Economic Model Predictive Control with a Non-Fixed Reference Trajectory for Optimal Microgrid Dispatch

Abstract: Economic Model Predictive Control (EMPC), instead of stabilizing a reference trajectory/state in the objective function like a Tracking MPC, optimizes the economic performance over the prediction horizon, making it attractive for economical microgrid (MG) dispatch. However, the demand charge component in the monthly electricity cost, make it difficult to be encapsulated in additive stage costs, and can make solutions violate the principle of optimality if naively introduced in the objective function. Moreover, previous EMPC based works mostly rely on a-priori knowledge of an optimal economic steady state or optimal periodic trajectory for performance guarantees, which are not useful or possibly don't exist respectively, for real-time economical MG dispatch where load/generation forecasts are known only 24-48 h in advance. This paper, first, proposes an EMPC formulation for a generic deterministic discrete non-linear time varying system with hard state and input constraints, without any a-priori requirements of an optimal economic steady state or optimal periodic trajectory. It is proved that under mild assumptions on terminal cost and region, the asymptotic average economic cost of the proposed method is no worse than the asymptotic average economic cost of any other non-fixed arbitrary reference trajectory which is known only until the current time-step. The EMPC framework is then leveraged for optimal MG dispatch by showing that the problem can be reformulated to satisfy the assumptions required for the asymptotic performance guarantee. Realistic simulations at the Port of San Diego MG demonstrated that the proposed method can also reduce monthly electricity costs in closed-loop with respect to reference trajectories generated by directly optimizing the electricity cost function over the prediction horizon or by tracking an ideal grid import curve in a majority of the cases.