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When an energy storage system comprises multiple batteries, the optimal scheduling of charging/discharging actions must take into account their different characteristics. To prolong battery lifetime, each battery must stay in their safety zones. Since load demand and energy price vary over time, the value function that reflects future power cost is both state- and time-dependent. To address this control-limited optimization problem, a new adaptive dynamic programming algorithm is proposed. The time-varying optimal value function is subdivided into a sequence of time-invariant functions which are solved by a periodic value iteration. These functions are further approximated by fuzzy systems, and the optimal charging/discharging actions are searched by the projected Newton method. Experiment results show the new algorithm is able to coordinate multiple batteries efficiently in their constrained control space.
Zhu et al. (Tue,) studied this question.