## 3 GSHP District System Modelling
### District Sharing Strategies  
Two sharing strategies were considered for the district GSHP system in this study: (1) Strategy 1 involved individual systems with borehole sharing (Figure 1b), and (2) Strategy 2 used a district central system (Figure 1c).  
**Sharing Strategy 1**: For the individual systems with borehole sharing, a GSHP system was designed for each building based on their individual energy demand, but all the individual systems within the certain district allowed the sharing of land with each other for borehole installation. The C/D ratio ((_C/D Ratio_)_District,ISBS_) and total required borehole number (\(BN_{Req,ISBS}\)) of the district under this sharing strategy were calculated according to the equations below.  
\[(C/D\,Ratio)_{District,ISBS}=(\sum_{i=1}^{n}BN_{Max,i}\Big{|}\sum_{i=1}^{n} BN_{Req,i})\times(1-P_{loss,ISBS}) \tag{4}\]  
\[BN_{Req,ISBS}=\sum_{i=1}^{n}BN_{req,i} \tag{5}\]  
\[BN_{Req,i}=\max[(INT(L_{h,i}/BL_{i})+1),\ (INT(L_{c,i}/BL_{i})+1)] \tag{6}\]  
where \(i\) is the \(i\)th building, \(n\) is the total number of buildings in the district, \(BN_{Max,i}\) is the maximum borehole number allowed to be installed for the \(i\)th building, \(BN_{Req,i}\) is the required borehole number by the \(i\)th building to satisfy its heating and cooling demands, \(P_{loss,ISBS}\) is the percentage of energy loss in the network, \(L_{h,i}\) is the total borehole length required to satisfy the \(i\)th building's heating demand, \(L_{c,i}\) is the total borehole length required to satisfy the \(i\)th building's cooling demand and \(BL_{i}\) is the borehole length of the \(i\)th building (150 m in this study).  
**Sharing Strategy 2**: For the district central system, the energy demands of all the buildings within the district was considered as a whole for GSHP system design. The C/D ratio ((_C/D Ratio_)_District,CS_) and total required borehole number (\(BN_{Req,CS}\)) of the district under this sharing strategy were calculated according to the equations below.  
\[(C/D\,Ratio)_{District,CS}=(\sum_{i=1}^{n}BN_{Max,i}\Big{/}BN_{Req,CS}) \times(1-P_{loss,CS}) \tag{7}\]  
\[BN_{Req,CS}=\max[(INT(L_{h,CS}/BL)+1),\ (INT(L_{c,CS}/BL)+1)] \tag{8}\]  
where \(i\) is the \(i\)th building, \(n\) is the total number of buildings in the district, \(BN_{Max,i}\) is the maximum borehole number allowed to be installed for the \(i\)th building, \(P_{loss,CS}\) is the percentage of energy loss in the network, \(L_{h,CS}\) is the borehole length required to satisfy the heating demand of the district as a whole, \(L_{c,CS}\) is the total borehole length required to satisfy the cooling demand of the district as a whole and BL is the borehole length (150 m in this study).  
For a district system, energy losses are mainly caused in distribution pipes due to the transportation of heat over long distances. Cold losses are normally quite small, especially in Europe, where the annual ground temperatures are close to the distribution temperatures [8]. In this study, \(P_{loss,ISBS}\) in Strategy 1 was ignored, because the working fluid passed directly out of the heat pump to the buildings; \(P_{loss,CS}\) in Strategy 2 was set to be 14% according to the value for the low-energy district system in Europe [24].