Comparison of time-invariant and adaptive linear grey-box models for model predictive control of residential buildings

Abstract

Model predictive control (MPC) is a promising optimal control technique for activating building energy flexibility using its thermal mass. The performance of the MPC controller is directly related to the accuracy of the model prediction. Grey-box models, based on physical laws and calibrated on measurement data, are commonly used to represent the building thermal dynamics in MPC. Most research works use Linear Time-Invariant (LTI) grey-box models even though weather conditions vary significantly throughout the heating season. This is critical as inaccurate model prediction can lead to a lower performance of the MPC controller. This study introduces two adaptive MPC schemes to overcome this limitation of LTI models. The first one, called the Partially Adaptive MPC, only updates the effective window area of the prediction model. The second one, called the Fully Adaptive MPC, updates all the parameters of the grey-box model. The adaptive MPC performance is compared with MPC using LTI models in two different tests. The simulation-based results show that MPC based on LTI performs well if the control model is trained during a period with similar weather conditions as the period when the MPC will be applied. The Partially Adaptive MPC is unable to deliver satisfactory prediction performance due to the limited number of parameters that are updated. The Fully Adaptive MPC has the best performance compared to the other MPCs, especially as it avoids thermal comfort violations.