Time-of-use Pricing for Energy Storage Investment

Time-of-use (ToU) pricing is widely used by the electricity utility to shave peak load. Such a pricing scheme provides users with incentives to invest in behind-the-meter energy storage and to shift peak load towards low-price intervals. However, without considering the implication on energy storage investment, an improperly designed ToU pricing scheme may lead to significant welfare loss, especially when users over-invest the storage, which leads to new energy consumption peaks. In this paper, we will study how to design a social-optimum ToU pricing scheme by explicitly considering its impact on storage investment. We model the interactions between the utility and users as a two-stage optimization problem. To resolve the challenge of asymmetric information due to users' private storage cost, we propose a ToU pricing scheme based on different storage types and the aggregate demand per type. Each user does not need to reveal his private cost information. We can further compute the optimal ToU pricing with only a linear complexity. Simulations based on real-world data show that the suboptimality gap of our proposed ToU pricing, compared with the social optimum achieved under complete information, is less than 5%.