Grey-box modeling of the building thermal dynamics for MPC applications: The case of residential space-heating

Abstract

The transition from a conventional energy system to a decarbonized energy system requires an increasing penetration of intermittent renewable energy sources, which brings more fluctuations to the electricity grid. Therefore, increased flexibility is required on the demand side. This thesis focuses on the energy flexibility of residential buildings by activating their thermal mass. Model predictive control (MPC) is acknowledged to be an appropriate control method for this purpose. The thesis addresses MPC using grey-box linear models of the building thermal dynamics. The research is split into two main parts, namely modeling and control. The modeling part can also be further split into data collection and model identification subsections. In the data collection part, the experiments for collecting the data are designed for both virtual and field experiments. The experimental design includes the selection of the excitation signal, the training period, and for field experiments, the influence of the sensor location and dynamics. Thus, different experiments with various excitation signals and training periods have been executed. The results show that the identified parameters are strongly dependent on the types of excitation and the training period for deterministic grey-box models. On the contrary, the identified parameters are less dependent on the excitation signal for stochastic grey-box models. Furthermore, there is no specific period of the space-heating season that is more suited to train a linear time invariant (LTI) grey-box model since weather conditions including solar radiation vary significantly during the entire space-heating season. In the model identification part, a suitable model structure is first investigated using different resistance-capacitance (RC) networks based on existing standards for building energy modeling (like the EN13790 and VDI 6007 standards) and the knowledge of building physics. The model selection is based on the structural and practical identifiability, the physical plausibility and the prediction performance of the grey-box model. The results show that for a mono-zone grey-box model, the second-order model is an appropriate trade-off between overfitting or poor model fidelity. The optimizer for the training of the model parameters is also investigated by comparing the parameters identified using traditional gradient-based optimization routines and global optimization routines. Results reveal that global optimization performs better than gradient-based optimization. The influence of data preprocessing on the grey-box modeling is investigated by using a low-pass filter as well as the influence of input data alignment using anti-causal shift (ACS). Results show that the pre-processing of data does not have a large influence on deterministic models. However, for stochastic models, the parameter values are significantly influenced by the data pre-processing. The identified parameters are strongly correlated with the sampling time (Ts). ACS can prevent the parameter value and variance from getting non-physical for large Ts. Pre-filtering only has a limited influence with ACS, while the pre-filtering influence without ACS does not have a clear trend. Some research is done in this thesis to compare the performance between grey-box and black-box models in the case of deterministic models. Results show that the second-order black-box model shows a similar performance to the second-order grey-box model. However, the physical interpretation of the hidden states and parameters is unknown for black-box models. In the control part, the performance of conventional MPC based on LTI models and adaptive MPC that are able to recalibrate the model parameters during operation is compared. The adaptive MPC is designed to overcome the influence of varying weather conditions during the heating season. Two different candidates for this adaptive control are investigated. Partially Adaptive MPC only updates the effective window area of the grey-box model. The 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 due to the limited number ofparameters updated. The Fully Adaptive MPC outperforms the conventional MPC based on LTI models, especially in avoiding thermal discomfort. Different types of models (e.g., ARX, NARX, SVM) are also compared in an MPC experiment in a supporting paper of this thesis. Results show that the seven states black-box statespace model has the best performance among the MPCs in the study. Using multistep ahead prediction error as the objective function when training the model is beneficial for guaranteeing its prediction performance.