## 3 Results and Discussion
### Analysis of Energy Performance of Heat Pump Systems
#### 3.2.3 Analysis of Water Transfer Performance of Ground Side and User Side  
There is always a guess that since the depth of DBHEs in MD-GHPs is much higher than the depth of GHEs in SD-GHPs, the water resistance of the ground side in MD-GHPs is much higher than that in SD-GHPs. Therefore, the water transfer performance of the ground side in MD-GHPs should be lower than that in SD-GHPs. However, as depicted in Figure 17, the field test results show that the \(WT_{g}\) in SD-GHPs varies from 11.1 to 53.9 with a median of 25.4. While the \(WT_{g}\) in MD-GHPs varies from 27 to 101.7 with a median of 36.4, which is better than that of SD-GHPs. As for the user side, the \(WT_{u}\) in SD-GHPs varies from 8.8 to 32.6 with a median of 21.3. While the \(WT_{u}\) in MD-GHPs varies from 13.5 to 63.7 with a median of 23.7. There is no obvious difference in \(WT_{u}\) in SD-GHPs and MD-GHPs, since they are applied for space heating with similar user side.  
Figure 16: _DCOP_ frequency distribution of the heat pump in MG-7 throughout the heating season.  
Figure 15: _DCOP_ distribution of permanent-magnetic synchronous frequency-convertible (PSF) heat pump in MG-7 throughout the heating season.  
As analyzed in Equation (14), the higher value of \(\Delta t\), \(\eta\), and the lower value of \(h\) contribute to the higher value of \(WTF\). The field test results of \(\Delta t,h,\)\(\eta\) are presented in Figures 18-20. It can be seen that benefitting from high-temperature heat source and long depth of DBHEs, the \(\Delta t\) of the ground side in MD-GHPs can reach as high as 18 \({}^{\circ}\)C with a median of 10.4 \({}^{\circ}\)C, which is much higher than that in SD-GHPs, where the median is only 2.2 \({}^{\circ}\)C. In conclusion, the high \(\Delta t\) of the ground side in MD-GHPs contributes much to the promotion of \(WTF_{g}\). Besides, the \(\Delta t\) of the user side in both SD-GHPs and MD-GHPs are not high enough, which concentrate lower than 5 \({}^{\circ}\)C. Therefore, the water pumps in the user side should be installed with variable speed drivers and adjust operation frequency to meet the flow rate demand, as well as avoid low \(\Delta t\) syndrome.  
The high \(\Delta t\) of the ground side in MD-GHPs also contributes to reducing the water resistance in DBHEs. Results show that the median of water resistance in DHBEs is 41.6 mH\({}_{2}\)O. While the water resistance in GHEs in SD-GHPs concentrates among 24.2 mH\({}_{2}\)O to 34 mH\({}_{2}\)O. Considering that the depth of DBHEs in MD-GHPs is nearly 20-25 times than the depth of GHEs in SD-GHPs, the increase in water resistance of DBHEs is not as high as imagine, which mainly comes from the high \(\Delta t\) and low flow rate of the ground side in MD-GHPs. However, as for the user side, due to the low \(\Delta t\) and high flow rate, as well as unreasonable local resistance, the water resistance is over than 30 mH\({}_{2}\)O, which further decrease the \(WTF_{u}\).  
Figure 17: Comparison of Water transport factor (\(WTF\)) in the user side and ground side.  
Figure 18: Comparison of water temperature difference in the user side and ground side.  
However, as for the energy efficiency of water pumps, due to the lack of specific design to meet the demand of high water resistance and low flow rate in DBHEs, the \(\eta\) of water pumps in the ground side of MD-GHPs concentrate on 0.31 to 0.43, which is much lower than \(\eta\) of water pumps in the ground side of SD-GHPs, which is mainly higher than 0.51. Therefore, the rated parameters of water pumps for DBHEs should be analyzed and optimized to meet the water flow characteristics of DBHEs; thus, the \(WTF_{g}\) of MD-GHPs could be further improved.