Two-Stage Robust Power Grid Optimization Problem

For both regulated and deregulated electric power markets, due to the integration of renewable energy generation and uncertain demands, both supply and demand sides of an electric power grid are volatile and under uncertainty. Accordingly, a large amount of spinning reserve is required to maintain the reliability of the power grid in traditional approaches. In this paper, we propose a novel two-stage robust integer programming model to address the power grid optimization problem under supply and demand uncertainty. In our approach, uncertain problem parameters are assumed to be within a given cardinality or polyhedral uncertainty set. We study cases with and without transmission capacity and ramp-rate limits. We also analyze solution schemes to solve each problem that include an exact solution approach, and an efficient heuristic approach that provides a tight lower bound for the general robust power grid optimization problem. The final computational experiments on a modified IEEE 118-bus system verify the effectiveness of our approaches, as compared to the worst-case scenario generated by the nominal model without considering the uncertainty.