Stochastic Optimization of Power Systems with Risk Constraints And Sparsely Distributed Storage

Abstract

The power grid is experiencing a profound transformation in recent years with the proliferation of renewable sources and the advance of bulk storage technologies. These changes have been anticipated in the literature of signal processing and control, where several new techniques for the optimal operation and design of the greed are reported. The present paper builds on the state of the art, proposing a novel stochastic approximation algorithm for optimizing the network under risk constraints. The method is capable of processing massive amounts of data, learning the distributions of the random generation and demand, and adapting to seasonal changes and system evolution. In addition, a parsimonious storage design is achieved by introducing a sparsifying penalty to the problem of siting and sizing. Numerical examples show that the optimization algorithm succeeds in guaranteeing that prescribed voltage limits are satisfied with an outage probability that stands below theoretical bounds.