## 2 Methods
### Theoretical Modelling and Simulation Tools  
The ASHP for space heating used in North China normally adopt single stage compression or quasi-two-stage compression refrigeration cycles. The thermal processes of refrigerants in the typical single stage vapor-compression and quasi-two-stage compression ASHP cycle are shown in Figures 3 and 4. \begin{table}
\begin{tabular}{l c c c c c} \hline
**Items** & **RHR-1** & **R134a** & **R10A** & **R407C** & **R22** \\ \hline Molecular weight (g mol\({}^{-1}\)) & 62.54 & 102.03 & 72.58 & 86.20 & 86.27 \\ Critical temperature (C) & 101.2 & 101.1 & 71.4 & 86 & 96.1 \\ Critical pressure (MPa) & 5.18 & 4.06 & 4.90 & 4.63 & 4.99 \\ Critical density (kg m\({}^{-3}\)) & 377 & 512 & 489 & 527 & 526 \\ boiling point at 101.3A (C) & \(-51.70-24\) & \(-26.1\) & \(-51.4\) & \(-43.6\) & \(-40.8\) \\ Toxicity/Flammability & A2 & A1 & A1 & A1 & A1 \\ GDP * & 0 & 0 & 0 & 0 & 0.04 \\ GWP (100 years) * & 279 & 1370 & 2100 & 1700 & 1790 \\ \hline \end{tabular}  
* Ozone Depression Potential,
* Global Warming Potential.  
\end{table} 
Table 1: Physical properties of compared refrigerants. Figure 4: The schematic and pressure-enthalpy diagram of quasi-two-stage vapor-compression air source heat pump (ASHP). Figure 3: The schematic and pressure-enthalpy diagram of single stage vapor-compression air source heat pump (ASHP). In the single stage cycle, refrigerant condenses from Point 2\({}^{\prime}\) to Point 3 and releases heat to circulation water which is used as heating medium. The high-pressure liquid refrigerants at pPoint 3 then depressurizes to low pressure and low temperature liquid-vapor mixture (Point 4) through throttling valve. The refrigerant evaporates from Point 4 to Point 1 and takes heat from outdoor environment. During the compression process from Point 1 to Point 2\({}^{\prime}\), electrical power is consumed by compressor. The theoretical \(COP_{h}\) of the heat pump can thus be calculated with the enthalpy differences of refrigerant during the condensing and compression process together with the refrigeration efficiency. The theoretical \(COP_{h}\) of a single stage compression ASHP system for heating can be calculated with Equation (3)  
\[COP_{h-th}=\frac{h_{2}^{\prime}-h_{3}}{h_{2}^{\prime}-h_{1}} \tag{3}\]  
where \(h_{1}\) is the refrigerant enthalpy at the inlet point of the compressor, kJ/kg. \(h_{2}^{\prime}\) is the refrigerant enthalpy at the outlet point of the compressor, kJ/kg. \(h_{3}\) is the enthalpy of refrigerant leaving the condenser, kJ/kg. \(h_{2}^{\prime}\) can be calculated by Equation (4)  
\[h_{2}^{\prime}=h_{1}+\frac{h_{2}-h_{1}}{\eta_{is}} \tag{4}\]  
where \(h_{2}\) is the enthalpy of refrigerant at condensing pressure and has equal entropy with the refrigerant at \(h_{1}\), kJ/kg. \(\eta_{is}\) is the isentropic efficiency of the compression. The \(COP_{h}\) calculated with Equation (3) is the theoretical COP of refrigerant cycle regardless of energy loss through power or heat transfer (energy transferred to surrounding environment which is not used for heating circulation water). Considering the energy loss through power-engine transfer in the compressor and heat loss during heat transfer between refrigerant and water in condenser, Equation (5) was used to formulate the actual \(COP_{h}\) of ASHP. \[COP_{h}=\eta_{e}\eta_{d}\eta_{m}\eta_{l}\frac{h_{2}^{\prime}-h_{3}}{h_{2}^{ \prime}-h_{1}} \tag{5}\]  
where \(\eta_{m}\), \(\eta_{d}\), and \(\eta_{e}\) are the motor efficiency, engine transmission efficiency (from motor to compressor) and friction efficiency of the compressor. \(\eta_{t}\) is the heat transfer efficiency from refrigerant to water in the condenser. In the quasi-two-stage vapor-compression ASHP, the high temperature and high-pressure refrigerant vapor discharged from the compressor condenses to high temperature and high-pressure refrigerant liquid in the condenser. The heat released from the condensing process of refrigerant is used for space heating in buildings. The refrigerant liquid from the condenser is then divided two ways.