Optimal end user energy storage sharing in demand response

Deregulated electricity markets with time varying electricity prices and opportunities for consumer cost mitigation makes energy storage such as a battery an attractive proposition; users can charge the battery when prices are low and discharge the battery for activities when prices are high. An electricity storage system with enough capacity to support hours of home use can be expensive for an individual consumer; a high capacity battery shared across a group of homes in a community or apartments in a building, can not only alleviate the economic deterrents but also exploit the fact that users' activity patterns do not necessarily overlap. The centralized control of such a shared battery is the focus of this work. In general, users may not have equal requirements from the shared battery, and the purchase and maintenance costs may be divided unequally. As these conditions vary, an achievable cost savings region exists for different users, wherein each point corresponds to a simultaneously achievable set of cost-savings for the group of users. In this work, the optimal cost savings region for a finite capacity battery assuming a zero tolerance for activity delay is studied using an infinite horizon discounted cost Markov Decision Process. When selling electricity back to the grid is allowed through net metering, it is shown that the cost optimization yields a policy structure wherein the optimal action is always independent of the state of the battery and the dynamic policy optimization can be reduced to an integer linear programming solution with significantly reduced complexity. When selling electricity back is not allowed, the optimal cost savings policy specifies a threshold on the total electricity stored in the battery below which the optimal action mirrors the net metering solution. The complexity of this policy optimization scales exponentially in the number of users, and a computationally scalable sub-optimal policy is proposed which, through numerical simulations on real electricity pricing and usage data, is shown to perform closely to the optimum.