Contract-based Time-of-use Pricing for Energy Storage Investment

Time-of-use (ToU) pricing is widely used by the electricity utility. A carefully designed ToU pricing can incentivize end-users' energy storage deployment, which helps shave the system peak load and reduce the system social cost. However, the optimization of ToU pricing is highly non-trivial, and an improperly designed ToU pricing may lead to storage investments that are far from the social optimum. In this paper, we aim at designing the optimal ToU pricing, jointly considering the social cost of the utility and the storage investment decisions of users. Since the storage investment costs are users' private information, we design low-complexity contracts to elicit the necessary information and induce the proper behavior of users' storage investment. The proposed contracts only specify three contract items, which guides users of arbitrarily many different storage-cost types to invest in full, partial, or no storage capacity with respect to their peak demands. Our contracts can achieve the social optimum when the utility knows the aggregate demand of each storage-cost type (but not the individual user's type). When the utility only knows the distribution of each storage-cost type's demand, our contracts can lead to a near-optimal solution. The gap with the social optimum is as small as 1.5% based on the simulations using realistic data. We also show that the proposed contracts can reduce the system social cost by over 30%, compared with no storage investment benchmark.