Robust economic MPC for a power management scenario with uncertainties

This paper presents a novel incorporation of probabilistic constraints and Second Order Cone Programming (SOCP) with economic Model Predictive Control (MPC). Hereby the performance of the controller is robustyfied in the presence of both model and forecast uncertainties. Economic MPC is a receding horizon controller that minimizes an economic objective function and we have previously demonstrated its usage to include a refrigeration system as a controllable power consumer with a portfolio of power generators such that total cost is minimized. The main focus for our work is power management of the refrigeration system. Whereas our previous study was entirely deterministic, models of e.g. supermarket refrigeration systems are uncertain, as are forecasts of outdoor temperatures and electricity demand. The linear program we have formulated does not cope with uncertainties and thus it is, liable to drive an optimal solution to an infeasible or very expensive solution. The main contribution of this paper is the Finite Impulse Response (FIR) formulation of the system models, allowing us to describe and handle model uncertainties in the framework of probabilistic constraints. Our new solution using this setup for robustifying the economic MPC is demonstrated by simulation of a small conceptual example. The scenario is primarily chosen to illustrate the effect of our proposed method in that it can be compared with our previous deterministic simulations.