Adaptive certainty-equivalent approach for optimal generator dispatch under uncertainty

The large-scale integration of renewable energy sources, in particular wind and solar, poses many challenges to power grid operations due to their stochastic and highly-variable nature. One of such challenges is the high cost associated with making real-time power balancing adjustments in order to compensate for forecast errors in renewable powers. To overcome this challenge, stochastic optimization techniques have been explored in the literature for planning generator dispatches taking into account renewable energy uncertainty and balancing costs. The techniques used are typically based on forming Sample Average Approximations (SAA) and applying deterministic optimization techniques that exploit the problem structure. In this work, the performance of alternative algorithms based on Stochastic Approximation (SA) and hybrid techniques for solving the stochastic optimal dispatch problem is analyzed. More specifically, an approach based on updating the certainty-equivalent problem with noisy gradient observations is compared against the stochastic gradient and two SAA-based algorithms on four test cases. This approach is shown to be equivalent to a stochastic proximal gradient algorithm with a non-Euclidean metric when applied to the stochastic optimal dispatch problem. The results obtained show that the adaptive certainty-equivalent algorithm produces better iterates compared to the other algorithms on the test cases considered.