On the operation and value of storage in consumer demand response

We study the optimal operation and economic value of energy storage operated by a consumer who faces (possibly random) fluctuating electricity prices and seeks to reduce its energy costs. The value of storage is defined as the consumer's net benefit obtained by optimally operating the storage. We formulate the operation problem as a dynamic program. Under the assumption that consumer utility (received from electricity consumption) is additively separable over time, we establish a threshold structure of the optimal operation policy for a consumer who faces random electricity prices and stochastic demand. For a more general setting that incorporates the inter-temporal substitution effect in consumer demand, if the consumer always faces the same (realized) purchasing and selling price, then it is optimal for her to use the storage only for arbitrage, and therefore the VoS does not depend on the consumer's demand.