  Chance constrained optimal power flow (CC-OPF) formulations have been
proposed to minimize operational costs while controlling the risk arising from
uncertainties like renewable generation and load consumption. To solve CC-OPF,
we often need access to the (true) joint probability distribution of all
uncertainties, which is rarely known in practice. A solution based on a biased
estimate of the distribution can result in poor reliability. To overcome this
challenge, recent work has explored distributionally robust chance constraints,
in which the chance constraints are satisfied over a family of distributions
called the ambiguity set. Commonly, ambiguity sets are only based on moment
information (e.g., mean and covariance) of the random variables; however,
specifying additional characteristics of the random variables reduces
conservatism and cost. Here, we consider ambiguity sets that additionally
incorporate unimodality information. In practice, it is difficult to estimate
the mode location from the data and so we allow it to be potentially
misspecified. We formulate the problem and derive a separation-based algorithm
to efficiently solve it. Finally, we evaluate the performance of the proposed
approach on a modified IEEE-30 bus network with wind uncertainty and compare
with other distributionally robust approaches. We find that a misspecified mode
significantly affects the reliability of the solution and the proposed model
demonstrates a good trade-off between cost and reliability.
