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Robust Optimization in Electric Energy Systems

 Gebonden Engels 2021 9783030851279
144,99
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Samenvatting

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).

Specificaties

ISBN13:9783030851279
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer International Publishing
Serie:International Series in Operations Research & Management Science

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Inhoudsopgave

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

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