Individual Welfare Maximization in Electricity Markets Including Consumer and Full Transmission System Modeling

ii RED-BORDERED FORM iii ABSTRACT This dissertation presents a new algorithm that allows a market participant to maximize its individual welfare in the electricity spot market. The use of such an algorithm in determining market equilibrium points, called Nash equilibria, is also demonstrated. The start of the algorithm is a spot market model that uses the optimal power flow (OPF), with a full representation of the transmission system. The OPF is also extended to model consumer behavior, and a thorough mathematical justification for the inclusion of the consumer model in the OPF is presented. The algorithm utilizes price and dispatch sensitivities, available from the Hessian matrix of the OPF, to help determine an optimal change in an individual's bid. The algorithm is shown to be successful in determining local welfare maxima, and the prospects for scaling the algorithm up to realistically sized systems are very good. Assuming a market in which all participants maximize their individual welfare, economic equilibrium points, called Nash equilibria, are investigated. This is done by iteratively solving the individual welfare maximization algorithm for each participant until a point is reached where all individuals stop modifying their bids. It is shown that these Nash equilibria can be located in this manner. However, it is also demonstrated that equilibria do not always exist, and are not always unique when they do exist. It is also shown that individual welfare is a highly nonconcave function resulting in many local maxima. As a result, a more global optimization technique, using a genetic algorithm (GA), is investigated. The genetic algorithm is successfully demonstrated on several systems. It is also shown that a GA can be developed using special niche methods, which allow a GA to converge to several local optima at once. iv Finally, the last chapter of this dissertation covers the development of a new computer visualization routine for power system analysis: contouring. The contouring algorithm is demonstrated to be useful in visualizing bus-based and transmission line-based quantities. v ACKNOWLEDGMENTS I would like to thank Professor Thomas J. Overbye for his knowledge, guidance, and support throughout my doctoral studies. He and his family have been a great help to me. I would also like to thank all the other professors who have helped and continue to help me in my academic career. I also say thanks the University of Illinois Power Affiliates Program and Grainger Foundation for their generous financial …