## 4 Results and Discussion
### Results  
In order to verify the performance superiority of the proposed optimization criteria, two strategies are used to plan the stations and networks. In Scheme 1, the scope of energy stations is divided according to the principle of the nearest distance. In Scheme 2, the relationship between the load points on the boundary and energy stations is considered through the relative-load-distance criterion. In this paper, the points on the boundary of the energy supply area are assigned and replaced. In Scheme 2, we assume that \(k=3\).  
Accordingly, the station and network planning results of Schemes 1 and 2 are represented in Figure 5 below, and Figure 6 shows the investment of each scheme.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Values** & **Units** & **Parameters** & **Values** & **Units** \\ \hline \(\chi_{t}^{EL}\) & 1/20 & 1/year & \(\tau\) & 3360 & h \\ \(C^{ES}\) & 10,000 & RMB/kW & \(P_{e}\) & 0.8 & RMB/(kW\(\cdot\)h) \\ \(f(d_{500})\) & 1567.21 & RMB/m & \(\lambda\) & 0.06 & W/(m\(\cdot\)\({}^{\circ}\)C) \\ \(\mu_{5}^{ES}\) & 0.01 & — & \(t_{c}\) & 10 & \({}^{\circ}\)C \\ \(\mu_{5}^{ES}\) & 0.015 & — & \(\delta_{i}\) & 0.5 & m \\ d & 0.5 & m & \(\delta_{ii}\) & 0.09 & m \\ \(\chi_{t}^{PL}\) & 1/20 & 1/year & \(COP\) & 4.2 & — \\ \(\alpha\) & 1 & \% & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Table of simulation parameters.  
Figure 5: Station and network planning results of Schemes 1 and 2.  
According to Figures 5 and 6, it can be observed that the load characteristics are considered, that is, adopting relative-load-distance, so that the load points (load 2 and load 4) are no longer supplied by the nearest energy station (Station 15), but belong to the energy station (Station 13) relatively far away from it. Therefore, the annual conversion cost of the pipe network in Scheme 2 is 87,000 RMB higher than that in Scheme 1, but the decreased cost in the network is significantly less than the increased cost in the energy station. On the contrary, owing to the scale effect, considering the load characteristics of some load points, the overall load characteristics in the energy supply range of each energy station are improved, in which the capacity of Station 13 is increased by 18%, while the capacity of Station 15 is reduced by 26%. Therefore, the total investment cost of the two energy stations is also reduced. In addition, in Figure 5c,d, compared with the differences in network distribution between the two schemes, Scheme 2 replaces multiple pipelines in Scheme 1 with public pipelines, which improves the concentration of loads in the region. Considering the annual cost of the energy station and network, compared with Scheme 1, the annual cost of the energy system in Scheme 2 is reduced by 9.1 million yuan. This comparison shows that considering the load characteristics of load points in the division of energy supply range can slightly increase the investment of pipe network, but it can allocate users to appropriate energy stations, effectively reduce the annual cost of energy stations, and is conducive to the economic construction of the energy system.