Optimal load following in power grids in the presence of battery-powered agents

We address the modeling and optimal control problems for load following in power grids in the presence of unconventional battery-powered agents. Compared to the traditional large-scale generators such as thermal and hydroelectric plants, these agents have significantly lower short-term response costs but higher long-term generation costs. Moreover, a battery-powered agent can act both as a supplier and as a load by operating in discharge or charge modes, respectively. In this work, we provide a tractable model that captures the multi-timescale and heterogeneous cost structures of conventional and unconventional systems, as well as the dual role of unconventional ones. Then, we pose and solve the problem of optimal finite-horizon control of the joint system to balance unpredicted fluctuations in the net load. The optimal controller takes a simple and intuitive form that is explicitly described in terms of cost parameters, the net load shift, and the time horizon of control. We further investigate numerically several characteristics of the controller to reveal the gains and dynamics associated with it under randomly changing net load.