Overview

This book covers robust optimization theory and applications in the electricity sector. The advantage of robust optimization with respect to other methodologies for decision making under uncertainty are first discussed. Then, the robust optimization theory is covered in a friendly and tutorial manner. Finally, a number of insightful short- and long-term applications pertaining to the electricity sector are considered. Specifically, the book includes: robust set characterization, robust optimization, adaptive robust optimization, hybrid robust-stochastic optimization, applications to short- and medium-term operations problems in the electricity sector, and applications to long-term investment problems in the electricity sector. Each chapter contains end-of-chapter problems, making it suitable for use as a text.  The purpose of the book is to provide a self-contained overview of robust optimization techniques for decision making under uncertainty in the electricity sector. The targeted audience includes industrial and power engineering students and practitioners in energy fields. The young field of robust optimization is reaching maturity in many respects. It is also useful for practitioners, as it provides a number of electricity industry applications described up to working algorithms (in JuliaOpt).

Full Product Details

Author:   Xu Andy Sun ,  Antonio J. Conejo
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2021
Volume:   313
Weight:   0.676kg
ISBN:  

9783030851279

ISBN 10:   3030851273
Pages:   329
Publication Date:   09 November 2021
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Chapter 1: Introduction and motivation 1.1.       Introduction 1.2.       Motivation 1.3.       Optimization vs. complementarity problems: definition and characterization 1.4.       Illustrative examples: of an optimization problem, equilibrium problem, optimization problem with equilibrium constraints and equilibrium problem with equilibrium constraints. 1.5.       Exercises   Chapter 2: Optimality conditions 2.1.       KKT conditions 2.2.       Constraint qualifications for necessary conditions 2.3.       Sufficiency conditions 2.4.       Simple optimization problem (analytically solvable) 2.5.       Simple optimization problem solved as an LCP or NLCP 2.6.       Simple equilibrium problem (analytically solvable) 2.7.       Simple MPEC (analytically solvable) 2.8.       Simple EPEC (analytically solvable) 2.9.       Nonconvex problems 2.10.   Exercises   Chapter 3: Introductory microeconomic principles relevant for complementarity problems and market equilibria 3.1.       Basics 1.1.   Supply curves 1.2.   Demand curves 1.3.   Notion of equilibrium as intersection of supply and demand curves 3.2.       Social Welfare Maximization 2.1.   Definition of social welfare and associated optimization problem 2.2.   Maximization of consumers’ + producers’ surpluses 3.3.       Modeling individual players 3.1.   Profit-maximization problem as paradigm 3.2.   Perfect vs. imperfect competition 3.2.1.      Price-taking producers 3.2.2.      Monopoly 3.2.3.      Oligopoly (Nash-Cournot, Bertrand games) 3.2.4.      Cartel 3.4.       Multi-level games 4.1.   Stackelberg leader follower games (MPECs) 4.2.   Multi-leader games (EPECs). 4.3.   Nash vs. Generalized Nash equilibria 3.5.       Exercises   Chapter 4: Equilibria as complementarity problems 4.1.       Equilibria  4.2.       Conditions involving primal and dual variables 4.3.       Combination of equations and KKT conditions 4.4.       LCP and Mixed LCP 4.5.       NLCP and Mixed NLCP 4.6.       Stochastic equilibrium problems 4.7.       Formulation issues 4.8.       Example: Electricity market equilibrium 4.9.       Example: Gas market equilibrium 4.10.   Exercises   Chapter 5: Variational Inequality problems 5.1.       Variational Inequality (VI) formulation 5.2.       VI vs. complementarity problems 5.3.       Example of electricity/gas equilibrium 5.4.       Quasi-Variational Inequality (QVI) formulation 5.5.       Generalized Nash games as QVIs 5.6.       Exercises   Chapter 6: MPECs 6.1.       Bilevel problems and MPEC 6.2.       Linearization of MPECs 6.3.       Stochastic MPECs 6.4.       Formulation issues 6.5.       Examples: Supply function offering strategy in electricity markets, transmission expansion planning 6.6.       Exercises   Chapter 7: EPECs 7.1.       EPECs 7.2.       Example: Supply function equilibrium in electricity markets. 7.3.       Exercises   Chapter 8: Basic solution algorithms 8.1.       Solving LCPs and mixed LCPs 8.2.       Solving NLCPs and mixed NLCPs 8.3.       Examples 8.4.       Exercises   Chapter 9: Advanced solution algorithms 9.1.       Solving MPECs 9.2.       Solving EPECs 9.3.       Decomposition techniques for deterministic and stochastic complementarity problems 9.4.       Numerical issues 9.5.       Examples 9.6.       Exercises   Chapter 10: Natural Gas markets 10.1.   Applications to gas markets. 10.2.   World Gas Model, GASTALE, GASMOD 10.3.   Exercises   Chapter 11: Electricity markets and environmental issues 11.1.   Application to electricity markets. 11.2.   Single commodity markets 11.3.   Multi-commodity markets 11.4.   Exercises   Chapter 12: Multicommodity equilibrium models 12.1.   Multicommodity markets 12.2.   Nonsymmetry conditions in cross price elasticities 12.3.   Nonmarginal cost-pricing rules and other regulatory distortions 12.4.   Models PIES, NEMS and MARKAL 12.5.   Exercises   Chapter 13: Summary and conclusions 13.1.   Summary 13.2.   Conclusions 13.3.   Future work   Appendix A: Convex sets and functions A.1.      Convexity of a set A.2.      Convexity of a function A.3.      Positive semidefinite matrices   Appendix B: GAMS models B.1.      GAMS code for an optimization problem B.2.      GAMS code for an LCP and mixed LCP B.3.      GAMS code for an NCP and mixed NCP B.4.      GAMS code for an MPEC

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Author Information

Andy Sun is an assistant professor in the Stewart School of Industrial & Systems Engineering at Georgia Tech, USA. Dr. Sun conducts research in optimization and stochastic modeling with applications in electric energy systems and electricity markets. He also works on theory and algorithms for robust and stochastic optimization, and large scale convex optimization. Antonio J. Conejo received an M.S. from MIT, US and a Ph.D. from the Royal Institute of Technology, Sweden. He has published over 190 papers in refereed journals and is the author or coauthor of books published by Springer, John Wiley, McGraw-Hill and CRC Press. He has been the principal investigator of many research projects financed by public agencies and the power industry and has supervised 19 PhD theses. He is an IEEE Fellow.

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