## 2 Establishment of the Simulation Model  
### Compressor Simulation Model  
The performance indicators of a compressor are mainly reflected by two parameters: the flow rate and power. The flow rate is determined by the suction volume and suction density of the compressor. Typically, the suction volume of a positive displacement compressor is not constant, which results in a deviation in the volumetric flow rate, represented by volumetric efficiency. Therefore, the actual mass flow rate is defined by the following formula:  
\[m_{r}=\frac{\eta_{v}\times N\times V_{d}}{60\times v_{suc}} \tag{1}\]  
where \(m_{r}\) is the mass flow rate of the refrigerant, kg/s, \(N\) is the compressor speed, rpm, \(v_{suc}\) is the suction specific volume, m\({}^{3}\)/kg, \(V_{d}\) is the theoretical swept volume, ml/rev, and \(\eta_{v}\) is the volumetric efficiency. The factors influencing volumetric efficiency include compression clearance and leakage due to the pressure ratio. Generally, the expression for volumetric efficiency can be defined as follows:  
\[\eta_{v}=1-C\times((\frac{P_{dis}}{P_{suc}})^{\sfrac{1}{n}}-1) \tag{2}\]  
where \(C\) is the clearance volume ratio, \(P_{dis}\) is discharge pressure, \(P_{suc}\) is suction pressure, and \(n\) is the polytropic index. According to the above formula, [PERSON] and others [14] expressed the compressor's volumetric efficiency as follows:  
\[\eta_{v}=b_{1}+b_{2}\times((\frac{P_{dis}}{P_{suc}})^{\sfrac{1}{n}}) \tag{3}\]  
where \(b_{1}\) and \(b_{2}\) are the volumetric efficiency coefficients, and \(k\) is the adiabatic index of the refrigerant. According to the ASHRAE Toolkit, the shaft power of the compressor can be expressed as  
\[W=(1+\alpha)W_{t}+W_{loss} \tag{4}\]  
where \(W_{loss}\) is the loss constant due to mechanical efficiency, and \(\alpha\) is the ratio of mechanical loss to power consumption \(W_{t}\). Assuming the compression process is considered an ideal isentropic process (\(pv^{k}=Const\)), the theoretical power per unit mass flow rate of the compressor can be expressed as follows:  
\[W_{i}=\int_{suc}^{dis}vdp= P_{suc}\times V_{suc}\times\frac{k}{k-1}\times\left[(\frac{P_{dis}}{ P_{suc}}\frac{k-1}{k}-1\right] \tag{5}\]  
where \(W_{i}\) is the ideal power consumption, \(W\). In the above formula, k cannot represent the actual polytropic compression process. Therefore, building on Negrao [14], [PERSON] [15] calculates the actual power of the compressor using the following equation:  
\[W=P_{suc}\times V_{suc}\times a_{1}\times\left[(\frac{P_{dis}}{P_{suc}})^{a_{ 2}+\frac{k-1}{k}}+a_{3}/P_{dis}\right]+W_{loss} \tag{6}\]  
Thus, the isentropic efficiency of the compressor can be calculated using the following equation:  
\[\eta_{is}=\frac{V_{suc}\times(h_{is}-h_{suc})}{v_{suc}\times W} \tag{7}\]  
where \(a_{1}\), \(a_{2}\), \(a_{3}\) are the shaft power coefficients, \(\eta_{is}\) is the isentropic efficiency, \(V_{suc}\) is the actual suction volume, m\({}^{3}\)/s, and \(W\) is the actual power consumption, \(W\). The above formulas apply to a compressor at a fixed frequency or a variable frequency compressor operating at its rated frequency. For variable frequency compressors operating at non-rated frequencies, the volumetric efficiency and isentropic efficiency need to be adjusted through speed or frequency.