Optimal control of energy storage under random operation permissions

This article studies the optimal control of energy storage when operations are permitted only at random times. At the arrival of a permission, the storage operator has the option, but not the obligation, to transact. A nonlinear pricing structure incentivizes small transactions spread out among arrivals, instead of a single unscheduled massive transaction, which could stress the energy delivery system. The problem of optimizing storage operations to maximize the expected cumulated revenue over a finite horizon is modeled as a piecewise deterministic Markov decision process. Various properties of the value function and the optimal storage operation policy are established, first when permission times follow a Poisson process and then for permissions arriving as a self-exciting point process. The sensitivity of the value function and optimal policy to the permission arrival process parameters is studied as well. A numerical scheme to compute the optimal policy is developed and employed to illustrate the theoretical results. Current distribution systems cannot support simultaneous and identical actions of a large number of agents reacting to an identical signal. That motivates transactive market frameworks when their access to transactions is restricted. Therefore, the optimal policy of an agent under this restriction is important to study. Being able to act at random arrival of permissions and to act under a nonlinear pricing structure are salient characteristics differentiating this study from existing work on energy storage optimization.