Gaussian Mixture Model Based Distributionally Robust Optimal Power Flow With CVaR Constraints

Abstract: This paper proposes a distributionally robust optimal power flow (OPF) model for transmission grids with wind power generation. The model uses the conditional value-at-risk (CVaR) constraints to control the reserve and branch flow limit violations caused by wind power forecast errors. Meanwhile, the Gaussian mixture model (GMM) is integrated into the CVaR constraints to guard against the non-Gaussian forecast error distributions. Unlike the previous studies considering the GMM with fixed parameters, this paper allows the GMM parameters to be variable within some credible regions and develops a data-driven GMM-based ambiguity set to achieve the distributional robustness. Also, rather than using the traditional sample-based approximation of CVaR with high computational burden, this paper designs a scalable cutting-plane algorithm to handle the distributionally robust CVaR constraints. Case studies on the IEEE 2736-bus system show the effectiveness and scalability of the proposed OPF model.