An Iterative Response-Surface-Based Approach for Chance-Constrained AC Optimal Power Flow Considering Dependent Uncertainty

A modern power system is characterized by a stochastic variation of the loads and an increasing penetration of renewable energy generation, which results in large uncertainties in its states. These uncertainties bring formidable challenges to the power system planning and operation process. To address these challenges, we propose a cost-effective, iterative response-surface-based approach for the chance-constrained AC optimal power-flow problem that aims to ensure the secure operation of the power systems considering dependent uncertainties. Starting from a stochastic-sampling-based framework, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose, instead of using the original complicated power-system model, to rely on a polynomial-chaos-based response surface. This response surface allows us to efficiently evaluate the time-consuming power-system model at arbitrary distributed sampled values with a negligible computational cost. This further enables us to efficiently conduct an online stochastic testing for the system states that not only screens out the statistical active constraints, but also assists in a better design of the tightened bounds without using any Gaussian or symmetric assumption. Finally, an iterative procedure is executed to fine-tune the optimal solution that better satisfies a predefined probability. The simulations conducted in multiple test systems demonstrate the excellent performance of the proposed method.