Approximate Chance-Constrained Unit Commitment Under Wind Energy Penetration

Abstract

We study a multi-period unit commitment problem under wind energy penetration, in which the load balance is enforced with a predefined confidence level across the whole system and over the planning horizon. Since, except for special cases, chance-constrained problems are non-convex, we analyze two relaxations of the load balance based upon robust optimization ideas and estimated quantiles of the marginal distributions of the net load processes. The approximation proposals are benchmarked against the well-known scenario approximation. Under the scenario approach, we also analyze a simple decomposition strategy to find a lower bound of the approximate problem, when the latter becomes intractable due the size of the set of scenarios. The reliability of the obtained solutions as well as their runtimes are examined on three widespread test systems.