Robust Optimization in Electric Energy Systems

ISBN-13: 9783030851279 / Angielski / Twarda / 2021 / 340 str.

Andy Sun; Antonio J. Conejo

Spis treści

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

O autorze

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.

Blurb

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).