Optimization of Predicted Mean Vote index within Model Predictive Control framework: Computationally tractable solution

Abstract

Recently, there has been an intensive research in the area of Model Predictive Control (MPC) for buildings. The key principle of MPC is a trade-off between energy savings and user welfare making use of predictions of disturbances acting on the system (ambient temperature, solar radiation, occupancy, etc.). Usually, according to international standards, the thermal comfort is represented by a static range for the operative temperature. By contrast, this paper is devoted to the optimization of the Predicted Mean Vote (PMV) index which, opposed to the static temperature range, describes user comfort directly. PMV index is, however, a nonlinear function of various quantities, which limits the applicability and scalability of the control problem formulation. At first, PMV-based formulation is stated, the main differences between typical MPC problem formulation and PMV based formulation are outlined, a computationally tractable approximation of the nonlinear optimal control problem is presented and its accuracy is validated. Finally, control performance is compared both to a conventional and predictive control strategies and it turns out that the proposed optimal control problem formulation shifts the savings potential of typical MPC by additional 10–15% while keeping the comfort within levels defined by standards.