Optimal and Compact Control Policies for Energy Storage Units With Single and Multiple Batteries

In this paper we investigate the use of energy storage units (ESUs) to reduce the average cost of power supply. Using a dynamic programming (DP) argument, we first show that the optimal control policy for a single-battery ESU, under piecewise linear cost functions, has a threshold structure that can be expressed and stored in a very compact form. We then extend the analysis to an ESU with multiple (heterogeneous) batteries, where DP is generally impractical because of the explosion of the computational complexity with the number of batteries. We hence define a simple method to map the optimal solution of a suitable single-battery ESU into an admissible policy for the multiple-battery ESU, whose complexity grows only linearly with the number of batteries. Extensive simulation results show that the proposed approach can yield significant cost reduction in comparison with other policies, under realistic users' power requests, and with different costs functions. Furthermore, the admissible policy for the multiple-battery ESU is shown to achieve almost optimal performance under realistic assumptions on the battery parameters.