Construction of Nonlinear Feedback Strategies for Energy Storage Systems: A Stochastic Dynamic Programming Approach

It is currently observed that rapid changes in generation and consumption can significantly impact the stability of a power system. In this light, this paper proposes a nonlinear feedback strategy for energy storage systems which operates under uncertainty conditions, and does not require statistical representations of future signals. We employ stochastic dynamic programming (SDP) to derive the nonlinear feedback policy and then verify its stability properties using a Lyapunov-based analysis. A central challenge in such problems arises due to the calculation of two-dimensional value functions at each time instant, which requires considerable computational resources. To address this challenge, we consider a quadratic cost function and model the load power as a first-order auto-regressive stochastic process. We show that these considerations help solve the optimal control problem using SDP, and evaluate a feedback policy which is sub-optimal and stable. Numerical experiments reveal that this proposed feedback policy always keeps the stored energy within bounds, and allows it to follow the optimal path.