A state-space modeling approach for predictive control of buildings with mixed-mode cooling

The paper presents a control-oriented modeling approach for multi-zone buildings with mixed-mode cooling. It extents previous work on physical or black-box modeling to a linear state-space representation with varying coefficient matrices to approximate the nonlinearity caused due to the heat extraction by natural ventilation. This approach is validated with experimental data collected in a two-zone test-building under various operation modes. The detailed (white-box) linear time-variant state-space (LTV-SS) model is then used as a true representation of the building to identify the parameters of a low-order LTV-SS model (gray-box) that predicts the south and north zone air temperature with mean square error of 0.59 degrees C and 0.50 degrees C respectively. A five-month simulation study showed that mixed-mode cooling strategies can effectively reduce building energy consumption by 40.7% when switching schedules are made based on heuristics and by 31.0% when a predictive control strategy is used. However, the heuristic strategy would lead to a total deviation of operative temperature of 459.7 degrees C from the desired range while the corresponding number for the predictive strategy was 45.2 degrees C. The predictive controller with the simplified model resulted in 5% less total window opening hours compared to the schedules predicted with the detailed model. However, this did not cause a notable difference in the MPC performance in terms of energy consumption and operative temperature violations.