A Robust Optimization Approach to the Self-scheduling Problem Using Semidefinite Programming

Abstract

In deregulated electricity markets, generating companies submit energy bids which are derived from a self-schedule. In this thesis, we propose an improved semidefinite programming-based model for the self-scheduling problem. The model provides the profit-maximizing generation quantities of a single generator over a multi-period horizon and accounts for uncertainty in prices using robust optimization. Within this robust framework, the price information is represented analytically as an ellipsoid. The risk-adversity of the decision maker is taken into account by a scaling parameter. Hence, the focus of the model is directed toward the trade-off between profit and risk. The bounds obtained by the proposed approach are shown to be significantly better than those obtained by a mean-variance approach from the literature. We then apply the proposed model within a branch-and-bound algorithm to improve the quality of the solutions. The resulting solutions are also compared with the mean-variance approach, which is formulated as a mixed-integer quadratic programming problem. The results indicate that the proposed approach produces solutions which are closer to integrality and have lower relative error than the mean-variance approach.