Information-Theoretic Privacy for Smart Metering Systems with a Rechargeable Battery

Smart-metering systems report electricity usage of a user to the utility provider on almost real-time basis. This could leak private information about the user to the utility provider. In this work we investigate the use of a rechargeable battery in order to provide privacy to the user. We assume that the user load sequence is a first-order Markov process, the battery satisfies ideal charge conservation, and that privacy is measured using normalized mutual information (leakage rate) between the user load and the battery output. We consider battery charging policies in this setup that satisfy the feasibility constraints. We propose a series reductions on the original problem and ultimately recast it as a Markov Decision Process (MDP) that can be solved using a dynamic program. In the special case of i.i.d. demand, we explicitly characterize the optimal policy and show that the associated leakage rate can be expressed as a single-letter mutual information expression. In this case we show that the optimal charging policy admits an intuitive interpretation of preserving a certain invariance property of the state. Interestingly an alternative proof of optimality can be provided that does not rely on the MDP approach, but is based on purely information theoretic reductions.