Complementarity Modeling in Energy Markets

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Springer Science & Business Media, Jul 20, 2012 - Business & Economics - 630 pages
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This addition to the ISOR series introduces complementarity models in a straightforward and approachable manner and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. In a nutshell, complementarity models generalize:
a. optimization problems via their Karush-Kuhn-Tucker conditions
b. non-cooperative games in which each player may be solving a separate but related optimization problem with potentially overall system constraints (e.g., market-clearing conditions)
c. economic and engineering problems that aren’t specifically derived from optimization problems (e.g., spatial price equilibria)
d. problems in which both primal and dual variables (prices) appear in the original formulation (e.g., The National Energy Modeling System (NEMS) or its precursor, PIES).
As such, complementarity models are a very general and flexible modeling format.

A natural question is why concentrate on energy markets for this complementarity approach? As it turns out, energy or other markets that have game theoretic aspects are best modeled by complementarity problems. The reason is that the traditional perfect competition approach no longer applies due to deregulation and restructuring of these markets and thus the corresponding optimization problems may no longer hold. Also, in some instances it is important in the original model formulation to involve both primal variables (e.g., production) as well as dual variables (e.g., market prices) for public and private sector energy planning. Traditional optimization problems can not directly handle this mixing of primal and dual variables but complementarity models can and this makes them all that more effective for decision-makers.

 

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Contents

Chapter 1 Introduction and Motivation
1
Chapter 2 Optimality and Complementarity
31
Chapter 3 Some Microeconomic Principles
71
Chapter 4 Equilibria and Complementarity Problems
127
Chapter 5 Variational Inequality Problems
180
Chapter 6 Optimization Problems Constrained by Optimization Problems
221
Chapter 7 Equilibrium Problems with Equilibrium Constraints
263
Chapter 8 Algorithms for LCPs NCPs and VIs
323
Chapter 11 Electricity and Environmental Markets
477
Chapter 12 Multicommodity Equilibrium Models Accounting for DemandSide Linkages
515
Appendix A Convex Sets and Functions
561
Appendix B GAMS codes
570
Appendix C DC Power Flow
607
Appendix D Natural Gas Engineering Considerations
612
List of Tables
618
List of Figures
623

Chapter 9 Some Advanced Algorithms for VI Decomposition MPCCs and EPECs
385
Chapter 10 Natural Gas Market Modeling
433

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About the author (2012)

Steven A. Gabriel received his M.A. and Ph.D. degrees in Mathematical Sciences from Johns Hopkins University in 1989 and 1992, respectively, and his M.S. in Operations Research from Stanford University in 1984. He is currently Associate Professor, Civil Systems Program, Department of Civil and Environmental Engineering, University of Maryland.

Antonio J. Conejo received the M.S. degree from Massachusetts Institute of Technology, Cambridge, MA, in 1987 and the Ph.D. degree from the Royal Institute of Technology, Stockholm, Sweden, in 1990. He is currently Professor of Electrical Engineering at the Universidad de Castilla – La Mancha, Ciudad Real, Spain.

J. David Fuller received his Ph.D. in Interdisciplinary Studies from the University of British Columbia in 1980. His research interests focus on Energy Economics and Operations Research; Mathematical Programming Models of Economic Equilibrium with Applications to Energy Markets Forecasting and Electricity Market Design; and Decomposition of Linear, Nonlinear and Equilibrium Programs. He is currently a Professor of Management Sciences, in the Faculty of Engineering at the University of Waterloo, in Waterloo, Ontario, Canada.

Benjamin F. Hobbs received his Ph.D. in Environmental Systems Engineering from Cornell University in 1983; his MS in Resource Management and Policy from Syracuse University in 1978, and his BS in Mathematics and Environmental Sciences from North Dakota State University in 1976. He has served as Chair of the JHU President’s Climate Change Task Force since 2008.

Carlos Ruiz is currently a Ph.D. candidate under Dr. Conejo at the University de Castilla.