## 4 Numerical Study  
### Essential Information and Preliminary Calculation  
In this study, a real PIES located in Shanghai, China, has been selected as a case study to verify the P-M model developed in this study. The energy production equipment of PIES mainly includes absorption refrigeration units, gas generators, photovoltaics, photothermal, heat pumps, boilers, chillers, energy storage equipment, wind power, and so on. The total area of energy supplying is 960,000 square meters, including an office building area of 479,000 square meters, commercial building area of 383,000 square meters, and hotel building area of 98,000 square meters. The hourly load of cooling, heating, and electricity in the typical day are illustrated in Figure 5. Meanwhile, there is no effect of DR, i.e., TR = 0. In addition, owing to the delayed effect of cooling and heating transport, achieving the DR of cooling and heating is very difficult. Hence, the TR only refers to the electrical shifted load caused by the DR. The annual hourly load, the basic data, and the constraints of the above-mentioned energy production equipment are input into the C-P sub-model. Then, the loop iterative method (Algorithm (1)) is applied in the case, and the annual hourly cost price of PIES is captured, which are shown in Figure 6. The curve of \(\sigma_{s}\) varies with the iteration steps in the solution process, as shown in Figure 7, which illustrates that the iteration process converges quickly. From Figure 7, the total cost of the PIES first increases; then, it decreases, and it finally stabilizes at the final cost. Figure 6 shows that the average cost price of cooling is the lowest, and the fluctuation in the cost price is smoothest. The fluctuation in the electricity cost price in winter and summer are similar, and the former is slightly higher than the latter. The heating cost price in zone D is lower than the price at other times during the winter heating period. The reason is that the CHP is chosen to supply electricity to the PIES because the electricity price of the large power grid is at a peak in zone D and can provide free heating through the additional waste heat. The heating cost price of zone F is higher because of the gas boi  
Figure 5: Load of cooling, heating, and electricity when TR = 0.  
of zone G and zone E differs greatly in the electricity cost price curve, the daily electricity cost price is divided into a peak segment (G) and a valley segment (E) in the following studies, as shown in Section 2. Figure 6: Cost of cooling, heating, and electricity when the ratio of the shifted load to the total peak load (TR) = 0. Figure 7: Curve of \(\sigma_{s}\) varying with iteration steps in the solution process. When the DR occurs, i.e., TR \(\
eq\) 0, the cost price of cooling, heating, and electricity should be recalculated by using the C-P sub-model and Algorithm (1) according to the load profile at this time. The TR and new load peaks under 12 scenarios of load profiles are illustrated in Table 1.  
The average daily electricity cost prices (\(Pt_{average}^{e}\)) are illustrated in Figure 6 under the 12 different load profiles. As shown in Figure 8, the configuration ratio is the ratio of the maximum installed capacity at a certain TR to the maximum installed capacity at TR = 0. Some interesting rules have been discovered by processing the solution results of the 12 different load profiles, as follows. First, from the perspective of the initial investment, as the TR increases, the configuration ratio drops from point B to point A and then rises to point C. At point A, the PIES has the smallest installed capacity. The installed capacity at point C is higher than the installed capacity before the load shifted, which means that the excessive load shift generates a new peak in electrical demand, as shown in Figure 9. From Figure 9, when TR = 30%, the peak load is shifted to 22:00 from 19:00, and the new peak is 3115 kW larger than the old peak. The emergence of the new peak means that the load shift does not reduce the initial investment.