Optimal Energy Management for Multi-Storage Grids

Modern power systems increasingly depend on energy storage devices to manage fluctuations in renewable generation and load demand. Coordinating multiple heterogeneous storage units in a grid-level system while enforcing individual state-of-charge (SoC) limits constitutes a complex, high-dimensional control problem that cannot be resolved by conventional proportional-sharing schemes. This work formulates the Distributed Optimal Energy Management (DOEM) problem for a grid comprising n parallel storage units with power-dependent efficiency and heterogeneous capacities. Optimality conditions are derived using Pontryagin’s Minimum Principle (PMP) and a smooth penalty function is introduced to handle hard SoC constraints without state-space discretisation. For the practically important class of lossless storage devices, an explicit closed-form control law is obtained, in which each unit is dispatched proportionally to its storage capacity. Numerical validation is performed on the Israeli power grid, modelling three pumped-hydro systems with a combined capacity of 8.0 GWh, using MATLAB/Simulink R2018b. Across the base net-load scenario and four additional load profiles, the cost achieved by the proposed method matches the dynamic programming (DP) benchmark within 1.1%, while the maximum state-of-charge violation is limited to 0.64% of total capacity at the default penalty setting. Computationally, the proposed update requires only 2.21 s for nine storage units compared to 59.30 s for DP, a 26.8-fold speedup, and scales with O(n) arithmetic operations per time step. The results confirm a clear pathway to optimal, safe, and scalable real-time control of large-scale heterogeneous energy storage ensembles.