Assessing the Value of Including Unimodality Information in Distributionally Robust Optimization Applied to Optimal Power Flow

Uncertainties, such as renewable generation and load consumption, has been a major source of risk in power system planning. To safely incorporate these uncertainties, we need to ensure all physical constraints affected are satisfied at high probability level. To manage the uncertainties, different stochastic optimal power flow formulations have been proposed. Conventional approaches either provide over-conservative results or rely on accurate estimates on uncertainty distributions. Recently, an alternative distributionally robust optimal power flow formulations with only data-driven moment information are shown to provide better trade-offs between objective and reliability. In this paper, we further consider a distributionally robust optimal power flow problems with both moment and unimodality information, based on the facts that most practical uncertainties are unimodal. We formulate the problem using chance constraint and provide various reformulations and approximations with efficient solving techniques. We evaluate the proposed approaches on the modified IEEE 118/300-bus system with high penetrated renewable generation and demonstrate the values of including the unimodality information and benefits against the conventional approaches.