Two-stage distributionally robust optimal power flow with flexible loads

In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.