Under the deregulated energy market environment, plus the integration of renewable energy generation, both the supply and demand of a power grid system are volatile and under uncertainty. Accordingly, a large amount of spinning reserve is required at each bus to maintain the reliability of the power grid system in the traditional approach. 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, the uncertain demand is assumed to be within a given cardinality or polyhedral uncertainty set. We study both the cases with and without transmission constraints, respectively. We analyze the solution schemes to solve each problem that include developing efficient separation algorithms, and providing lower and upper bounds for the general robust power grid optimization problem. The final computational experiments on a revised 118-bus system from Midwest ISO verify the effectiveness of our approach, as compared to the worst case scenario generated by the nominal model without considering the uncertainty.
This paper is accepted by European Journal of Operational Research with the title "Two-stage network constrained robust unit commitment problem". The paper is available at http://www.sciencedirect.com/science/article/pii/S0377221713007832. The citation is J. Ruiwei, M. Zhang, G. Li and Y. Guan. Two-stage network constrained robust unit commitment problem, European Journal of Operational Research, 234 (3): 751-762, 2014.