An analysis of energy storage and regulation

We focus on a region whose power system is controlled by an operator that relies on a regulation service to balance the total system supply to the total system load in quasi real-time. We consider the existing contractual framework in which a regulation unit declares its regulation parameters at the beginning of the contract, the operator guarantees that the regulation signals will be within the range of these parameters, and the regulation unit is rewarded proportionally to what it declares. Our purpose is twofold. We first want to obtain formulas for the regulation parameters that a unit with non-ideal storage should declare to the operator given its state of charge at the beginning of a contract. Second, we want to analytically quantify, ahead of time, the reward that such a unit could obtain in successive contracts by performing this regulation service. Since the state of charge at the beginning of a contract depends on what happened in the previous contract and, hence, is a random variable, we quantify this reward analytically using bounds and expectation. We then provide engineering insights by applying our results to three specific energy storage technologies that are often considered as candidates for regulation. In particular, we show the impact of the storage parameters and the length of one contract on the potential reward over a given period.