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Computational Methods in Power System Analysis

:	Reijer Idema, Domenico Lahaye
:	Computational Methods in Power System Analysis
:	Atlantis Press
:	9789462390645
:	1
:	CHF 114.00
:

:	Allgemeines, Lexika
:	English

:	113
:	DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book treats state-of-the-art computational methods for power flow studies and contingency analysis. In the first part the authors present the relevant computational methods and mathematical concepts. In the second part, power flow and contingency analysis are treated. Furthermore, traditional methods to solve such problems are compared to modern solvers, developed using the knowledge of the first part of the book. Finally, these solvers are analyzed both theoretically and experimentally, clearly showing the benefits of the modern approach.

	Preface	6
	Contents	7
	1 Introduction	10
	Part IComputational Methods	12
	2 Fundamental Mathematics	13
	2.1 Complex Numbers	13
	2.2 Vectors	14
	2.3 Matrices	15
	2.4 Graphs	17
	References	18
	3 Solving Linear Systems of Equations	19
	3.1 Direct Solvers	20
	3.1.1 LU Decomposition	20
	3.1.2 Solution Accuracy	21
	3.1.3 Algorithmic Complexity	21
	3.1.4 Fill-in and Matrix Ordering	21
	3.1.5 Incomplete LU decomposition	22
	3.2 Iterative Solvers	22
	3.2.1 Krylov Subspace Methods	23
	3.2.2 Optimality and Short Recurrences	24
	3.2.3 Algorithmic Complexity	24
	3.2.4 Preconditioning	24
	3.2.5 Starting and Stopping	26
	References	27
	4 Solving Nonlinear Systems of Equations	28
	4.1 Newton--Raphson Methods	29
	4.1.1 Inexact Newton	30
	4.1.2 Approximate Jacobian Newton	31
	4.1.3 Jacobian-Free Newton	31
	4.2 Newton--Raphson with Global Convergence	32
	4.2.1 Line Search	32
	4.2.2 Trust Regions	34
	References	35
	5 Convergence Theory	36
	5.1 Convergence of Inexact Iterative Methods	36
	5.2 Convergence of Inexact Newton Methods	40
	5.2.1 Linear Convergence	44
	5.3 Numerical Experiments	45
	5.4 Applications	49
	5.4.1 Forcing Terms	49
	5.4.2 Linear Solver	50
	References	51
	Part IIPower System Analysis	52
	6 Power System Analysis	53
	6.1 Electrical Power	55
	6.1.1 Voltage and Current	55
	6.1.2 Complex Power	56
	6.1.3 Impedance and Admittance	57
	6.1.4 Kirchhoff's Circuit Laws	58
	6.2 Power System Model	58
	6.2.1 Generators, Loads, and Transmission Lines	59
	6.2.2 Shunts and Transformers	60
	6.2.3 Admittance Matrix	61
	6.3 Power Flow	62
	6.4 Contingency Analysis	63
	References	63
	7 Traditional Power Flow Solvers	64
	7.1 Newton Power Flow	64
	7.1.1 Power Mismatch Function	65
	7.1.2 Jacobian Matrix	66
	7.1.3 Handling Different Bus Types	67
	7.2 Fast Decoupled Load Flow	68
	7.2.1 Classical Derivation	69
	7.2.2 Shunts and Transformers	71
	7.2.3 BB, XB, BX, and XX	72
	7.3 Convergence and Computational Properties	76
	7.4 Interpretation as Elementary Newton--Krylov Methods	76
	References	77
	8 Newton--Krylov Power Flow Solver	78
	8.1 Linear Solver	78
	8.2 Preconditioning	79
	8.2.1 Target Matrices	80
	8.2.2 Factorisation	80
	8.2.3 Reactive Power Limits and Tap Changing	81
	8.3 Forcing Terms	82
	8.4 Speed and Scaling	83
	8.5 Robustness	84
	References	85
	9 Contingency Analysis	87
	9.1 Simulating Branch Outages	87
	9.2 Other Simulations with Uncertainty	90
	References	90
	10 Numerical Experiments	91
	10.1 Factorisation	91
	10.1.1 LU Factorisation	92
	10.1.2 ILU Factorisation	95
	10.2 Forcing Terms	96
	10.3 Power Flow	99
	10.3.1 Scaling	102
	10.4 Contingency Analysis	104
	References	106
	11 Power Flow Test Cases	107
	11.1 Construction	107
	References	109
	Index	110