Distributionally Robust CVaR Constraints for Power Flow Optimization

Abstract

Recent research on optimal power flow (OPF) in networks with renewable power involves optimizing both first and second stage variables that adjust the decision once the uncertainty is revealed. In general, only partial information on the underlying probability distribution of renewable power production is available. This paper considers a distributionally robust framework for solving the OPF problem. The formulation stipulates a probability mass function of wind power production, whose probabilities and scenario locations vary in a box of ambiguity with bounds that can be tuned based on historical data. Distributionally robust optimization (DRO) is used to derive new conditional value-at-risk (CVaR) constraints that limit the frequency and severity of branch flow limit violations whenever the renewable power generation deviates from its forecast. Numerical results are reported on networks with up to 2736 nodes and contrasted with classical robust optimization (RO) and stochastic optimization (SO) solutions. The results show an advantage to adopting the proposed DRO for load flow control. In particular, the solution benefits from the observed correlation amongst the uncertain parameters to mitigate branch flow limit violations, and yet maintain an acceptable worst-case expected operational cost as compared to RO and SO solutions.