Wasserstein Metric Based Distributionally Robust Approximate Framework for Unit Commitment

Abstract

This paper proposed a Wasserstein metric-based distributionally robust approximate framework (WDRA), for unit commitment problem to manage the risk from uncertain wind power forecasted errors. The ambiguity set employed in the distributionally robust formulation is the Wasserstein ball centered at the empirical distribution. The proposed framework minimizes the generating cost, start-up cost, shut-down cost, reserve cost, and the expected thermal generation adjusting cost under the worst-case distribution in the ambiguity set. The more historical available, the smaller the ambiguity set is and, hence, the less conservativeness the decision is. The size of the Wasserstein metric based robust counterpart (WDRC) model mainly depends on the size of sample set, which has a computation burden when more historical data are available. To overcome this drawback, this paper proposed an upper approximate of WDRC and verified the condition that makes the approximate model become exact. Comparisons with robust optimization and stochastic optimization illustrate that the proposed model can balance the economy and conservativeness effectively. Monte Carlo simulations on a modified IEEE-118 and a real 703-bus systems show that the proposed WDRA framework could reduce the computational time by several times when compared with WDRC.