Uniqueness of Optimal Power Management Strategies for Energy Storage Dynamic Models

This paper contributes to the field of analytic and semi-analytic solutions for optimal power flow problems involving storage systems. Its primary contribution is a rigorous proof establishing the uniqueness of the “shortest path” optimal solution, a key element in this class of algorithms, building upon a graphical design procedure previously introduced. The proof is constructed through five consequential lemmas, each defining a distinct characteristic of the optimal solution. These characteristics are then synthesized to demonstrate the uniqueness of the optimal solution, which corresponds to the shortest path of generated energy within defined bounds. This proof not only provides a solid theoretical foundation for this algorithm class but also paves the way for developing analytic solutions to more complex optimal control problems incorporating storage. Furthermore, the efficacy of this unique solution is validated through two comparative tests. The first one uses synthetic data to benchmark the proposed solution in comparison to recent reinforcement learning algorithms, including actor–critic, PPO, and TD3. The second one compares the proposed solution to the optimal solutions derived from other numerical methods based on real-world data from an electrical vehicle storage device.