Modular Load Flow for Restructured Power Systems (eBook)

Prof. M.V. Hariharan is Gold Medal awardee for his performance in B.Tech in the entire state of Madras (1954) and a UNESCO scholar (1959). He has been a popular faculty at IIT Bombay, Mumbai (1962 – 93) and is known for his down-to-earth teaching methods. He has been Visiting Professor at University of Manitoba, Canada (1987) and at University of Western Ontario London, Canada (1988). He was consultant to Tata Consulting Engineers, Maharashtra State Electricity Board, now restructured as Mahagenco (MSPGCL), Mahatransco (MSETCL) and Mahadiscom (MSEDCL). Prof. Hariharan has carried out research projects for Department of Science and Technology, India and has published papers in international journals. He has guided many PhD students. Prof. S.D. Varwandkar, PhD (IIT Kanpur, India) was faculty at VJTI, Mumbai (1969 – 2004) and has taught courses on Electrical Machines, Power System Analysis, and Planning and Reforms and has published in international journals and guided three PhD students. He has carried out projects for Board of Research in Nuclear Sciences, India and was Expert Consultant at Global R & D, Crompton Greaves, Mumbai (2007 – 08).  Ms. Pragati P. Gupta topped in BE among all branches of Engineering at Dibrugarh University in 1991 and in M.Tech (Power Systems) at VJTI. She is currently Assistant Professor of Electrical Engineering at VJTI and is associated with teaching of courses in Power Systems, especially Deregulated Systems.

Preface 7
Acknowledgements 10
Contents 12
About the Authors 16
Abbreviations and Symbols 17
1 Introduction 19
1.1 Review of Graph Theory 19
1.1.1 Fundamental Cutsets (f-Cutsets) 22
1.1.2 Incidence Matrices 23
1.1.3 Kirchhoff's Laws 24
1.1.4 Primitive Network 24
1.1.5 Network Structure 25
1.1.6 Network Matrices 26
1.1.7 Power Network 27
1.2 Iterative Load Flow 28
1.3 Issues with Iterative Load Flow 28
1.3.1 Premise 28
1.3.2 Voltage Specification at PV Buses 28
1.4 Load Representation 28
1.5 Concept of Port 29
1.6 Matrix xi 29
References 30
2 Circuit Solutions 31
2.1 Multi-terminal Representation 31
2.2 Solution for Element Variables 32
2.2.1 Single Current Source 32
2.2.2 Example 33
2.2.3 Single Voltage Source 34
2.2.4 Example 34
2.2.5 Single Power Source 35
2.2.6 Example 36
References 37
3 Kirchhoff State 38
3.1 Kstate-Variables 39
3.2 Kpowers 39
3.3 Kvoltages 40
3.3.1 Example 40
3.4 The Superposition Challenge 42
3.5 Quantum Perspective 42
Reference 43
4 Modular Load Flow 44
4.1 Concept of Modularity 44
4.2 Power Distribution in Kstates 47
4.3 Line Flows 47
4.4 Superposition of Line Flows 49
4.5 Voltages 49
4.6 Phase Angles 49
4.7 Modular Load Flow Algorithm 50
4.8 Comparison with Conventional Load Flow 51
4.9 HVDC, FACTS and DSG 52
References 53
5 Load Flow Examples 54
5.1 The 3-Bus System 54
5.1.1 Results for 3-Bus System 54
5.2 The IEEE 30-Bus System [1] 56
5.2.1 Results for 30-Bus System 59
5.3 The Ill-Conditioned 43-Bus System 61
5.3.1 Results for 43-Bus System 65
References 67
6 Outage Analysis 68
6.1 Line Outage 68
6.1.1 Example 69
6.2 Power Flow Fractions Versus Distribution Factors 71
6.3 Identifying Outaged Generator 73
6.3.1 Example 73
6.4 Selective Computation of Line Flows 74
6.4.1 Example 74
Reference 75
7 Voltage Behaviour 76
7.1 Problem Formulation 77
7.2 Modular Approach 78
7.2.1 Example: Ill-Conditioned System 80
7.3 Variation of Voltage 82
7.4 Voltage Dependency of Loads 82
7.5 PQ-reserve and PQ-deficit Condition 83
7.5.1 Example: The Switchover 84
7.6 Conclusion 86
References 86
8 Optimization 87
8.1 Optimal Use of Injected Powers 87
8.2 Multi-generator Case 88
8.2.1 Example 89
8.3 Load Voltage Optimization 90
8.3.1 Example 92
8.4 Flow Optimization 93
8.4.1 Example 95
8.5 Tieline Dispatch 96
8.5.1 Example 97
8.6 State Estimation 98
8.7 Conclusion 98
References 99
9 Blackout Incipient 100
9.1 Introduction 100
9.2 Limitations in Blackout Related Studies 101
9.3 Blackout-Incipient and Vulnerability 101
9.4 The Indian Grid---Overview 102
9.5 Case Study 1: Grid Disturbance on 30th July 2012 103
9.6 Load Representation 104
9.7 Radial-Mesh Representation for Sub-grids 105
9.8 Benchmarking 106
9.9 Algorithm 106
9.10 Case Study 2: Grid Disturbance on 31st July 2012 112
9.11 Conclusion 116
References 116
10 Dirac Structures 118
10.1 Function Spaces with Inner Products 119
10.2 Hilbert Spaces and Orthoframes 119
10.2.1 Relation Between Orthoframes 120
10.3 Dirac Structures 122
10.3.1 Dual Spaces 122
10.3.2 Duality Product 123
10.3.3 Bilinear Form 123
10.3.4 Orthogonal Complement 123
10.3.5 Dirac Structure: Definition 124
10.4 Dirac Structure for Generators 124
10.5 Geometric Interpretation 124
10.5.1 Electrical Variables in Hilbert Spaces 124
10.5.2 Superposition of Dirac Structures 125
10.5.3 Example 126
10.6 Summary 127
References 127