used in modern power system operation. It offers a practical, hands-on guide to theoretical developments and to the application of advanced optimization methods to realistic electric power engineering problems. Although the topic areas and depth of coverage remain about the same, the book has been updated to reflect the changes that have taken place in the electric power industry since the First Edition was published five years ago. The research and application of renewable energy and smart grid have being widely addressed in recent years, which have brought a host of new opportunities and challenges to modern power system operation. Thus, in this edition two new Chapters have been added—Chapter 10 on “Application of renewable energy” and Chapter 14 on “Operation of smart grid.” The original Chapter 10 on “Reactive power optimization” in the first edition is removed because of limitation of the space. But some contents related to reactive power optimization can still be found in Chapter 8 on “Optimal power flow” and Chapter 13 on “Uncertainty analysis in power systems”. In the new Chapter 10, in addition to the introduction of renewable energy resources and the corresponding mathematical models, the optimization operation of renewable energy in power systems, such as maximum power point tracking, voltage calculation for the grid-connected PV system, and voltage analysis in power system with wind energy, is focused. In the new Chapter 14, applications of optimization techniques to smart grid are addressed and the following topics are included: smart grid economic dispatch, two-stage-approach for optimal operation of a smart grid, optimal operation of virtual power plant, smart distribution operation, microgrid operation with wind and PV resources, optimal power flow for smart microgrid, renewable energy and distributed generation technologies, and a new phase angle measurement algorithm.
The author appreciated the suggestions and feedback offered by professors and engineers who have used the first edition. Some professors commented that this book comprehensively applies all kinds of optimization methods to solve power system operation problems, but it needs to provide some problems or exercises at the end of each chapter so that it can be used as a textbook. Some students remarked that they like the examples in the book, and they even have tried to use different methods or written some programs to resolve them. Some readers did an excellent job to find some errors and typos. I have gone through the book and made necessary corrections. Over ten exercises and problems at the end of each chapter have been included in the second edition.
I wish to express my gratitude to IEEE book series editor, Wiley Acquisitions Editor, Project Editor, and the reviewers of the book for their valuable comments and suggestions.
Jizhong Zhu
PREFACE TO THE FIRST EDITION
I have been undertaking the research and practical applications of power system optimization since the early 1980s. In the early stage of my career, I worked in universities such as Chongqing University (China), Brunel University (UK), National University of Singapore, and Howard University (USA). Since 2000 I have been working for ALSTOM Grid Inc. (USA). When I was a full-time professor at Chongqing University, I wrote a tutorial on power system optimal operation, which I used to teach my senior undergraduate students and postgraduate students in power engineering until 1996. The topics of the tutorial included advanced mathematical and operations research methods and their practical applications in power engineering problems. Some of these were refined to become part of this book.
This book comprehensively applies all kinds of optimization methods to solve power system operation problems. Some contents are analyzed and discussed for the first time in detail in one book, although they have appeared in international journals and conferences. These can be found in Chapter 9 “Steady-State Security Regions”, Chapter 11 “Optimal Load Shedding”, Chapter 12 “Optimal Reconfiguration of Electric Distribution Network”, and Chapter 13 “Uncertainty Analysis in Power Systems.”
This book covers not only traditional methods and implementation in power system operation such as Lagrange multipliers, equal incremental principle, linear programming, network flow programming, quadratic programming, nonlinear programming, and dynamic programming to solve the economic dispatch, unit commitment, reactive power optimization, load shedding, steady-state security region, and optimal power flow problems, but also new technologies and their implementation in power system operation in the last decade. The new technologies include improved interior point method, analytic hierarchical process, neural network, fuzzy set theory, genetic algorithm, evolutionary programming, and particle swarm optimization. Some new topics (wheeling model, multiarea wheeling, the total transfer capability computation in multiareas, reactive power pricing calculation, congestion management) addressed in recent years in power system operation are also dealt with and put in appropriate chapters.
In addition to the rich analysis and implementation of all kinds of approaches, this book contains considerable hands-on experience for solving power system operation problems. I personally wrote my own code and tested the presented algorithms and power system applications. Many materials presented in the book are derived from my research accomplishments and publications when I worked at Chongqing University, Brunel University, National University of Singapore, and Howard University, as well as currently with ALSTOM Grid Inc. I appreciate these organizations for providing me such good working environments. Some IEEE papers have been used as primary sources and are cited wherever appropriate. The related publications for each topic are also listed as references, so that those interested may easily obtain overall information.
I wish to express my gratitude to IEEE book series editor Professor Mohammed El-Hawary of Dalhousie University, Canada, Acquisitions Editor Steve Welch, Project Editor Jeanne Audino, and the reviewers of the book for their keen interest in the development of this book, especially Professor Kit Po Wong of the Hong Kong Polytechnic University, Professor Loi Lei Lai of City University, United Kingdom, Professor Ruben Romero of Universidad Estadual Paulista, Brazil, and Dr. Ali Chowdhury of California Independent System Operator, who offered valuable comments and suggestions for the book during the preparation stage.
Finally, I wish to thank Professor Guoyu Xu, who was my PhD advisor twenty years ago at Chongqing University, for his high standards and strict requirements for me ever since I was his graduate student. Thanks to everyone, including my family, who has shown support during the time–consuming process of writing this book.
Jizhong Zhu
ACKNOWLEDGMENTS
I would like to express my appreciation to the IEEE Press Power Engineering book series editor, Professor Mohamed El-Hawary of Dalhousie University, Canada, Wiley-IEEE Press Acquisitions Editor Mary Hatcher, and the technical reviewers of the book for their keen interest and valuable comments in the development of this new edition. I would also like to thank all editors and technical reviewers of the first edition of the book for their constructive suggestions and encouragement during the preparation stage of the book.
I would also like to extend my thanks to Professor Guoyu Xu of Chongqing University, who was my PhD advisor 25 years ago, for his patient guidance, enthusiastic encouragement, and useful critiques of my research work related to the book.
Finally, I wish to thank my family for their support and encouragement throughout the process of writing this book.
AUTHOR BIOGRAPHY
Jizhong Zhuis currently working at ALSTOM Grid Inc. as a senior principal power systems engineer, as well as a Fellow of the ALSTOM Expert Committee. He received his Ph.D. degree from Chongqing University, P.R. China, in February 1990. Dr. Zhu was a full professor in Chongqing University. He won the “Science and Technology Progress Award of State Education Committee of China” in 1992 and 1995, respectively, “Sichuan Provincial Science and Technology Advancement Award” in 1992, 1993, and 1994, respectively, as well as the “Science and Technology Invention Prize of Sichuan Province Science and Technology Association” in 1992. In recognition of Dr. Zhu's work, the Chongqing City Government conferred on him the award of Excellent Young Teacher by in 1992. He was selected as an Outstanding Science and Technology Researcher and won the annual Science and Technology Medal of Sichuan Province in 1993. He was also selected as one of four outstanding young scientists working in China by The Royal Society of UK and China Science and Technology Association and awarded the Royal Society Fellowship in 1994 and the national research prize “Fok Ying-Tong Young Teacher Research Medal” in 1996. He has worked in a number of different institutions all over the world, including Chongqing University in China, Brunel University in the United Kingdom, the National University of Singapore, and the Howard University in the United States, and has been with ALSTOM Grid Inc. (since 2000). He is also an advisory professor at Chongqing University. His research interest is in the analysis, operation, planning, and control of power systems as well as application of renewable energy. He has published six books as an author and co-author, and has published over 200 papers in international journals and conferences.
CHAPTER 1INTRODUCTION
The electric power industry is being relentlessly pressured by governments, politicians, large industries, and investors to privatize, restructure, and deregulate. Before deregulation, most elements of the power industry, such as power generation, bulk power sales, capital expenditures, and investment decision, were heavily regulated. Some of these regulations were at the state level, and some at the national level. Thus new deregulation in the power industry meant new challenges and huge changes. However, despite changes in different structures, market rules, and uncertainties, the underlying requirements for power system operations to be secure, economical, and reliable remain the same.
This book attempts to cover all areas in power system operations. It also introduces some new topics and new applications of the latest new technologies that have appeared in recent years. This includes the analysis and discussion of new techniques for solving old problems as well as the new ones arising as a result of deregulation.
According to the different characteristics and types of the problems as well as their complexity, power system operation is divided into the following aspects that are addressed in this new edition of the book:
Power flow analysis (Chapter 2)
Sensitivity calculation (Chapter 3)
Classical economic dispatch (Chapter 4)
Security-constrained economic dispatch (Chapter 5)
Multiarea systems economic dispatch (Chapter 6)
Unit commitment (Chapter 7)
Optimal power flow (Chapter 8)
Steady-state security regions (Chapter 9)
Application of renewable energy (Chapter 10)
Optimal load shedding (Chapter 11)
Optimal reconfiguration of electric distribution networks (Chapter 12)
Uncertainty analysis in power systems (Chapter 13)
Operation of smart grids (Chapter 14)
From the viewpoint of optimization, various techniques including traditional and modern optimization methods, which have been developed to solve these power system operation problems, are classified into three groups [1–13]:
Conventional optimization methods including
Unconstrained optimization approaches
Nonlinear programming (NLP)
Linear programming (LP)
Quadratic programming (QP)
Generalized reduced gradient method
Newton method
Network flow programming (NFP)
Mixed integer programming (MIP)
Interior point (IP) methods.
Intelligence search methods such as
Neural network (NN)
Evolutionary algorithms (EAs)
Tabu search (TS)
Particle swarm optimization (PSO).
Nonquantitative approaches to address uncertainties in objectives and constraints including
Probabilistic optimization
Fuzzy set applications
Analytic hierarchical processes (AHPs).
Power systems basics are introduced first in the following sections, followed by brief descriptions of various optimization techniques that are used to solve power system operation problems.
1.1 POWER SYSTEM BASICS
1.1.1 Physical Components
A power system can be broadly divided into the generation system that supplies the power, the transmission network that carries the power from the generating centers to the load centers, and the distribution system that feeds the power to nearby homes and industries. Figure 1.1 is a simple power system that shows some basic components.
Figure 1.1 A simple power system.
Generating Unit
All power systems have one or more generating units, which are sources of power. Direct current (DC) power can be supplied by batteries, fuel cells, or photovoltaic cells. Alternating current (AC) power is typically supplied by a rotor that spins in a magnetic field in a device known as a turbo generator in a power station. There have been a wide range of techniques used to spin a turbine's rotor, from superheated steam heated using fossil fuel (including coal, gas, and oil) to water itself (hydroelectric power), and wind (wind power). Even nuclear power typically depends on water heated to steam using a nuclear reaction.
The speed at which the rotor spins in combination with the number of generator poles determines the frequency of the AC produced by the generator. All generators on a single system rotate synchronously (i.e., at an identical speed) and will target a set frequency—in China and European countries, this is 50 Hz, and in the United States, 60 Hz. If the load on the system increases, the generators will require more torque to spin at that speed and, in a typical power station, more steam must be supplied to the turbines driving them. Thus the steam used and the fuel expended are directly dependent on the quantity of electrical energy supplied.
Transformer
A transformer is a pair of mutually inductive coils used to convey AC power from one coil to the other. It is a static device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field through the secondary winding. This varying magnetic field induces a varying electromotive force (EMF) or “voltage” in the secondary winding. This effect is called mutual induction.
Transformers provide an efficient means of changing voltage and current levels, and make the bulk power transmission system practical. The transformer primary is the winding that accepts power, and the transformer secondary is the winding that delivers power. In an ideal transformer, the induced voltage in the secondary winding is proportional to the primary voltage , and is given by the ratio of the number of turns in the secondary to the number of turns in the primary as follows:
Transmission Line or Conductor
Transmission lines are used to transfer power/energy from sources to loads such as an overhead power line, which is an electric power transmission line suspended by towers or utility poles. Since most of the insulation is provided by air, overhead power lines are generally the lowest-cost method of transmission of large quantities of electrical energy. Towers for support of the lines are made of wood (as-grown or laminated), steel (either lattice structures or tubular poles), concrete, aluminum, and, occasionally, reinforced plastics. The bare wire conductors on the line are generally made of aluminum (either plain or reinforced with steel or sometimes composite materials), although some copper wires are used in medium-voltage distribution and low-voltage connections to customer premises.
An object of uniform cross section has a resistance proportional to its resistivity and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for superconductors, which have a resistance of zero. The resistance of an object is defined as the ratio of voltage across it to current through it:
For a wide variety of materials and conditions, the electrical resistance is constant for a given temperature; it does not depend on the amount of current through or the potential difference (voltage) across the object. Such materials are called ohmic materials. For objects made of ohmic materials, the definition of the resistance, with being a constant for that resistor, is known as Ohm's law.
Load
Loads are also called energy consumptions, which use the electrical energy to perform a function. These loads range from household appliances to industrial machinery. Loads are supplied by the energy sources such as generating units through the transmission system (or the grid). The change in the power system load over time—that is, the change in the power consumed or the current in the network as a function of time—is called the load curve. Loads determined by the rated power of the users are random quantities that may assume various values with a certain probability.
The real power of an individual load, a load group, or the entire system is defined as
where is the apparent power ( is the voltage, and is the current), is the power factor, and , where is the reactive power of the load.
Capacitor
A capacitor (formerly known as condenser) is a device for storing electrical charge. The forms of practical capacitors vary widely, but all of them contain at least two conductors separated by a non-conductor. Capacitors used as parts of electrical systems, for example, consist of metal foils separated by a layer of insulating film.
The current associated with capacitors leads the voltage because of the time it takes for the dielectric material to charge up to full voltage from the charging current. Therefore, it is said that the current in a capacitor leads the voltage. The units (measurement) of capacitance are called farads.
Fundamental Properties of Circuits
Electric power is a measurable quantity that is the time rate of increase or decrease in energy. Power is also the mathematical product of two quantities: current and voltage. These two quantities can vary with respect to time (alternating current, AC power) or can be kept at constant levels (direct current, DC power).
An instantaneous power supplied, or consumed by a component of a circuit can be expressed as follows.
It means that the power supplied at any instant by a source, or consumed by a load, is given by the current through the component times the voltage across the component. When current is given in amperes, and voltage in volts, the units of power are watts (W).
There are two fundamental properties of circuits, one is about the current, which is Kirchhoff's first law, and another is about voltage, which is Kirchhoff's second law. The former is also called as Kirchhoff's current law (abbreviated KCL). The latter is also called as Kirchhoff's voltage law (abbreviated KVL). KCL states that, at every instant of time, the sum of the currents flowing into any node of a circuit must equal the sum of the currents leaving the node, where a node is any spot where two or more conductors/wires are joined. KCL can be written as below.
where is a node of a circuit and is a collection of conductor branches. The symbol “” means the branch connects to the node . The direction of the current is defined as positive if the current flows into the node; it is negative if the current leaves the node.
The second of Kirchhoff's fundamental laws, that is KVL, states that the sum of the voltages around any loop of a circuit at any instant is zero.
KVL can be written as below.
where is a closed circuit (or loop), and is one of branches in the loop . The symbol “” means the branch belongs to loop .
1.1.2 Renewable Energy Resources
Traditionally, power plants in the power system produce electricity by use of conventional energy sources, which consist primarily of coal, natural gas, and oil. Once a deposit of these fuels is depleted, it cannot be replenished. Thus, renewable energy is now receiving considerable attention. Renewable energy is energy that comes from natural resources such as sunlight, wind, rain, tides, and geothermal heat, which are renewable. Renewable energy sources differ from conventional sources in that, generally, they cannot be scheduled, and they are often connected to the electricity distribution system rather than the transmission system.
Most renewable energy sources originate either directly or indirectly from the sun. They are continually replenished, literally, as long as the sun continues to shine. The following five renewable sources are used most often:
Solar
Wind
Water (hydropower)
Biomass—including wood and wood waste, municipal solid waste, landfill gas, and biogas, ethanol, and biodiesel
Geothermal.
1.1.3 Smart Grid
A smart grid, also called smart electrical/power grid, intelligent grid, future grid, inter-grid, or intra-grid, is an enhancement of the twentieth century power grid. Traditional power grids are generally used to carry power from a few central generators to a large number of users or customers. In contrast, the smart grid is a modernized electrical grid that uses information and two-way, cyber-secure communications technology to gather and act on information, such as information about the behaviors of suppliers and consumers, in an automated fashion to improve the efficiency, reliability, economics, and sustainability of the production and distribution of electricity. As a globally emerging industry, smart grids include many fresh and vital technologies that are needed to make enormous progress in power grid development. With the development of information technology and computer-based remote control and automation, the systems and technologies for the smart grid are made possible by two-way communication technology and computer processing that has been used for decades in other industries. They are beginning to be used on electricity networks, from the power plants and wind farms all the way to the consumers of electricity in homes and businesses. They offer many benefits to utilities and consumers—mostly seen in big improvements in energy efficiency on the electricity grid and in the energy users' homes and offices. This modernized electricity network, which sends electricity from power suppliers to consumers using digital technology to save energy, reduce cost, and increase reliability and transparency is being promoted by many governments as a way of addressing energy independence, global warming, and emergency resilience issues.
1.2 CONVENTIONAL METHODS
1.2.1 Unconstrained Optimization Approaches
Unconstrained optimization approaches are the basis of the constrained optimization algorithms. In particular, most of the constrained optimization problems in power system operation can be converted into unconstrained optimization problems. The major unconstrained optimization approaches that are used in power system operation are the gradient method, line search, Lagrange multiplier method, Newton-Raphson optimization, trust-region optimization, quasi-Newton method, double dogleg optimization, conjugate gradient optimization, and so on. Some of these approaches are used in Chapters 2–4, 7, 9, and 14.
1.2.2 Linear Programming
Linear programming (LP)-based techniques are used to linearize nonlinear power system optimization problems so that objective functions and constraints of power system optimization problems have linear forms. The simplex method is known to be quite effective for solving LP problems. The LP approach has several advantages. Firstly, it is reliable, especially in regard to the convergence properties. Secondly, it can quickly identify infeasibility. Thirdly, it accommodates a large variety of power system operating limits, including the very important contingency constraints. The disadvantages of LP-based techniques are inaccurate evaluation of system losses and insufficient ability to find an exact solution compared with an accurate nonlinear power system model. However, a large number of practical applications have shown that LP-based solutions generally meet the requirements of engineering precision. Thus LP is widely used to solve power system operation problems such as security-constrained economic dispatch, optimal power flow, steady-state security regions, and so on.
1.2.3 Nonlinear Programming
Power system operation problems are nonlinear. Thus nonlinear programming (NLP)-based techniques can easily handle power system operation problems such as the optimal power flow (OPF) problem with nonlinear objective and constraint functions. To solve a NLP problem, the first step in this method is to choose a search direction in the iterative procedure, which is determined by the first partial derivatives of the equations (the reduced gradient). Therefore, these methods are referred to as first-order methods, an example being the generalized reduced gradient (GRG) method. NLP-based methods have higher accuracy than LP-based approaches, and also have global convergence, which means convergence can be guaranteed independent of the starting point, but a slow convergent rate may occur because of zigzagging in the search direction. NLP methods are used in this book in Chapters 5–10, as well as in Chapter 14.
1.2.4 Quadratic Programming
Quadratic programming (QP) is a special form of NLP. The objective function of the QP optimization model is quadratic, and the constraints are in linear form. QP has higher accuracy than LP-based approaches. The most-used objective function in power system optimization is the generator cost function, which generally is a quadratic. Thus there is no simplification for such an objective function for power system optimization problem solved by QP. QP is used in Chapters 5 and 8.
1.2.5 Newton's Method
Newton's method requires the computation of the second-order partial derivatives of the power-flow equations and other constraints (the Hessian) and is therefore called a second-order method. The necessary conditions of optimality commonly are the Kuhn-Tucker conditions. Newton's method, which is used in Chapters 2, 4, and 8, is favored for its quadratic convergence properties.
1.2.6 Interior Point Methods
The interior point (IP) method was originally used to solve LP problems. It is faster and is perhaps better than the conventional simplex algorithm in LP. IP methods were first applied in 1990s to solve OPF problems, and the method has been extended and improved recently to solve OPF problems in QP and NLP forms. The analysis and implementation of IP methods are discussed in Chapter 8.
1.2.7 Mixed-Integer Programming
The power system problem can also be formulated as a mixed-integer programming (MIP) optimization problem with integer variables such as transformer tap ratio, phase shifter angle, and unit on or off status. MIP is extremely demanding of computer resources and the number of discrete variables is an important indicator of how difficult an MIP will be to solve. MIP methods that are used to solve OPF problems are the recursive MIP technique using an approximation method and the branch-and-bound (B&B) method, which is a typical method for integer programming. A decomposition technique is generally adopted to decompose the MIP problem into a continuous problem and an integer problem. Decomposition methods such as Benders decomposition method (BDM) can greatly improve the efficiency in solving a large-scale network by reducing the dimensions of the individual subproblems. The results show a significant reduction in the number of iterations, required computation time, and memory space. In addition, decomposition allows the application of a separate method for the solution of each subproblem, which makes the approach very attractive. MIP can be used to solve the unit commitment, OPF, as well as optimal reconfiguration of the electric distribution network.
1.2.8 Network Flow Programming
Network flow programming (NFP) is a special form of LP. NFP was first applied to solve optimization problems in power systems in the 1980s. The early applications of NFP were mainly on a linear model. Recently, nonlinear convex NFP has been used in power system optimization problems. NFP-based algorithms have the features of fast speed and simple calculation. These methods are efficient for solving simplified OPF problems such as security-constrained economic dispatch, multiarea systems economic dispatch, and optimal reconfiguration of an electric distribution network.
