Page 91 - Mathematical Models and Algorithms for Power System Optimization

CHAPTER 4
New Algorithms Related to Power Flow

Chapter Outline
4.1 Introduction 82

4.1.1 Way of Processing Variables in Traditional Power Flow Equation 82
4.1.2 Way of Processing Variables in New Power Flow Equation 83
4.1.3 Overview of Unconstrained Power Flow with Objective Function (based on SA Method) 83
4.1.4 Overview of Constrained Power Flow with Objective Function (based on OPF Method) 84
4.1.5 Overview of This Chapter 85
4.2 Ideas of Modeling for Unconstrained Power Flow with Objective Function 85
4.2.1 Description of Ill-Conditioned Power Flow Problem 85
4.2.2 Outline of Simulated Annealing Method 87
4.2.3 Way of Modifying Iteration Step Size by SA Method 88
4.2.4 Way of Constructing a Nonlinear Quadratic Objective Function 88
4.3 Formulation of Unconstrained Power Flow Model with Nonlinear Quadratic
Objective Function 88
4.3.1 Notation 88
4.3.2 Formulation of Power Flow with Quadratic Function 89
4.4 Calculation Procedure of SA based N-R Method 89
4.5 Implementation of SA based N-R Method 92

4.5.1 Initial Conditions of 197-Bus System 92
4.5.2 Conditions and Results of Four Cases 93
4.6 Formulation of Discrete Optimal Power Flow 99
4.6.1 Similarities and Differences Between LF and OPF 99
4.6.2 Description of the Problem 100
4.6.3 Features of the Problem 101
4.6.4 Mathematical Model 103
4.7 Discrete OPF Algorithm 105

4.7.1 Main Solution Procedure of Discrete OPF 105
4.7.2 Linearization of the Problem 107
4.7.3 SLP-based Solution Procedure for Linear MIP Problem 107
4.8 Implementation of Discrete OPF 110
4.8.1 Verification by the Concrete Formulation of 5-Bus System 110
4.8.2 Conditions and Results of Four Cases for 135-Bus Large-scale System 114
4.9 Conclusion 118

Mathematical Models and Algorithms for Power System Optimization. https://doi.org/10.1016/B978-0-12-813231-9.00004-2
# 2019 China Electric Power Press. Published by Elsevier Inc. All rights reserved.
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