## 3 Results and Discussion
### Analysis of Energy Performance of Heat Pump Systems
#### 3.2.2 Analysis of Operation Characteristics for Heat Pump in MD-GHPs  
Figure 11 compares the \(T_{\alpha c}\) in SD-GHPs and MD-GHPs. The \(T_{ce}\) in SD-GHPs varies from 29.9 \({}^{\circ}\)C to 41.4 \({}^{\circ}\)C with a median of 37.8 \({}^{\circ}\)C. While the \(T_{\alpha c}\) in MD-GHPs varies from 22 \({}^{\circ}\)C to 32.6 \({}^{\circ}\)C with a median of 25.8 \({}^{\circ}\)C, which is nearly 11 \({}^{\circ}\)C lower than that of SD-GHPs benefitting from high-temperature heat source. Consequently, the heat pumps applied in MD-GHPs should match the operating condition with a high-temperature heat source and operate with high _DCOP_ under small \(T_{ce}\). In this section, several cases are analyzed in detail from this point. Figure 10: Comparison of Internal efficiency of heat pumps (_DCOP_). Figure 9: Comparison of Theoretical coefficient of performance (_COP\({}_{t}\)_). Regarding MD-GHPs in MG-5--where the heat pumps use constant speed compressor like heat pumps in SD-GHPs, fail to perform well with a high-temperature heat source. The designed \(T_{u,s}\) and \(T_{g,i}\) are 50 \({}^{\circ}\)C and 20 \({}^{\circ}\)C; thus, the \(T_{c}\) and \(T_{e}\) are calculated to be 52 \({}^{\circ}\)C and 18 \({}^{\circ}\)C. So the designed \(T_{ce}\) is calculated to be 34 \({}^{\circ}\)C. As shown in Figure 12, during the whole heating season, the heat pumps hardly operate at rated \(T_{ce}\), with only 0.5% at 29\(\sim\)31 \({}^{\circ}\)C, but mainly concentrates on 25\(\sim\)28 \({}^{\circ}\)C, with the proportion of 59.8%. Besides, 32% operates with \(T_{ce}\) lower than 25 \({}^{\circ}\)C. That is to say, due to the high-temperature heat source, the practical \(T_{ce}\) is generally lower than the designed value. Moreover, for the operation load ratio (\(LR\)), Figure 13 shows that the operating conditions with \(LR\) higher than 90% only accounted for 10.9% among the whole heating season. Most conditions concentrate on \(LR\) between 70-90%, which accounted for 85.4%. Similarly, the heat pumps operate with lower efficiency under part \(LR\) most the time, due to the constant speed compressors. Figure 11: Comparison of Temperature difference between condensing and evaporating temperature (\(T_{ce}\)). Figure 12: \(T_{ce}\) frequency distribution of the heat pump in MG-5 throughout the heating season. As shown in Figure 14, caused by the operation with part \(LR\) and lower \(T_{ce}\), the _DCOP_ of heat pumps in MG-5 stays at a poor level for most of the time. Field test results show that the highest value of _DCOP_ is only 0.54, while 98.4% of values are lower than 0.50 and 27.9% of values are lower than 0.40. Even though the high-temperature heat source provides better operating conditions for heat pumps in MG-5 where the _COP\({}_{t}\)_ reaches 10.53-25.58. However, due to the low _DCOP_, the practical highest _COP_ of heat pumps only reaches 6.60. Even in 27.0% conditions, the _COP_ is lower than 5, and the high-temperature heat source is underutilized and wasted. That is to say, when the medium-geothermal energy provides a high-temperature heat source for MD-GHPs, it creates operating conditions with relatively low \(T_{ce}\). However, the conventional constant speed compressor fails to meet the highest _DCOP_ under these conditions. In the meantime, the \(LR\) of heat pumps mainly concentrates between 70% and 90%, hardly meet the full \(LR\). Therefore, a kind of variable speed compressor which has high _DCOP_ among a wide range of \(T_{ce}\) and \(LR\), especially suitable for lower \(T_{ce}\) should be analyzed and designed. As for MG-7, the heat pump uses a permanent-magnetic synchronous frequency-convertible (PSF) centrifugal compressor [11]. The PSF centrifugal compressor can perform with high _DCOP_ among a wide range of operating conditions through adjusting of compressor frequency, which is suitable for application in MD-GHPs. Figure 15 then depicts the _DCOP_ distribution of PSF heat pump in MG-7 during the operation.