Analyzing and Quantifying the Intrinsic Distributional Robustness of CVaR Reformulation for Chance-Constrained Stochastic Programs

Chance-constrained program (CCP) is a popular stochastic optimization method in power system planning, and operation problems. Conditional Value-at-Risk (CVaR) provides a convex approximation for chance constraints which are nonconvex. Although CCP assumes an exact empirical distribution, and the optimum of a stochastic programming model is thought to be sensitive in the designated probability distribution, this letter discloses that CVaR reformulation of a chance constraint is intrinsically robust. A pair of indices are proposed to quantify the maximum tolerable perturbation of the probability distribution, and can be computed from a computationally-cheap dichotomy search. An example on the coordinated capacity optimization of energy storage, and transmission line for a remote wind farm validates the main claims. The above results demonstrate that stochastic optimization methods are not necessarily vulnerable to distributional uncertainty, and justify the positive effect of the conservatism brought by the CVaR reformulation.