Equilibrium models and algorithms, with applications to energy market design, operation and policy analysis

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In the operation of a competitive market for electricity, complex computer-based models determine which generators will supply electricity each hour, and the prices that will be paid for electricity generation. These models combine economic ideas, and realistic descriptions of generation and transmission technology, with modern mathematical knowledge about optimization, i.e., getting the greatest benefit from limited resources. Related optimization models are also used to explore the implications of policies on energy and the environment. This research aims to improve the state of the art in building these models, in the corresponding operation of electricity markets, and in the use of such models for analysis of energy-environment policies. Many of the models to be studied go beyond optimization from the point of view of one agent, such as a company, and consider instead the "equilibrium" of several interacting agents who each try to optimize. Part of the research effort will also be devoted to improving the speed of the computations, so that solutions are available quickly enough to be used in the operation of electricity markets. The speedup strategy is a "divide and conquer" approach called "decomposition." Another technical challenge in creation and use of equilibrium models is due to the need to represent binary decisions such as turning a generator on or off, or building a new generation facility or not. Compared with the mathematical representation of deciding on the amount of power from a generator, or the size of a new facility, which is well known now, the inclusion of binary decisions tremendously complicates the equilibrium models. The research aims to improve the state of the art in equilibrium models with binary decision variables.