Robust optimization in electric energy systems
著者
書誌事項
Robust optimization in electric energy systems
（International series in operations research & management science, v. 313）
Springer, c2021
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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).
目次
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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