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Summary
Summary
Overloaded, under-maintained electrical power grids are a growing problem not only in the U.S. but around the world
Load flow analysis allows electrical engineers to optimise the flow of electricity across the grid, preventing blackouts and accurately mapping future needs.
This book teaches the tricky, mathematical art of load flow analysis to the scores of EEs looking to move into this growing market.
Author Notes
Lynn Powell is an electrical engineer who is now retired after spending 40 years with various U.K. organizations: the South Wales Electricity Board, the Central Electricity Generating Board, the British Steel Corporation, and the Ministry of Defense. For virtually all that time he was engaged in power system design, for land-based and ship-based systems. He holds a master's degree in power systems engineering from the University of Manchester Institute of Science and Technology and is a Fellow of the Institution of Electrical Engineers. A Welshman by birth, he lives in Wiltshire, England.
Table of Contents
Preface | p. xi |
Introduction | p. xiii |
Chapter 1 System Representation | p. 1 |
1.1 Introduction | p. 3 |
1.2 The Per-Unit System | p. 4 |
1.3 Per-Unit Transformer Representation | p. 6 |
1.4 Per-Unit Power System Representation | p. 8 |
Chapter 2 The Load-Flow Problem | p. 13 |
2.1 Physical Statement of the Problem | p. 15 |
2.2 Mathematical Statement of the Problem | p. 16 |
2.3 Representation of System Elements | p. 19 |
2.3.1 Lines and cables | p. 19 |
2.3.2 Generators | p. 20 |
2.3.3 Transformers | p. 20 |
2.3.4 Loads | p. 20 |
2.3.5 Shunt elements | p. 20 |
Chapter 3 Reference System | p. 21 |
3.1 Introduction | p. 23 |
3.2 System Configuration | p. 23 |
3.3 Formulation of System Admittance Matrix | p. 23 |
Chapter 4 Jacobi Method | p. 29 |
4.1 Introduction | p. 29 |
4.2 Development of the Algorithm | p. 29 |
4.3 Jacobi Method Solution for Reference System | p. 32 |
Chapter 5 Gauss-Seidel Method | p. 37 |
5.1 Introduction | p. 39 |
5.2 Development of the Algorithm | p. 39 |
5.3 Gauss-Seidel Solution for Reference System | p. 41 |
5.4 Acceleration | p. 43 |
Chapter 6 Z-Matrix Methods | p. 47 |
6.1 Introduction | p. 49 |
6.2 Development of the Method | p. 49 |
6.3 Z-Matrix Method: Algorithm for Block Substitution | p. 51 |
6.4 Z-Matrix (Block Substitution) Solution for Reference System | p. 53 |
6.5 Z-Matrix Method: Algorithm for Forward Substitution | p. 56 |
6.6 Z-Matrix (Forward Substitution) Solution for Reference System | p. 56 |
Chapter 7 Newton-Raphson Methods | p. 63 |
7.1 Solution of Equation y = f(x) | p. 65 |
7.2 Solution of Multivariable Nonlinear Equations | p. 66 |
7.3 Newton-Raphson and the Load-Flow Problem | p. 68 |
Chapter 8 Newton-Raphson Method Using Cartesian Coordinates | p. 71 |
8.1 Development of the Algorithm | p. 73 |
8.2 Newton-Raphson (Cartesian Coordinates) Solution for Reference System | p. 76 |
Chapter 9 Newton-Raphson Method Using Polar Coordinates | p. 83 |
9.1 Development of the Algorithm | p. 85 |
9.2 Newton-Raphson (Polar Coordinates) Solution for Reference System | p. 92 |
Chapter 10 Fast Decoupled Method | p. 97 |
10.1 Introduction | p. 99 |
10.2 Decoupled Newton-Raphson Method | p. 101 |
10.3 Development of the Fast Decoupled Method | p. 101 |
10.4 Development of the Algorithm | p. 104 |
10.5 Fast Decoupled Solution for Reference System | p. 104 |
Chapter 11 DC Load Flow | p. 111 |
11.1 Introduction | p. 113 |
11.2 Development of the Method | p. 114 |
11.3 Development of the Algorithm | p. 116 |
11.4 DC Load-Flow Solution for Reference System | p. 116 |
Chapter 12 Voltage Control (1): Generators | p. 119 |
12.1 Introduction | p. 121 |
12.2 Performance of a Synchronous Machine | p. 121 |
12.3 Generator Representation in the Load-Flow Problem | p. 125 |
12.4 Solution for Reference System Including a Generator Busbar | p. 127 |
Chapter 13 Voltage Control (2): On-Load Tap-Changing (OLTC) Transformers | p. 133 |
13.1 Introduction | p. 135 |
13.2 Development of Transformer Equivalent Circuit for Tap Changing | p. 136 |
13.3 Transformer Tap Changing: Illustrative Example | p. 139 |
13.4 Changes in Admittance Matrix Resulting from Tap Changing | p. 140 |
13.5 Tap Changing within the Load-Flow Process | p. 143 |
13.6 Reference System Including OLTC Transformers | p. 145 |
13.7 Gauss-Seidel Solution for Modified Reference System | p. 147 |
Chapter 14 Results Output | p. 151 |
14.1 Introduction | p. 153 |
14.2 Original Reference System | p. 153 |
14.2.1 Busbar conditions | p. 153 |
14.2.2 Line flows | p. 155 |
14.3 Reference System Including Generator | p. 157 |
14.3.1 Busbar conditions | p. 158 |
14.3.2 Line flows | p. 158 |
14.4 Reference System Including OLTC Transformers | p. 159 |
14.4.1 Busbar conditions | p. 159 |
14.4.2 Line flows | p. 159 |
Chapter 15 Solution Difficulties | p. 161 |
15.1 Introduction | p. 163 |
15.2 Common Considerations | p. 163 |
15.2.1 Conditioning | p. 163 |
15.2.2 Sparsity | p. 164 |
15.2.3 Storage of matrix elements | p. 165 |
15.2.4 Use of implicit functions | p. 165 |
15.2.5 Ordered elimination and matrix inversion | p. 166 |
15.3 Starting Conditions | p. 166 |
Appendix | p. 169 |
References | p. 173 |
Further Reading | p. 175 |
Index | p. 177 |