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Time-of-use (ToU) pricing is widely used by the electricity utility. Acarefully designed ToU pricing can incentivize end-users' energy storagedeployment, which helps shave the system peak load and reduce the system socialcost. However, the optimization of ToU pricing is highly non-trivial, and animproperly designed ToU pricing may lead to storage investments that are farfrom the social optimum. In this paper, we aim at designing the optimal ToUpricing, jointly considering the social cost of the utility and the storageinvestment decisions of users. Since the storage investment costs are users'private information, we design low-complexity contracts to elicit the necessaryinformation and induce the proper behavior of users' storage investment. Theproposed contracts only specify three contract items, which guides users ofarbitrarily many different storage-cost types to invest in full, partial, or nostorage capacity with respect to their peak demands. Our contracts can achievethe social optimum when the utility knows the aggregate demand of eachstorage-cost type (but not the individual user's type). When the utility onlyknows the distribution of each storage-cost type's demand, our contracts canlead to a near-optimal solution. The gap with the social optimum is as small as1.5% based on the simulations using realistic data. We also show that theproposed contracts can reduce the system social cost by over 30%, compared withno storage investment benchmark.

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