Interval Methods for Uncertain Power System Analysis

In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples.

The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as:

• A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators
• Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis
• In-depth examinations of uncertain optimal power flow analysis
• Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices

Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.

Alfredo Vaccaro, PhD, is an Associate 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 Authors

Preface

Acknowledgements

Acronyms

Introduction

1. Introduction to reliable computing

1.1 Elements of Reliable Computing

1.2 Interval analysis

1.3 Interval-based operators

1.4 Interval Extensions of elementary functions

1.5 Solving systems of linear interval equations

1.6 Finding zeros of nonlinear equations

1.7 Solution of systems of non-linear interval equations

1.8 The overestimation problem

1.9 Affine Arithmetic

1.9.1 Conversion between AA and IA

1.9.2 AA-based operators

1.9.3 Chebyshev approximation of univariate non-affine functions

1.9.4 Multiplication of Affine Forms

1.9.5 Effects of recursive solution schemes

1.10 Integrating AA and IA

2.  Uncertain Power Flow Analysis

2.1 Sources of uncertainties in power flow analysis

2.2 Solving Uncertain Linearized Power Flow Equations

2.3 Solving Uncertain Power Flow Equations

2.3.1 Optimization-based method

2.3.2 Domain contraction method

3. Uncertain Optimal Power Flow Analysis

3.1 Range analysis-based solution

3.1.1 Optimal Economic Dispatch

3.1.2 Reactive Power Dispatch

3.2 AA-based solution

4. Uncertain Markov Chain Analysis

4.1 Mathematical Preliminaries

4.2 Effects of Data Uncertainties

4.3 Matrix Notation

4.4 AA-based Uncertain Analysis

4.5 Application Examples

4.5.1 Case Study 1: Grid resilience analysis

4.5.2 Case Study 2: Energy storage model

4.5.3 Summary

5. Small-signal stability analysis of uncertain power systems

5.1 Problem formulation

5.2 The interval eigenvalue problem

5.3 Applications

5.3.1 Case Study 1

5.3.2 Case Study 2

6. Uncertain power components thermal analysis

6.1 Thermal rating assessment of overhead lines

6.1.1 Sources of data uncertainties

6.1.2 AA-based thermal rating assessment

6.1.3 Application examples

6.2 Thermal rating assessment of power cables

6.2.1 Thermal modeling of power cables

6.2.2 Sources of data uncertainties

6.2.3 Tolerance analysis of cable thermal dynamics by IA

6.2.4 Application examples

7. Bibliography

8. Index

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