Risk-Based Distributionally Robust Optimal Power Flow With Dynamic Line Rating

In this paper, we propose a risk-based data-driven distributionally robust approach to investigating the optimal power flow with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To robustify the solution, we consider a distributional uncertainty set based on the second-order moment, that captures the correlation between wind generation outputs and line ratings, and also the Wasserstein distance, that hedges against data perturbations. We show that the proposed model can be reformulated as a convex conic program. Approximations of the proposed model are suggested, which leads to a significant reduction of the number of the constraints. For practical large-scale test systems, a distributionally robust optimal power flow model with Wasserstein-distance-based distributional uncertainty set and its convex reformulation are also provided. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.