# Techno-Economic Analysis of the Peak Shifting Strategy Based on Time-of-Use Tariff for Cold Stores
## 3 Methodology
### Thermodynamic Model  
To supplement the missing cooling load, a thermodynamic model of the refrigeration system is developed in this paper. Generally speaking, the modeling process should start by considering three fundamental conservation relations, including the continuity equation, the momentum equation, and the energy equation. The flow of the refrigerant in the pipeline is relatively smooth and therefore can be seen as a steady flow state, and the pressure drop is negligible, which means the continuity equation and the momentum equation naturally hold. Hence, only the energy equation needs to be considered while modeling. The positions of the key points in the refrigeration cycle are tagged as 1, 2, 3, and 4 in Figure 1b. Points 1 and 2 represent the suction and the discharge state of the compressor unit. Point 3 represents the state before throttling, and point 4 represents the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operation Pattern** & **Low Load** & **Medium Load** & **High Load** \\ \hline Load Calculation & \textless{}100\% & 100–150\% & \textgreater{}150\% \\ Load Setting & 100\% + 0\% & 75\% + 75\% & 100\% + 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Compressor operation pattern under different loads.  
Figure 3: Detailed calculation flow of the peak shifting strategy.  
state before evaporation. By quantitatively determining the thermodynamic state of the refrigerant at the import and export of each component, the enthalpy changes during each working process can be calculated [36].  
The compression process can be simplified as an isentropic process whose isentropic compression power is given by Equation (4). The isentropic efficiency is introduced to evaluate the imperfection of the compression process. In this paper, the efficiency is defined as the ratio of the isentropic compression power to the input power of the drive motor, determined by Equation (5). According to experience, the isentropic efficiency of the compressor is strongly related to the pressure ratio [36]. In this paper, the efficiency is fitted based on the actual experimental data of the compressor. The fitting formula of the efficiency is shown in Equation (6):  
\[P_{\text{is,com}}=m\cdot(h_{\text{2,is}}-h_{1}) \tag{4}\]  
\[P_{\text{com}}=m\cdot(h_{\text{2,is}}-h_{1})/\eta_{\text{is}} \tag{5}\]  
\[\eta_{\text{is}}=-0.0015\cdot\epsilon^{2}+0.0044\cdot\epsilon+0.7515 \tag{6}\]  
The evaporation process can be regarded as an isobaric process. The amount of heat exchange is given by Equation (7). The throttling process is irreversible, while the enthalpy of the inlet and the outlet are equal (Equation (8)).  
\[Q_{\text{eva}}=m\cdot(h_{1}-h_{4}) \tag{7}\]  
\[h_{3}=h_{4} \tag{8}\]  
By associating Equations (5)-(8), the relationship between cooling capacity and the input power of the drive motor can be expressed as Equation (9). Due to the existence of the centralized high-pressure ammonia storage and the separator, the refrigerant steam quality at the termination of condensation and the beginning of compression is 0 and 1 respectively. As shown in Equations (10)-(12), the key enthalpies in Equation (9) can be determined quantitatively by invoking the CoolProp property library [37]. In summary, the cooling capacity can be determined as the input power of the drive motor and its suction and discharge pressure are determined.  
\[Q_{\text{eva}}=P_{\text{com}}\cdot\eta_{\text{is}}\cdot(h_{1}-h_{3})/\left(h_ {\text{2,is}}-h_{1}\right) \tag{9}\]  
\[[h_{1},s_{1}]=f\big{(}p=p_{exp},q=1\big{)} \tag{10}\]  
\[h_{\text{2,is}}=f(p=p_{con},s=s_{1}) \tag{11}\]  
\[h_{3}=f(p=p_{con},q=0) \tag{12}\]