Economic Model Predictive Control for Time-Varying Cost and Peak Demand Charge Optimization

With the increasing prevalence of variable-supply electricity production, dynamic market structures, including time-varying prices and/or peak demand charges are becoming more common for electricity consumers. This framework requires consumers to consider both the time-varying amount of electricity (i.e., energy) consumed throughout the day as well as the maximum rate of electricity purchase (i.e., power) over a given period, typically a month. Because of this complexity, online optimization techniques such as economic model predictive control (MPC) are a natural tool for consumers to use to minimize cost. However, while closed-loop optimization of these pricing structures is already being proposed for various applications, little has been established about stability or performance properties of the closed-loop system. Due in particular to the peak penalty (which violates the principle of optimality if naively included in the objective function), this theoretical gap leaves the potential for pathological closed-loop behavior despite high-quality open-loop solutions. In this paper, we derive asymptotic performance and stability results for general time-varying economic MPC. We then present a novel extended-state formulation to convert peak demand charges into a time-varying stage cost that can be optimized using economic MPC. In addition, we give a terminal cost and constraint for the augmented system that avoids reducing the feasible set in the original space. Finally, we demonstrate these structures and the closed-loop properties that they satisfy via two illustrative examples.