A state-space modeling approach and multi-level optimization algorithm for predictive control of multi-zone buildings with mixed-mode cooling

• Developed MPC strategies for buildings with mixed-mode cooling.
• Developed a linear time-variant state-space modeling representation.
• Implemented a model validation procedure.
• Formulated a multi-level optimization topology with progressive refinement.

The paper presents a control-oriented modeling approach for multi-zone buildings with mixed-mode cooling, based on the linear state-space representation with varying coefficient matrices. Key features are the time-variant thermal resistances, associated with the heat extraction due to airflow, calculated using an airflow network model. This approach was validated with experimental data collected in a two-zone test-building under four operation modes. A forward linear time-variant state-space (LTV-SS) model, developed based on first principles, was then used as a true representation of the building, to identify the parameters of a low-order LTV-SS gray-box model. The low-order model can predict the building thermal dynamics with sufficient accuracy with a root mean square error (RMSE) of 0.58 °C for the air and 1.08 °C for the area-weighted mean surface temperature in the south direct gain zone. Furthermore, the study develops a progressive refinement (ProRe) optimization method, following the multi-level optimization topology and branch and bound decision trimming strategy, to find sequences of binary (open/close) decisions for the motorized windows. Due to the significant improvement in computing time, the models and algorithms presented in this paper enable long-term simulation for MPC performance evaluation and implementation of predictive strategies in real controllers.