Cost and Pricing of Differential Privacy in Demand Reporting for Smart Grids

In smart grid, the highly dynamics of electrical loads introduce uncertainty to the system, which also brings new challenges for the power grid control and optimization. Reporting demand information by customers in solving the economic dispatch control (EDC) problem in power grids is a promising approach, but it raises important privacy concerns. One solution is to add random noise to aggregate queries of demand reports can provide differential privacy (DP) for the individual customers. However, the noisy query information can adversely degrade the EDC's optimality. In this paper, we first analyze the cost in demand reporting in terms of how DP-induced noise will increase the total generation cost. We show that the noise amounts for different customers are intricately coupled with one another in determining the total cost. To deal with the coupling, we apply the principle of Shapley value to attribute fair shares of the total cost to the power grid buses and study the properties of this cost sharing approach. For efficient sharing of the privacy cost, in a manner scalable to large power systems with many buses, we propose heuristic algorithms to approximate the Shapley value. Moreover, we study important network effects of the per-customer DP cost within a privacy group attached to the same bus, in that this cost depends on how many other customers choose the same privacy group. Accordingly, we design a pricing scheme for the customers that we prove to be truthful, i.e., customers have no incentives to deviate from the group that represents their true privacy needs. We also discuss the impact of the high-demand customer on other customers' cost and propose an approach in the pricing scheme to charge higher cost on the high-demand customer. Trace-driven simulations based on a 5-bus power system model validate our analysis and illustrate the performance of the proposed cost sharing algorithms.