Adaptive Linear Grey-Box Models for Model Predictive Controller of Residential Buildings

¹ Department of Energy and Process Engineering, Faculty of Engineering, NTNU - Norwegian University of Science and Technology, 7034 Trondheim, Norway
² Department of Engineering Cybernetics, Faculty of Information Technology and Electrical Engineering, NTNU - Norwegian University of Science and Technology, 7034 Trondheim, Norway

^* corresponding author: xingji.yu@ntnu.no

Abstract

Model predictive control (MPC) is an advanced optimal control technique to minimize a control objective while satisfying a set of constraints and is well suited to activate the building energy flexibility. The MPC controller performance depends on the accuracy of the model prediction. Inaccurate predictions can directly lead to low control performance. Linear time-invariant (LTI) models are often used in MPC in buildings. However, LTI models do not adapt to the weather conditions varying throughout the whole space-heating season, which makes the MPC based on LTI models not perform well over a long period of time. Therefore, this study introduces an adaptive MPC where the parameters of a linear grey-box model are continuously updated in real-time. Two alternative versions of this adaptive control are investigated. The first one, called partially adaptive MPC, only updates the effective window area of the grey-box model, while the second one, called fully adaptive MPC, updates all the parameters of the grey-box model. Results show that the partially adaptive MPC is not able to deliver satisfactory prediction performance. The fully adaptive MPC shows better performance compared to the other models when implemented in a MPC, especially in avoiding thermal comfort violation.