## 4 Numerical Study
### Essential Information and Preliminary Calculation
Therefore, in Figure 8, the load shift scenario above the black dotted line (original configuration line) does not produce a positive effect for the initial investment reduction. Second, from the perspective of operating costs, on the one hand, with the reduction in the PIES installed capacity, the energy conversion efficiency increases for a partial load. Therefore, the cost price of electricity decreases at this time. On the other hand, the load shift transfers the electricity from the peak electricity price period of the large power grid to the valley electricity price period. This means that the valley electricity consumption increases as TR increases, which causes a reduction in the daily average cost of electricity in the PIES. Comprehensively considering initial investments and operating costs, the average cost price drops rapidly before point A', and then the falling speed is reduced after point A', as shown in Figure 8. The changing process in the average electricity cost price \(Pt_{average}^{e}\) can be fitted to Equation (18), where \(TR\) is the ratio of the shifted load from G zone to E zone (Figure 6) to the total peak load. In particular, the necessary condition of Equation (18) is that the PIES is rationally configured under different load profiles. In fact, in the solution process, the C-P sub-model, which is a sub-module of the P-M model, should be re-optimized in each call. Algorithm (3) can be used to solve the P-M model, and the flowchart of Algorithm (3) is shown in Figure 10. However, because the C-P sub-model involves a large amount of calculation and long calculation time, a regression equation is used to simplify the solution process. This is to say, Equation (18) is substituted into Equation (16). \[Pt_{average}^{e}=5.57 TR^{3}-3.098 TR^{2}-0.1133 TR+0.8633\;R^{2}=0.991 \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline TR/\% & \(-\)5 & 0 & 5 & 10 & 12.5 & 15 \\ Maximum load/kW & 35,673 & 33,974 & 32,275 & 30,577 & 29,727 & 28,878 \\ Number & 7 & 8 & 9 & 10 & 11 & 12 \\ TR/\% & 17.5 & 20 & 21.5 & 25 & 27.5 & 30 \\ Maximum load/kW & 28,028 & 27,353 & 28,813 & 32,221 & 34,655 & 37,089 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Twelve different scenarios of load profiles due to load shift. The average daily cost prices of cooling and heating are shown in Figure 11. The shift in demand of cooling and heating is ignored in this study, and TR refers to the proportion of power demand shift illustrated in Figure 11. It can be seen from Figure 11 that as the TR increases, the change in the average cooling cost price is just miniscule, but the heating cost price gradually increases. The increase in the heating cost price is caused by the following progressive relationship: (1) a load shift causes the increase in valley electricity consumption; (2) consequently, the installed capacity and operating hours of CHP (combined heating and power) are reduced; (3) this leads to a reduction in the free heating provided by the CHP; (4) eventually, the heating cost price increases. Since the proportion of free cooling provided by the CHP to the total cooling is low, the change in the cooling cost price is small. However, the maximum increase in the heating cost price is only 0.04 yuan/kWh. Therefore, the changes in the cooling and heating cost price caused by the electricity DR are ignored in this study. Figure 8: Electricity cost price curves for the 12 different load profiles. Figure 9: Peak load change due to load shift. Figure 11: Cost price curves of heating and cooling. Figure 10: Flow chart of Algorithm (3).