## 3 GSHP District System Modelling  
### Model Set-up  
The ArcGIS-based simulation model with an embedded GSHP design code was used to evaluate the allowed GSHP capacity for the parameter analysis [15; 16]. The embedded GSHP design code in the model is based on the cylinder and line source method, as this method has been considered the most accurate model through a comparison with calibrations from actual operation [21] and is widely used to design ground heat exchangers (GHEs) in commercial software packages. The embedded GSHP design model was verified with commercial software; the standards and verification results are demonstrated in detail in the study of [PERSON] et al. [16]. Both heating and cooling are considered in this code, and the main equations related to the design calculation are described below:  
\(L_{h}\) for heating:  
\[L_{h}=\frac{q_{a}R_{ga}+(q_{lh}-\overline{W}_{h})(R_{b}+PLF_{nt}R_{gm}+R_{gd}F_ {sc})}{t_{g}-\frac{t_{zi}+t_{g0}}{2}-t_{p}} \tag{1}\]  
and \(L_{c}\) for cooling:  
\[L_{c}=\frac{q_{a}R_{ga}+(q_{lc}-\overline{W}_{c})(R_{b}+PLF_{m}R_{gm}+R_{gd}F_ {sc})}{t_{g}-\frac{t_{zi}+t_{g0}}{2}-t_{p}} \tag{2}\]  
where \(F_{sc}\) is the short-circuit heat loss factor, \(PLF_{m}\) is the part-load factor during design month, \(q_{a}\) is the net annual average heat transfer to the ground (W), \(q_{lh}\) is the building design heating block load (W), \(q_{lc}\) is the building design cooling block load (W), \(R_{ga}\) is the effective thermal resistance of the ground in annual pulses (mK/W), \(R_{gd}\) is the effective thermal resistance of the ground in daily pulses (mK/W), \(R_{gm}\) is the effective thermal resistance of the ground in monthly pulses (mK/W), \(R_{b}\) is the thermal resistance of the borehole (mK/W), \(t_{g}\) is the undisturbed ground temperature (K), \(t_{p}\) is the temperature penalty for the interference of adjacent boreholes (K), \(t_{zi}\) is the liquid temperature at the heat pump inlet (K), \(t_{zw}\) is the liquid temperature at the heat pump outlet (K), \(W_{h}\) is the power input at the designed heating load (W) and \(W_{c}\) is the power input at the designed cooling load (W). To evaluate the GSHP district application potential, the C/D ratio (capacity to demand ratio) was used as an indicator and calculated according to Equation (3):  
\[(C/D\,Ratio)_{District}=\sum_{i=1}^{n}BN_{Max,i}\sum_{i=1}^{n}BN_{Req,i} \tag{3}\]  
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 and \(BN_{Req,i}\) is the required borehole number by the \(i\)th building to satisfy its heating and cooling demands. Four parameters were required as inputs for the model, which were heating (\(q_{lh}\)) and cooling demand (\(q_{lc}\)), thermal conductivity (\(k_{g}\)), thermal diffusivity (\(\alpha_{g}\)) and ground temperature (\(t_{g}\)). The related conditions and assumptions used for the GSHP system and the borehole in addition to the spatial data are listed in Table 1.  
The ground thermal conductivity and diffusivity across Westminster was obtained based on the geological map and the thermal property look-up table. The geological map was developed according to the British Geological Survey (BGS) geological map of London. The geological cross-section at a depth of 150 m is illustrated in Figure 2. The measured ground temperatures of London were used in the design. According to the well data from [PERSON] et al. [22], the ground temperature in the design was set to be the average ground temperature value at a certain given depth. The annual heating and cooling loads per building were used in this design calculation. The intensity of heating and cooling demand per building type (in kWh/m\({}^{2}\) per year) was gathered from DECC certificates (compiled and released by the UK Centre for Sustainable Energy), Chartered Institution of Building Services Engineers Guide F and TM 46 and 2011 energy distribution charts (EDCs) [23].