The Privacy Analysis of Battery Control Mechanisms in Demand Response: Revealing State Approach and Rate Distortion Bounds

Demand response systems in the electricity grid, which rely on two way communication between the consumers and utility, require the transmission of instantaneous energy consumption to utilities. Perfect knowledge of a user's power consumption profile by a utility is a violation of privacy and can be detrimental to the successful implementation of demand response systems. It has been shown that an in-home energy storage system (such as a battery/inverter) that provides a viable means to achieve the cost savings of instantaneous electricity pricing without inconvenience can also be used to hide a user's power usage pattern. A fundamental tradeoff exists between the costs saved and the degree of privacy achievable, and in this paper, the tradeoff achievable by a finite capacity battery assuming a zero tolerance for activity delay is studied using a Markov process model for user's demands and instantaneous electricity prices. Due to high computational complexity (continuous state-action space) of the stochastic control model, inner and upper bounds are presented on the optimal tradeoff. In particular, a class of battery charging policies based on minimizing revealing states is proposed to derive achievable privacy-cost savings tradeoff. The performance of this algorithm is compared with lower bounds derived using a greedy heuristic and upper bounds derived using an information theoretic rate distortion approach. The framework proposed is shown to be applicable even when users only desire partial information protection, such as presence/absence of activity or specific appliances they wish to hide. Numerical results based on real electricity and pricing data show that the proposed algorithm performs close to the upper bound demonstrating its efficacy.