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Chance constrained optimal power flow (CC-OPF) formulations have beenproposed to minimize operational costs while controlling the risk arising fromuncertainties like renewable generation and load consumption. To solve CC-OPF,we often need access to the (true) joint probability distribution of alluncertainties, which is rarely known in practice. A solution based on a biasedestimate of the distribution can result in poor reliability. To overcome thischallenge, recent work has explored distributionally robust chance constraints,in which the chance constraints are satisfied over a family of distributionscalled the ambiguity set. Commonly, ambiguity sets are only based on momentinformation (e.g., mean and covariance) of the random variables; however,specifying additional characteristics of the random variables reducesconservatism and cost. Here, we consider ambiguity sets that additionallyincorporate unimodality information. In practice, it is difficult to estimatethe mode location from the data and so we allow it to be potentiallymisspecified. We formulate the problem and derive a separation-based algorithmto efficiently solve it. Finally, we evaluate the performance of the proposedapproach on a modified IEEE-30 bus network with wind uncertainty and comparewith other distributionally robust approaches. We find that a misspecified modesignificantly affects the reliability of the solution and the proposed modeldemonstrates a good trade-off between cost and reliability.

Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes