Importance Sampling Approach to Chance-Constrained DC Optimal Power Flow

Despite significant economic and ecological effects, a higher level of renewable energy generation leads to increased uncertainty and variability in power injections, thus compromising grid reliability. To improve power grid security, we investigate a joint chance-constrained (CC) dc approximation of the ac optimal power flow (OPF) problem. The problem aims to find economically optimal power generation while guaranteeing that all power generation, line flows, and voltages remain within their bounds at the same time with a predefined probability. Unfortunately, the CC-dc-OPF problem is computationally intractable even if the distribution of renewables' fluctuations is specified. Moreover, existing approximate solutions to the joint CC OPF problem are overly conservative and computationally demanding and, therefore, have less value for the operational practice. This article proposes an importance sampling approach for constructing an efficient and reliable scenario approximation for CC-dc-OPF with theoretical guarantees on the number of samples required, which yields better sample complexity and accuracy than current state-of-the-art methods. The algorithm efficiently reduces the number of scenarios by generating and using only a few most important, thus enabling real-time solutions for test cases with up to several hundred buses.