# Techno-Economic Analysis of the Peak Shifting Strategy Based on Time-of-Use Tariff for Cold Stores
## 3 Methodology
### System Simulation Approach  
Two optional modes A and B are proposed in this paper for selection in practical production. The specific control principles for the two modes are as follows:  
* Mode A: All-day cooling load needs to be shifted to the valley period and the compressor unit should maintain shutdown as much as possible in other periods. The operation mode during the valley period is set directly through the average load calculation result. Temperature set point control is adopted in off-valley periods, which means the unit shuts down before the temperature exceeds the upper limit and operates at high load when it does. * Mode B: The cooling load of the whole day is divided into multiple intervals according to the TOU tariff and thus is met separately. The operation mode control is adopted in the valley as well as the flat_1# period. The compressor unit should both meet the cooling load of the above two periods and charge the storage to meet the demand from  
Figure 4: Structure of the repetition module in the LSTM algorithm. the peak_1# and peak_2# periods. Similar to Mode A, temperature set point control is adopted in other periods. The upper temperature limit can usually be determined by the storage requirements of the products, and it is set as \(-18\)\({}^{\circ}\)C in this paper [21,22]. To compare the advantages and disadvantages of the above two modes, it is essential to analyze the trends of key parameters such as warehouse temperature, cooling capacity, and operation cost. Therefore, it is necessary to establish a simulation algorithm to analyze the control effect taking several actual working days as a case study. When the optimized temperature at the previous moment \(i\) is known to be \(T_{\text{opti},i}\), the temperature at the following moment (\(T_{\text{opti},i+1}\)) can be calculated as Equation (19). \(Q_{\text{ori},i}\) and \(Q_{\text{opti},i}\) indicate the cooling capacity supply before and after peak shifting, respectively, whose difference is given in Equation (20). \[T_{\text{opti},i+1}=T_{\text{opti},i}+\left(Q_{\text{opti},i}-Q_{\text{dis}, \text{opti},i}/c\cdot M\right) \tag{19}\]  
\[\Delta Q_{i}=Q_{\text{opti},i}-Q_{\text{ori},i} \tag{20}\]  
Similar to Equation (19), the relationship between the original temperature at adjacent moments can be expressed in Equation (21). \[T_{\text{ori},i+1}=T_{\text{ori},i}+\left(Q_{\text{ori},i}-Q_{\text{dis}, \text{ori},i}/c\cdot M\right) \tag{21}\]  
For the cold store discussed in this paper, the dissipation at the building envelope is positively correlated with the temperature difference between the inside and outside. Owing to the large reserve of products, the change in the warehouse temperature is very limited before and after peak shifting. Consequently, the cooling dissipation can be approximated as unchanged in the simulation calculation (Equation (22)). The recurrence relation for the optimized temperature can be determined by associating Equations (19)-(22), as shown in Equation (23). As the initial value, its temperature should be equal at the beginning moment when the control strategy is introduced (Equation (24)). In this research, the product in the cold store is mainly pork, and the specific heat capacity is given in Equation (25) [39]. \[Q_{\text{dis},\text{opti},i}=Q_{\text{dis},\text{ori},i} \tag{22}\]  
\[T_{\text{opti},i+1}=T_{\text{opti},i}+T_{\text{ori},i+1}-T_{\text{ori},i}+( \Delta Q_{i}/c\cdot M) \tag{23}\]  
\[T_{\text{opti},1}=T_{\text{ori},1} \tag{24}\]  
\[c=0.00286\cdot T^{2}+0.1826\cdot T+5.83 \tag{25}\]  
Analyzing the control effect of the strategy, it is worthwhile to compare the trends of the cooling capacity and the operation cost of the system. The cooling capacity provided by the system during operation can be calculated as Equation (26). The operation cost is dominated by the consumed electrical power of the compressor unit, so it can be formulated as Equation (27). Furthermore, the cost reduction rate is used to measure the economic effect before and after peak shifting (Equation (28)).