Methods and Models for Stochastic Energy Market Equilibria

University Of Maryland, College Park, College Park MD

Investigators

Abstract

The project will develop energy market equilibrium models with probabilistic components and analyze conditions that ensure existence and uniqueness of solutions. Two modes will be considered, the first one in which a specific sector such as natural gas will be examined and the second one corresponding to the overall energy market where sectors (e.g., the coal market) will be modeled from a high-level perspective. In the sector-specific approach, individual market players (e.g., natural gas producers, electric power generators) will be depicted as solving profit maximization problems subject to operational constraints as well as uncertain demand or other stochastic elements. These market participants will either be modeled as Nash-Cournot players and thereby have the potential to assert market power, or perfectly competitive players that take market prices as given. The simultaneous solution of each of these optimization problems along with market clearing conditions will lead to a nonlinear complementarity or variational inequality problem whose solution will be sought. In the second mode considered, the overall energy sector will be modeled allowing for certain key elements (e.g., pipeline capacity) to be uncertain due to man-made or natural occurrences. Existence and uniqueness issues for the related market equilibria also based on a nonlinear complementarity/variational inequality approach will be examined. The project will also develop and analyze efficient algorithms to solve these stochastic market equilibrium problems making use of decomposition, matrix factorizations, or recourse approaches. As such, the project will join the two important disciplines of stochastic optimization and equilibrium modeling. Lastly, the project will analyze key energy policy scenarios using these models. Modern society depends heavily on many types of infrastructure to operate efficiently. This infrastructure is in many forms such as the electric power grid, transportation networks, water treatment facilities, etc. However, many of these infrastructure elements face risks that threaten to seriously degrade the societal benefits. For example, recent energy market deregulation and restructuring have in some cases contributed to large volatility in energy prices which have adversely affected society. The instability in certain aspects of the energy sector is troublesome since energy is vital to many parts of the economy. Thus, risk management in energy can benefit many areas. To combat these energy infrastructure problems, one can develop mathematical models to predict how the energy sector will function under a wide range of scenarios and then plan accordingly by building redundant systems, using financial instruments or other measures. This project will both develop and analyze energy market equilibrium models as well as build and analyze efficient algorithms to solve such problems. These models will directly take into account uncertain demand or other probabilistic elements to more accurately reflect the market players' actions when faced with uncertainty. These models will then be used to analyze certain key energy policy scenarios in consultation with U.S. energy officials as well as those of other countries as appropriate.