## 4 Empirical Analysis
### Sensitivity Analysis  
RES is the internal energy supply unit of the electric-gas interconnection system. This section discusses the influence that the change of RES output power restriction has caused on the declared strategy of the energy purchase and sale and the output power of the internal coupling unit. Under each scenario, let the upper limit of RES output power change by 20%, 10%, \(-\)10% and \(-\)20% in each period, and compare the original optimization results with the four scenarios set in this section. The expected profits of the electric-gas interconnection system participating in the market bidding under the four scenarios are shown in Table 2. The expected profit is the expected value of the profit under the probability distribution of each price sample, while the actual profit is the average value of the obtained profit assuming that a certain sample in the price sample set will actually occur. It can be seen from the table that the expected profit generated by the system participating in the market bidding is positively related to the change of the upper limit of RES output power, and when the upper limit of RES output power changes in a negative direction, the change range of the expected profit is larger. When the upper limit of RES output power changes positively, only the optimal output power of RES in periods 8 and 9 changes (as shown in Figure 9), and when the upper limit of RES output power changes negatively, the optimal output power of RES in the periods 7-9, 11 and 19 changes simultaneously (as shown in Figure 9). Compared with the positive change, the negative change of the upper limit of RES output power is more significant, which is one of the reasons why the expected profit is more sensitive to the negative change of RES output power. Figures 10-13 show the bidding strategy of the electric-gas interconnection system in four scenarios and the variance ratio of the declared strategy in each period compared with the control scenario. It can be seen from the figure that under the parameter setting in this paper, when the upper limit of the internal power supply unit output changes, the internal power supply unit output changes correspondingly, but the power declared strategy does not change. Considering that the power transaction price is more advantageous than the natural gas transaction price, the system decision-makers are more inclined to reduce the natural gas declaration volume in periods 8-9 on the \begin{table}
\begin{tabular}{c c c c c} \hline  & **Scenario 1** & **Scenario 2** & **Scenario 3** & **Scenario 4** \\ \hline Profit (EUR) & 12398 & 12382 & 12150 & 11973 \\ Profit change (\%) & 0.92 & 0.79 & \(-\)1.1 & \(-\)2.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Changes in profit under four scenarios. Figure 9: Variation results of the output power in the RES system. premise of meeting the internal load demand, so as to ensure the optimal declared strategy of energy purchase and sale. In scenario 1 and scenario 2, the power consumption of internal energy supply units is promoted by reducing the purchase of natural gas in general, and the power generation consumption of the internal energy supply unit is reduced more in the 8 th period when the natural gas purchase amount is relatively large, which directly leads to the increase of expected profits. In scenario 3 and scenario 4, the power generation reduction of the internal energy supply unit is generally compensated by increasing the purchase of natural gas, and the purchase of natural gas increases substantially in the periods 7-9 and 19, which also directly leads to the reduction of expected profits. Figure 11: Variation results of declared strategy in scenario 2. Figure 10: Variation results of declared strategy in scenario 1. Figures 14-17 show the output variation ratio of the internal coupling unit in each period of the electric-gas interconnection system compared with the control scenario.