Interval Methods for Uncertain Power System Analysis

Alfredo Vaccaro, PhD, is a Full Professor of Electric Power Systems in the Department of Engineering at the University of Sannio. He is Editor-in-Chief of Technology and Economics of Smart Grids and Sustainable Energy, Springer Nature and Chair of the PES-IEEE Task Force on Enabling Paradigms for High-Performance Computing in Wide Area Monitoring Protective and Control Systems.

• About the Author ixPreface xiAcknowledgments xiiiAcronyms xvIntroduction 11 Introduction to Reliable Computing 31.1 Elements of Reliable Computing 41.2 Interval Analysis 71.3 Interval-Based Operators 81.4 Interval Extensions of Elementary Functions 91.5 Solving Systems of Linear Interval Equations 111.6 Finding Zeros of Nonlinear Equations 151.7 Solution of Systems of Nonlinear Interval Equations 161.8 The Overestimation Problem 201.9 Affine Arithmetic 221.9.1 Conversion Between AA and IA 251.9.2 AA-Based Operators 251.9.3 Chebyshev Approximation of Univariate Nonaffine Functions 281.9.4 Multiplication of Affine Forms 311.9.5 Effects of Recursive Solution Schemes 351.10 Integrating AA and IA 352 Uncertain Power Flow Analysis 372.1 Sources of Uncertainties in Power Flow Analysis 392.2 Solving Uncertain Linearized Power Flow Equations 412.3 Solving Uncertain Power Flow Equations 462.3.1 Optimization-Based Method 482.3.2 Domain Contraction Method 523 Uncertain Optimal Power Flow Analysis 593.1 Range Analysis-Based Solution 613.1.1 Optimal Economic Dispatch 633.1.2 Reactive Power Dispatch 663.2 AA-Based Solution 704 Uncertain Markov Chain Analysis 754.1 Mathematical Preliminaries 774.2 Effects of Data Uncertainties 784.3 Matrix Notation 794.4 AA-Based Uncertain Analysis 804.5 Application Examples 834.5.1 Case Study 1: Grid Resilience Analysis 834.5.2 Case Study 2: Energy Storage Model 844.5.3 Summary 865 Small-Signal Stability Analysis of Uncertain Power Systems 875.1 Problem Formulation 895.2 The Interval Eigenvalue Problem 905.3 Applications 925.3.1 Case Study 1 925.3.2 Case Study 2 936 Uncertain Power Components Thermal Analysis 956.1 Thermal Rating Assessment of Overhead Lines 966.1.1 Sources of Data Uncertainties 986.1.2 AA-Based Thermal Rating Assessment 996.1.3 Application Examples 1006.2 Thermal Rating Assessment of Power Cables 1046.2.1 Thermal Modeling of Power Cables 1056.2.2 Sources of Data Uncertainties 1076.2.3 Tolerance Analysis of Cable Thermal Dynamics by IA 1086.2.4 Application Examples 109References 112Index 119