Stochastic optimal power flow based on conditional value at risk and distributional robustness

We present a computationally-efficient approach for solving stochastic, multiperiod optimal power flow problems. The objective is to determine power schedules for controllable devices in a power network, such as generators, storage, and curtailable loads, which minimize expected short-term operating costs under various device and network constraints. These schedules are chosen in a multistage decision framework to include planned power output adjustments, or reserve policies, which track errors in the forecast of power requirements as they are revealed, and which may be time-coupled. Such an approach has previously been shown to be an attractive means of accommodating uncertainty arising from highly variable renewable energy sources. Given a probabilistic forecast describing the spatio-temporal variations and dependencies of forecast errors, we formulate a family of stochastic network and device constraints based on convex approximations of chance constraints, and show that these allow economic efficiency and system security to be traded off with varying levels of conservativeness. Our formulation indicates two broad approaches, based on conditional value and risk and distributional robustness, that provide alternatives to existing methods based on chance and robust constraints. The results are illustrated using a case study, in which conventional generators plan schedules around an uncertain but time-correlated wind power injection.