The Value of Including Unimodality Information in Distributionally Robust Optimal Power Flow

Abstract

To manage renewable generation and load consumption uncertainty, chance-constrained optimal power flow (OPF) formulations and various solution methodologies have been proposed. However, conventional solution approaches often rely on accurate estimates of uncertainty distributions, which may not exist. When the distributions are not known but can be limited to a set of plausible distributions, termed an ambiguity set, distributionally robust (DR) optimization can be used to ensure that chance constraints hold for all distributions in that set. However, DR OPF yields conservative solutions if the ambiguity set is too large. In this paper, we assess the value of using both moment and unimodality information, which shrinks the ambiguity set and reduces conservatism, in DR OPF problems. Most practical uncertainty distributions in power systems are unimodal. Exact reformulations, approximations, and efficient solving techniques were developed in a previous paper. This paper develops an optimal parameter selection approach that searches for an optimal approximation, significantly improving the computational efficiency and solution quality. We evaluate the performance of the approach against existing chance-constrained OPF approaches using modified IEEE 118-bus and 300-bus systems with high penetrations of renewable generation. Results show that including unimodality information reduces solution conservatism and cost without significantly degrading reliability.