## 4 Case Studies  
### Natural Gas Supply Chain and Power System Initial Parameter Setting  
A natural gas system with a 14-node power system of a certain area [43], as shown in Figure 4, is used to illustrate the effectiveness of the proposed model. The stations in the natural gas pipeline network system are categorized into pressure stations, sub-transmission stations, and pressure sub-transmission stations [44]. These station types are represented topologically using squares, circles, and hexagons, respectively.  
In the natural gas pipeline network system, each line can be viewed as a series of stations and pipelines that can be operated independently. The system consists of three gas-transmission lines, with the second and third lines sharing some station and pipeline sections. It also includes two natural gas sources (red arrows represent the directions of gas flow), six compressor stations, four compressor sub-transmission stations, six sub-transmission stations, and 24 gas-transmission pipelines.  
The search tree [15,16] shown in Figure 5 is then sought, with line 1 represented by box A, the independent pipeline segment of line 2 by B, the common pipeline segment with line 3 by D, the independent pipeline segment of line 3 by C, and the common pipeline segment with line 2 by E. The number 1 represents the gas sources, number 2,3 represent the sharing station (sta9), number 4 represents the load side (i.e., the 14-node power system).  
Figure 4: Topology diagram of the natural gas system with a 14-node power system of a certain area.  
The maximum volume of gas delivered by line \(A\) of cut set 1 is \(C_{1,A}\), and the working volume is \(S_{1,A}\). Similarly, the maximum and working volumes of the other lines can be expressed. A margin of \(h\%\) is set for each line (\(h=10\) for this paper) [45]. The values of gas delivery for each line are set in Table 1, and the failure parameters of each component of the natural gas pipeline system in the initial state are set in Table 2[46].  
In this case, the key factors are set as policy regulations and economic market fluctuations [47]. The amount of natural gas delivered to each gas-fired unit by the three transmission lines is obtained after 10,000 Monte Carlo simulations, and the output and upper and lower limits of each generating unit's output are modified accordingly. Table 3 shows that the units at nodes 1 and 8 of the power grid of an area correspond to coal-fired units, while the units at nodes 2, 3, and 6 correspond to gas-fired units. In this paper, the flow rate of the transmission line in the initial state is used as the benchmark, and 1.5 times the power flowing through each transmission line is used as the upper limit of the transmission capacity of the line.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Line Name** & \
\begin{tabular}{c} **Maximum Gas Delivery** \\ **Volume/m3** \\ \end{tabular} &
\begin{tabular}{c} **Gas Delivery Volume during** \\ **Operation/m3** \\ \end{tabular} \\ \hline A & 5000 & 4500 \\ B & 6000 & 5400 \\ C & 7000 & 6300 \\ D & 6000 & 5400 \\ E & 7000 & 6300 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The gas-transmission parameters of the line.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Equipment Components** & **Failure Probability** \\ \hline Compressor station & 0.14 \\ Sub-transmission substation & 0.20 \\ Compressor and sub-transmission station & 0.15 \\ Independent pipeline & 0.10 \\ Collinear pipeline & 0.13 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fault parameters of components in the initial natural gas pipe network system.  
Figure 5: Simplified topology diagram of natural gas pipe network system and the power grid of an area.