Uniqueness Proof of Shortest Path Method For Optimal Power Management in Fueled Systems With Finite Storage Capacity

Energy storage devices are increasingly vital in modern power systems, offering solutions to enhance efficiency, reduce costs, manage peak demands, and improve stability across diverse applications such as electric vehicles, grid operations, and power electronics. Optimal management of these devices is critical, involving the determination of efficient power generation strategies that minimize operational costs while meeting demand. Current methods predominantly rely on numerical algorithms such as Linear Programming (LP), Dynamic Programming (DP), stochastic control methods like Model Predictive Control (MPC). Pontryagin’s Minimum Principle is also used, but usually it doesn’t yield a singular, definitive solution; instead, it outlines necessary conditions that may serve as guidance in numerical search of optimal control strategies. These methods, while effective, typically require extensive computational resources and provide limited intuitive understanding of solutions.

This reseach introduces a novel analytical technique for optimizing energy storage management. To the best of our knowledge, there aren’t any papers that suggest simple and intuitive analytic solutions with graphical interpretation, as may be seen in this research. The graphical solution may provide a better understanding of the systems dynamics, and provide a strong intuition regarding the optimal power management of the energy storage and the optimal storage capacity. Moreover, the mathematical clarity of the proposed methods, promises low computational costs and fast run-time, making the aforementioned algorithm superior for implementing the solution in real-time or planning and evaluating many possible systems, since short run-time in these cases is important. The work in the research completes the proof given in a paper by the same name from 2010, for which the proof was not complete until today.

M.SE Under the supervision of Prof. Yoash Levron.