Two-Scale Stochastic Optimization for Controlling Distributed Storage Devices

This paper is motivated by a power system with storage devices at multiple locations which need to be controlled at a much finer timescale than that necessary for conventional generation units. We present a stochastic optimization model of the power system which captures interactions of decisions at these two timescales through a novel state-variable formulation. The model also includes transmission constraints approximated by a linearized dc network, fast response operating reserves, and renewable generation. To tackle this high-dimensional multistage stochastic optimization problem, we present a sequential sampling method which we refer to as the stochastic dynamic linear programming. This algorithm is a dynamic extension of regularized two-stage stochastic decomposition for stagewise independent multistage stochastic linear programs, and is targeted at the class of problems where decisions are made at two different timescales. We compare our algorithm with the stochastic dual dynamic programming (SDDP) which has been effectively applied in planning power systems operations. Our computational results show that our sequential Monte-Carlo approach provides prescriptive solutions and values which are statistically indistinguishable from those obtained from SDDP, while improving computational times significantly.