## 2 Materials and Methods
### Case Study  
To evaluate the model performance and test different modes of control, a case study is conducted. The building considered is a modern and highly energy efficient teaching and office building located at the Odense Campus of the University of Southern Denmark. Finished in 2015, the building consists of three floors and a basement with a total area of around 8500 m\({}^{2}\). It contains 21 teaching rooms, eight study zones and a number of smaller spaces including personal offices, meetings rooms, toilets, copy rooms and tea kitchens. The teaching and office building has four separate ventilation systems, which each service a building quadrant. It is commonly used for building energy studies and is further described by [PERSON] et al. [23]. From the building schematics, a total of 73 ventilated building spaces are identified and included in the model. Occupancy measurements are only available for a few building spaces with poor data quality, so except for the model validation, the simulations utilize generated occupancy schedules based on space type, space size, time of day, category of day (weekday, holiday, etc.) and an element of randomness. The applied occupancy generation method is included in the model framework as a general occupancy estimation tool, which can be scaled to other buildings and space types. Currently, the ventilation damper openings in the teaching and office building are documented to be controlled with a four step rule-based strategy dependent on space CO\({}_{2}\) concentration:  
\[C_{S}<600\;\mathrm{ppm}: 0\%\;\mathrm{opening}\] \[600\;\mathrm{ppm}\leq C_{S}<750\;\mathrm{ppm}: 45\%\;\mathrm{opening}\] \[750\;\mathrm{ppm}\leq C_{S}<900\;\mathrm{ppm}: 70\%\;\mathrm{opening}\] \[900\;\mathrm{ppm}\leq C_{S} : 100\%\;\mathrm{opening}\]  
These rules will also be used for the rule-based CO\({}_{2}\) controller model in this study to replicate the actual operation of the building. Both the supply and exhaust fan in all of the building's four ventilation systems have the same technical specifications according to the building documentation: \(Q_{fan,max}\) = 35,000 m\({}^{3}\)/h and \(W_{fan,max}\) = 8667.4 W. The fan constants \(c_{1}-c_{5}\) are not documented, but are instead estimated using operational data from 2022. This parameter estimation in conducted using data from \"ventilation system 1\" (VEN1) and the determined fan constants are assumed to apply for all four ventilation systems. Figure 3 illustrates the relation between the measured flow rate and power consumption as well as flow rate and specific power consumption (i.e., power-to-flow-ratio) for the supply fan in 2022. While not evident from Figure 3, data analysis shows that both the supply and exhaust fan in VEN1 are completely turned off with no power consumption 21.7% of the time (typically during night). To correctly model these instances, it is chosen that \(c_{1}=0\) (i.e., no power consumption for \(Q_{fan}=0\)) for all fans. Close inspection of Figure 3 reveals that for \(Q_{fan}>\) 1.2 m\({}^{3}\)/h, the data point forms two separate \"belts\" with a clear relation between flow rate and power consumption. Additionally, it is noted that for low flow rates (around 0.25 to 0.6 m\({}^{3}\)/h) there is seemingly little correlation between flow rate and power usage. In Figure 4, the data points are grouped based on flow rate and specific power consumption to highlight the different identified operation areas. With larger graph sizes, the clear separation between \"Group 1\" and \"Group 2\" is more evident. Data analysis shows that over 99% of the data points in \"Group 1\" (Figure 4) are measurements from before 17 June 2022 00:00:00 and over 99% of the data points in \"Group 2\" are measurements from after this time. A similar change around the same time point is observed for the exhaust fan in VEN1. Clearly some change to the system occurred  
Figure 4: Flow vs. specific power consumption for the supply fan in “ventilation system 1”. The data points are separated in three color groups according to graph coordinates.