## 4 Case Studies
### Analysis of Optimization Results  
The PCCP-ADMM algorithm proposed in this paper is used to solve and the OMEF problem. In order to analyze the impact of the dynamic characteristics of the natural gas system on the optimal scheduling of the system, this paper analyzes the following two cases:  
1. **Case 1**: Regardless of the dynamic characteristics of the natural gas system (i.e., removing the Equations (24)-(26)), the objective is to optimize the cost of energy supply.
2. **Case 2**: Considering the dynamic characteristics of the natural gas system, the objective is to optimize the cost of energy supply.  
This paper uses PCCP-ADMM algorithm to optimize two cases and analyzes the results to research the impact of the line pack on the optimal operation of the system, as shown in Figures 6 and 7.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Algorithm**} & \multicolumn{1}{c}{**Objective(5)**} & \multicolumn{1}{c}{**Iteration**} & \multicolumn{1}{c}{**Time(s)**} \\ \hline centralized optimization & NLP & \(5.3164\times 10^{6}\) & 83 & 4.19 \\ \cline{2-5}  & PCCP & \(4.9680\times 10^{6}\) & 5 & 45.26 \\ \hline decentralized optimization & PCCP-ADMM & \(4.9881\times 10^{6}\) & 22 & 68.18 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of PCCP-ADMM algorithm.  
Figure 5: Iterative process of PCCP-ADMM: (**a**) The number of iterations of ADMM in each iteration of PCCP; (**b**) The convergence process of residuals in the overall iteration.  
According to the optimization results, during the period of 1-6 h, the system's electric and gas loads are in the trough period. Compared with Case 1, Case 2 has more gas sources output, and part of the gas is stored in the natural gas pipeline. As shown in Figure 6, the value of the total line pack rises. During the period of 8-12 h, the system load is at its peak. The load in the natural gas system in Case 1 is mainly satisfied by the output of the gas sources; in Case 2, during this period, there is a certain amount of the line pack to release, and the output of the gas sources is less. Therefore, considering the dynamic characteristics of natural gas systems, IEGS can buffer the gas inflow and gas outflow. The gas network has a certain energy storage capacity, which can effectively buffer load fluctuations. It improves the flexibility of the system operation while ensuring the quality of energy supply.  
The cost of energy supply in each case is shown in Table 3. In Case 2, the cost is reduced due to the release of the line pack during the peak load period and used for system scheduling, with a reduction of 0.77%.  
Figure 6: Change of the total line pack.  
Figure 7: Output of gas sources in different cases.  
This paper focuses on Case 2. The output of some devices in the IEGS is shown in Figure 8.  
For the power system, according to Figure 8,d, it can be obtained that during the periods of 1-6 h and 22-24 h (load trough periods), the wind power output is relatively high. In order to absorb wind power, the excess power is injected into the natural gas system through P2 Gs. In this period, P2 Gs are basically close to full load operation. As shown in Figure 8, during the period of 8-21 h, because the generating cost of coal-fired units is generally lower than that of gas turbines, coal-fired units are basically close to full power output; meanwhile the output of gas turbines is relatively flat, which is mainly output at peak loads.  
For the natural gas system, as shown in the Figure 8, it can be found that during the period of 2-6 h, the excess wind power is injected into the gas network through P2 Gs and a part of it is stored in the gas storage tanks, and the gas inflow of the gas storage tanks is large. During the period of 8-12 h, due to the increase of system load, the gas storage tanks increase the gas outflow to meet the load demand.