Nonlinear model predictive control of chiller plant demand response with Koopman bilinear model and Krylov-subspace model reduction

The demand response (DR) operation of chiller plants has been approached with model predictive control (MPC) strategies, based on day -ahead electricity price, knowledge of upcoming weather and load profiles. Since chiller plants feature significant nonlinearities across wide variations in ambient and load conditions, nonlinear MPC (NMPC) is the typical alternative to piecewise linear MPC design, however, suffers from high computational loads. In this paper, an NMPC based chiller plant DR operation is proposed based on data -driven Koopman bilinear form (KBF) dynamic model structure. A generalized tangential interpolation based Krylovsubspace model reduction procedure is applied to the KBF model to yield parsimonious model in the Koopman lifted subspace. Then, the McCormick relaxation is applied to convexify the bilinear terms for the constrained optimization problem formulation associated with the MPC design of the reduced -order KBF system. The KBF based convexified MPC design minimizes the overall energy cost that combines the time -of -use (TOU) and demand charges, with the cooling load regulated in real time. The effectiveness of the proposed control strategy is shown with a Modelica-based dynamic chiller plant model via a Functional Mockup Interface (FMI) based Modelica-Python co -simulation platform.