## 2 Methodology
### Analysis Methodology  
As shown in Figure 1, during the field test, the water temperature, flow rate and water pressure of the user-side distribution system and ground-side distribution system were monitored; and the electric power of heat pumps and water pumps were measured at the same time. Among those 17 systems, the longest monitoring lasted for two heating seasons (15 November to 15 March) and the shortest lasted for 1 week, both with the sample interval of 10 min. After gathering plentiful data, some indexes were put forward to evaluate the energy performance of heat pump systems, as well as the heat transfer performance of GHEs. (1) As for the ground side, heat extraction rate (\(Q_{g}\)) can be calculated with Equation (1)  
\[Q_{g}=G_{g}\cdotp\cdot C_{p}\Big{(}T_{g,\rho}-T_{g,i}\Big{)}, \tag{1}\]  
where \(G_{g}\) is the flow rate of the ground side in m\({}^{3}\)/h, \(\rho\) is the water density in kg/m\({}^{3}\), \(C_{p}\) is the water heat capacity in kW/(kg\(\cdot\)\({}^{\circ}\)C), \(T_{g,\rho}\) and \(T_{g,i}\) are outlet and inlet water temperature of GHEs in \({}^{\circ}\)C.  
Figure 1: Typical system diagram and measuring points of heat pump systems for space heating ((1) indoor heating systems; (2) user-side water pump; (3) condenser; (4) compressor; (5) electronic expansion valve; (6) evaporator; (7) ground side water pump; (8) heat source (ground heat exchangers—GHEs)). Figure 2: A diagram of the deep borehole heat exchangers (DBHEs). (2) Accumulated heat extraction (\(Q_{g,a}\)) in 24 h can be calculated with Equation (2)  
\[Q_{g,a}=\int\limits_{0}^{24}Q_{g,i}\cdot di, \tag{2}\]  
where \(Q_{g,i}\) is the average heat extraction in \(i\) hour in kW. (3) Heat transferred per unit length (\(q_{g}\)) is raised to evaluate the heat transfer performance of GHEs, which can be calculated with Equation (3). \[q_{g}=\frac{Q_{g}}{N\cdot H}, \tag{3}\]  
where \(N\) is the number of GHEs and \(H\) is the length of GHEs in m.  
(4) As for the user side, the heat load is calculated with Equation (4). \[Q_{u}=G_{u}\cdot p\cdot C_{p}\cdot(T_{u,s}-T_{u,r}), \tag{4}\]  
where \(G_{u}\) is the flow rate of the user side in m\({}^{3}\)/h, \(T_{u,s}\) and \(T_{u,r}\) are supply and return water temperature in the user side in \({}^{\circ}\)C.  
(5) As for the heat pump systems, the coefficient of performance (\(COP\)) is put forward to evaluate the energy performance of heat pumps, which is calculated with Equation (5). \[COP=\frac{Q_{u}}{W_{hp}}, \tag{5}\]  
where \(W_{hp}\) is the electric power of heat pumps in kW. (6) Theoretical \(COP\) (\(COP_{t}\)) represents the upper limit value of \(COP\) under the specific operating conditions, which was determined by the external factors of the user side and heat source side. It could be calculated with Equation (6), and the higher \(COP_{t}\) means the better operating conditions. \[COP_{t}=\frac{T_{c}}{T_{c}-T_{e}}, \tag{6}\]  
where \(T_{e}\) and \(T_{c}\) are evaporating and condensing temperature in K. Due to the difficulty in monitoring the \(T_{e}\) and \(T_{c}\), the values could be reckoned with Equations (7) and (8),  
\[T_{c}=T_{u,s}+2, \tag{7}\]  
\[T_{e}=T_{g,i}-2. \tag{8}\]  
(7) Internal efficiency of heat pumps (\(DCOP\)) [22] is the ratio of \(COP\) and \(COP_{t}\), which is put forward to evaluate the proximity between \(COP\) and \(COP_{t}\) caused by the internal factors of the heat pumps. It could be calculated with Equation (9),  
Figure 1:0  
(8) Temperature difference between condensing and evaporating temperature (\(T_{ce}\)) is used to reflect the compressor ration heat pumps under specific condition. It could be calculated with Equation (10),  
Figure 1:1(9) Operation load ratio (\(LR\)) is the ratio of practical heating load with rated heating capacity, which could be calculated with Equation (11),  
Figure 1:2  
where \(Q_{u,0}\) is the rated heating capacity of the heat pump in kW.