## 3 P-M Model
### S-P Sub-Model  
#### 3.2.1 Construction of S-P Sub-Model  
How is the selling price used to trade with consumers determined from the hourly cost price of cooling, heating, and electricity? The easiest method is to set the energy selling price as a constant over the entire year. Then, the selling price can be calculated by a given annual profit rate and obtained cost price. The annual profit rate of the PIES, \(p^{\prime}\), can be calculated by Equation (9) [25]. \[p^{\prime}=\frac{\sum_{t=1}^{8760}(Q_{t}^{e}(Pr^{e}-Pr_{t}^{e})+Q_{t}^{e} \big{(}Pr^{e}-Pr_{t}^{e}\big{)}+Q_{t}^{h}\big{(}Pr^{h}-Pr_{t}^{h}\big{)}\big{)}} {\sum_{t=1}^{8760}\big{(}fval_{t}^{e}+fval_{t}^{e}+fval_{t}^{h}\big{)}} \tag{9}\]  
where \(Pr^{e}\), \(Pr^{e}\), and \(Pr^{h}\) represent the selling prices of electricity, cooling, and heating, respectively. Under the assumption mentioned above, when the selling prices of cooling, heating, and electricity vary independently, the linear relationship of annual profit rate with energy selling price can be obtained by using Equation (9). Furthermore, \(Pr^{e}\), \(Pr^{e}\), and \(Pr^{h}\) are determined by black calculation. From the perspective of cooling and heating, owing to the large delay in the supply and delivery of cooling and heating [26], it is meaningless to adjust the selling price of cooling and heating on an hourly basis. Therefore, in this study, the same cooling or heating selling price throughout the year is adopted. From the perspective of electricity, the pricing mode with the same electricity price through the entire year will increase the polarization of the load. This is because compared with the time-of-use pricing mode of the large power grid, the lower-priced electricity supplied by the PIES during the  
Figure 2: Flow chart of Algorithm (1). hours of peak demand leads to higher electricity consumption, and the higher-priced electricity during the hours of valley demand leads to less electricity consumption. Evidently, the static pricing mode is very inappropriate for the PIES. The time-of-use pricing mode and real-time pricing mode, which are advantageous for load leveling, should be adopted. For consumers, there are two electricity suppliers: the large power grid and the PIES, as shown in Figure 1. The consumers, having no generation capability, need to purchase all their required energy from the PIES or the large power grid or other suppliers. However, there are no municipal heating networks and other cooling suppliers in the hot summer and cold winter zones in China. Hence, the consumers can only obtain cooling and heating from the PIES. From the perspective of economic efficiency, the consumers will choose the lowest electricity supplier. This study assumes that a consumer cannot select two electricity suppliers simultaneously and can switch, at most, once a day. Hence, the constraint when consumers select PIES as the electricity supplier is shown in Equation (10), where \(Q_{t}^{e}\) is the amount of electricity from the PIES consumed by the consumers at time \(t\); \(P_{t}^{e,s}\) is the selling price of electricity at time \(t\); \(Q_{t}^{pg}\) is the amount of electricity from the large power grid consumed by the consumers at time \(t\); and \(P_{t}^{pg}\) is the time-of-use electricity price of the large power grid. \[\sum_{t=1}^{24}(Q_{t}^{e}P_{t}^{e,s})\leq\sum_{t=1}^{24}(Q_{t}^{pg}P_{t}^{pg}) \tag{10}\]  
In general, the buying price set by the large power grid is considerably lower than its selling price without subsides [27]. Hence, the feed-in tariff scheme of the PIES is unreasonable when the renewable energy penetration is not high. In addition, when the electrical load reaches its peak, the electricity cost price also reaches its peak. From an economical perspective, \(P_{t}^{e,s}\) needs to be formulated for the following reasons: (1) decrease the electricity consumption at the peak; (2) increase the electricity consumption at the valley; (3) promote the profitability of the PIES; and (4) reduce the electricity bill of the consumers.