Optimal Control of Energy Storage Devices Based on Pontryagin's Minimum Principle and the Shortest Path Method

Optimal control strategies for storage devices have been extensively explored in recent years. Two leading approaches are solutions based on dynamic programming and solutions that stem from Pontryagin's minimum principle. Recent studies propose an optimal control strategy for storage devices which is based on the idea of the shortest path: the optimal generated energy must follow the shortest path within two bounds set by the load profile and the device capacity. The current paper continues these studies and shows that the shortest path principle may be derived directly from Pontryagin's minimum principle. This result is of theoretical interest since it demonstrates that the intuitive shortest path method can be easily extended to handle more complex systems. Based on this result we also develop a low-complexity algorithm for calculating the shortest path, which is tested in several case studies.