## 4 Calibration Methodology
### Heat Pump Calibration  
For the Apartments building, heating is covered by means of a centralized water-to-water geothermal HP system that provides hot water for the indoor fan coil units and the Domestic Hot Water (DHW) tanks. This HP model has been calibrated using real data from a test bench facility installed at the IREC laboratory. The method used is based on the work presented in [27] for HP identification and the water-to-water HP model developed in [28]. Equations (6) and (7) from [28] displayed below represent the fitting of the heating thermal power and of the electric power consumed by the HP. The experimental data used to fit the equations have been obtained by operating the HP at full load in heating mode (control of return temperature to the condenser of the HP).  
\[\frac{Q_{h}}{Q_{h_{ref}}} =D1+D2\left[\frac{T_{L_{in}}}{T_{ref}}\right]+D3\left[\frac{T_{S_{ in}}}{T_{ref}}\right]+D4\left[\frac{\dot{V}_{L}}{\dot{V}_{L_{ref}}}\right]+D5 \left[\frac{\dot{V}_{S}}{\dot{V}_{S_{ref}}}\right] \tag{6}\] \[\frac{P_{h}}{P_{h_{ref}}} =E_{1}+E_{2}\left[\frac{T_{L_{in}}}{T_{ref}}\right]+E3\left[\frac{ T_{S_{in}}}{T_{ref}}\right]+E4\left[\frac{\dot{V}_{L}}{\dot{V}_{L_{ref}}}\right]+E5 \left[\frac{\dot{V}_{S}}{\dot{V}_{S_{ref}}}\right] \tag{7}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Index** & **ASHRAE** & **Cooling** & **Average** & **Cooling** & **TZ-05** \\  & & **Energy** & **Indoor** & **Supply** & **Indoor** \\ \hline \multirow{2}{*}{**(Hourly)**} & & **Consumption** & **Temperature** & **Air** & **Temperature** \\  & & **(VRV)** & **(Main Building)** & **(AHU)** & **(Atrium)** \\ \hline \multirow{2}{*}{Date} & \multirow{2}{*}{—} & June-August & June-August & May-July & May-July \\  & & 2020 & 2020 & 2020 & 2020 & 2020 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} NMBE (\%) \\ CV(RMSE) \\ R2 (\%) \\ \end{tabular} } & within 10\% & 6.40\% & 0.33\% & 1.43\% & 0.42\% \\  & \(\leq\)30\% & 29.26\% & 1.16\% & 3.62\% & 1.69\% \\ \cline{1-1} \cline{2-6}  & \(\geq\)75\% & 75.23\% & 92.73\% & 85.57\% & 86.98\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of Variable Refrigerant Volume (VRV) and Air Handling Unit (AHU) system evaluation for cooling period, June to August 2020.  
where:  
* \(D1\)-\(D5\), \(E1\)-\(E5\): Fitting coefficients for heating mode
* \(T_{ref}=283.15\): Reference temperature, [K]
* \(T_{Lu}\): Temperature of water entering the load side, [K]
* \(T_{Sin}\): Temperature of water entering the source side, [K]
* \(\dot{V}_{L}\): Load side volumetric flow rate, [m\({}^{3}\)/s]
* \(\dot{V}_{Lref}\): Reference load side volumetric flow rate, [m\({}^{3}\)/s]
* \(\dot{V}_{S}\): Source side volumetric flow rate, [m\({}^{3}\)/s]
* \(\dot{V}_{S_{ref}}\): Reference source side volumetric flow rate, [m\({}^{3}\)/s]
* \(P_{h}\): Power consumption [kW]
* \(P_{h_{ref}}=3.89\): Rated heating power consumption [kW]
* \(Q_{h}\): Condenser heating rate [kW]
* \(Q_{h_{ref}}=42.49\): Rated condenser heating rate [kW]  
A constant volumetric flow rate was used in the experiment as the pump was operating with a constant flow, hence \(\dot{V}_{L}=\dot{V}_{Lref}\) and \(\dot{V}_{S}=\dot{V}_{S_{ref}}\). Coefficients were fitted to the data using ordinary least squares. The \(Q_{h}\) calculation residuals range from 0.01-3.94% of the \(Q_{h}\) value (max. deviation of 1.45 kW for a nominal consumption of 36.8 kW heating power) and are displayed in Figure 0(a). The corresponding \(R^{2}\) value for the heating power fitting is 0.985. \(P_{h}\) residuals range from 0.02-4.78% of the electric power consumption value (max. deviation of 0.29 kW for an electrical power consumption of 6.24 kW). The \(R^{2}\) value for the electric power fitting is 0.988. The residuals are depicted in Figure 0(b).