Distributed Differentially Private Model Predictive Control for Energy Storage

Abstract

Smart meters enable a variety of new and useful applications for achieving a smart grid. Unfortunately, they also pose privacy risks by revealing sensitive information about consumers. In this work, techniques that exploit the benefits of smart meters and at the same time mitigate privacy risks are explored. More specifically, we consider the control of local energy storage devices of a group of consumers with the goal of minimizing energy cost and providing aggregate load smoothing to the grid. A differentially private distributed model predictive controller (MPC) is proposed by extending a framework recently proposed in the literature for this application. By using a distributed proximal gradient algorithm, the energy cost of consumers is minimized while keeping the load profile of each consumer private. Aggregate load smoothing is achieved by exchanging net consumption information between consumers. Since information about the consumer load profiles could be inferred from theses exchanges, the proposed controller is designed to ensure Differential Privacy (DP) and to protect this information. Numerical experiments are used to study a case with 30 consumers. The resulting trade-off between privacy and performance is studied as well as the effects of having a trustworthy or untrustworthy mediator handling the information exchanges between consumers.