  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.
