## 3 Results  
To validate the performance of the developed model, it is first used to simulate the operation of two spaces (O22-508-1 and O22-511-2) from the 9-13 April 2018, where measurements for occupancy and CO\({}_{2}\) concentration are available for comparison. For this validation, the CO\({}_{2}\) generation per (measured) occupant is estimated to be \(K_{gen}\) = 10 L/h based data from a prior week. The models predicted CO\({}_{2}\) development and damper position for O22-511-2 is compared to measurements in Figure 6. From this comparison, it seems the model replicates real operation fairly well, although it appears that the actual system keeps the damper \(\sim\)20% open for some time after the CO\({}_{2}\) concentration falls below 600 ppm and consequently has significantly lower CO\({}_{2}\) concentration at night than predicted. Five scenarios are explored for the operation of ventilation in the teaching and office building: one with the rule-based control (\"Baseline\") and four using MPC with different objective weights (\"Balanced\", \"Air quality\", \"Economic\" and \"Environmental\"). Relative weighting in the scenarios is illustrated by Figure 7. The different MPC strategies in the scenarios are designed to represent different objective priorities:  
* Balanced: Aims to improve both air quality and cost compared to the baseline. * Air quality: Focus on achieving optimal air quality without excessive electricity consumption. * Economic: Focus on cost reduction while preserving acceptable air quality. * Environmental: Focus on CO\({}_{2}\) emission reduction while preserving acceptable air quality. At equal weighting the KPI-cost relation is: 1000 ppm-h-person = 0.81 DKK, i.e., raising the CO\({}_{2}\) concentration by 1000 ppm above the threshold in one hour for one person produces the same penalty as increasing the electricity cost by 0.81 DKK. The emission-cost relation at equal weighting is 4.49 kg\({}_{\text{CO}_{2}}\) = 1 DKK, since the average electricity price (January-June 2024) in DKK is 4.49 times the average CO\({}_{2}\) emission in kg. The electricity prices and CO\({}_{2}\) emission factors for the simulated period are shown in Figure 8.  
Figure 6: Simulated and measured values for CO\({}_{2}\) concentration (**left**) and ventilation damper position (**right**) in the building space “O22-511-2” (139 m\({}^{2}\) teaching room) during a workweek in 2018. The MPC controllers are not provided with perfect occupancy predictions, as this would be unrealistic for a real application. Since the optimization often keeps CO2 levels just below the concentration threshold, a larger than expected number of occupants will often lead to peaks significantly above the threshold even if the controller is prioritizing air quality. To counter this, the MPC optimization uses a 50 ppm lower threshold in the \"Air quality\" scenario and a 25 ppm lower threshold in the \"Balanced\" scenario. Figure 9 shows the operation in building space \(\mathcal{O}\)22-511-2 in the \"Balanced\" MPC scenario. The few hours with fully opened damper on the 9 th and 10 th of March are due to negative electricity prices. Figure 10 illustrates the performance of ventilation system 1 with rule-base control. Figure 8: Electricity prices and CO2 emission factors for the one-week simulation period used in MPC simulation. Figure 7: Relative weightings of each objective in the multi-objective optimization performed in the four simulated scenarios using MPC. Figure 9: Operation of \(\mathcal{O}\)22-511-2 (139 m\({}^{2}\) teaching space) with the “Balanced” MPC controller for one week (Wednesday–Tuesday). parameter values from building descriptions, parameter estimation based on historical operation data and parameter estimation based on experiments in the literature. The model validation showed that model predictions matched the actual system behavior with reasonable accuracy. Some of the deviation between model predictions and measurements seems to be caused by discrepancy between the expected and actual control strategy.