Steven A. Gabriel & Antonio J. Conejo 
Complementarity Modeling in Energy Markets 

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. on-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. conomic and engineering problems that aren’t specifically derived from optimization problems (e.g., spatial price equilibria) d. roblems 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? s 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.

Table of Content

Introduction and Motivation.- Optimality and Complementarity.- Some Microeconomic Principles.- Equilibria and Complementarity Problems.- Variational Inequality Problems.- Optimization Problems Constrained by Optimization Problems.- Equilibrium Problems with Equilibrium Constraints.- Algorithm for LCPs, NCPs, and VIs.- Some Advanced Algorithms for VI Decomposition, MPCCs and EPECs.- Natural Gas Market Modeling.- Electricity and Environmental Markets.- Multicommodity Equilibrium Models: Accounting for Demand-Side Linkages.

About the author

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.