Stochastic optimal power flow based on convex approximations of chance constraints

This paper presents 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 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 relaxations of chance constraints, and show that these allow economic efficiency and system security to be traded off with varying levels of conservativeness. The results are illustrated using a simple case study, in which conventional generators plan schedules around an uncertain but time-correlated wind power injection.