Supplementary material for "Real option valuation of a decremental regulation service provided by electricity storage".

This paper is a quantitative study of a reserve contract for real-time balancing of a power system. Under this contract, the owner of a storage device, such as a battery, helps smooth fluctuations in electricity demand and supply by using the device to increase electricity consumption. The battery owner must be able to provide immediate physical cover, and should therefore have sufficient storage available in the battery before entering the contract. Accordingly, the following problem can be formulated for the battery owner: determine the optimal time to enter the contract and, if necessary, the optimal time to discharge electricity before entering the contract. This problem is formulated as one of optimal stopping, and is solved explicitly in terms of the model parameters and instantaneous values of the power system imbalance. The optimal operational strategies thus obtained ensure that the battery owner has positive expected economic profit from the contract. Furthermore, they provide explicit conditions under which the optimal discharge time is consistent with the overall objective of power system balancing. This paper also carries out a preliminary investigation of the ‘lifetime value’ aggregated from an infinite sequence of these balancing reserve contracts. This lifetime value, which can be viewed as a single project valuation of the battery, is shown to be positive and bounded. Therefore, in the long run such reserve contracts can be beneficial to commercial operators of electricity storage, while reducing some of the financial and operational risks in power system balancing.