On the privacy-cost tradeoff of an in-home power storage mechanism

Demand response systems in the electricity grid, which rely on two way communication between the consumers and utility, requires the transmission of instantaneous energy consumption to utilities. Perfect knowledge of a users´ power consumption profile by a utility is a violation of privacy and can be detrimental to the successful implementation of demand response systems. An in-home storage system, which provides a viable means to achieve the cost savings of instantaneous electricity pricing without the inconvenience (delay) caused by demand response, can also be used to maintain the privacy of a user´s power profile. In this work, the design of battery charging and discharging algorithms in response to time varying demand and prices are studied. In particular, a fundamental tradeoff between how much privacy can be provided to individual consumers by a finite capacity battery and the cost savings that can be achieved assuming a zero tolerance for delay is studied using a Markov process model for user´s demands and instantaneous electricity prices. When the demands and prices follow a Markovian evolution, the optimization problem is shown to be equivalent to a Partially Observable Markov Decision Process with belief dependent rewards (ρ-POMDP). Due to high computational complexity of the model, computable inner and upper bounds are presented on the optimal tradeoff. In particular, inner bounds are derived using specific strategies for battery scheduling including the cost optimal, optimal fixed deterministic strategy and the greedy algorithm. Upper bounds are provided using a standard rate-distortion optimization. These bounds are derived for a binary model, where the battery state is binary, and the demand and prices are distributed i.i.d. Bernoulli.