An application of interval analysis and optimization to electric energy markets

In this paper, we address the issue of quantifying model uncertainties in a deregulated power market. We are interested in a worst-case analysis of effects of network parameter uncertainties on optimization problems that are solved on the level of an independent system operator (ISO). The focus is on linear programming (LP) formulations because of their practical relevance. After briefly reviewing applications of different interval analysis tools (interval matrix inversion and various contractors and solvers for systems of interval equations), we propose two tailored algorithms. In the first (basic LP approach), we propose another solver for a system of linear interval equations, while in the second (power system-customized LP approach), we use features of the power system model to reduce the width of the interval solution. The interval-based results are compared with a deterministic robust noninterval matrix inversion-based solution of a model of the benchmark 68-node New England/New York interconnected power system. Presented analyzes demonstrate that even small parameter variations can have significant impact on optimization.