## 4 Empirical Analysis  
### Parameter Setting  
In order to simplify the model, the following assumptions are made: the daily clearing prices of the power market and the natural gas market in each period meet the normal distribution in a certain range; the mean value is taken from the actual market data of European energy exchange (EEX) and Nord pool, respectively; and the standard deviation is 3 EUR/MWh. Under the above data settings, 1000 daily clearing price scenarios of the natural gas market and the power market are generated respectively through LHS. After reduction, typical daily clearing price scenarios are obtained. The penalty price is set as 50% of the daily clearing price of the day-ahead market. The price data of typical daily clearing price scenarios are shown in Figure 4, the specific price data can be found in Supplementary Materials  
The structure of the electric-gas interconnection system in the example analysis of this paper is shown in Figure 1, the specific load data can be seen in Supplementary Materials. The load data of power, heat, cooling and natural gas in the calculation example is shown in Figure 5. The conversion efficiency and the upper and lower limits of each coupling unit output power are shown in Table 1.  
Figure 4: Scenario data of typical daily price. Figure 5: Load data of the system. Figure 6 shows the declared strategy of the electric-gas interconnection system in each period of the natural gas market and the power market, the specific decision result data can be found in Supplementary Materials, with positive value representing sale and negative value representing purchase. As can be seen from the figure, the electric-gas interconnection system sells natural gas in the natural gas market in the periods 1-5, purchases natural gas from the natural gas market in the periods 6-24, and sells power in all the periods. In general, due to the relatively low price of natural gas, the system decision-makers in this case tend to participate in the multi energy market transaction by purchasing natural gas and selling surplus electric energy, that is, internal demand is mostly transformed into supply through purchased natural gas. The uncontrollable component is the RE system, and the output power of electric energy in the system comes from the renewable energy units. After the output power of some renewable energy units is converted into other energy forms or supplies power to the coupling units, the remaining part is the declared value of the output power of electric energy in the system for bidding. Therefore, the optimal output power of the renewable energy units is actually the output power of the renewable energy unit ensuring the optimal purchase and sale strategy of the system, and it is not the actual output of the next day. If the decision-makers declare according to the declared strategy of energy purchase and sale corresponding to the optimal output power of the renewable energy units, the deviation of system output power will be minimized and the income will be maximized. In Figure 7, the upper and lower curves respectively correspond to the upper and lower limits of the RES output power in the system, and this value can be predicted according to the historical actual data. The shaded part is the predicted confidence interval of the RES output power within 24 h. The red curve in the middle represents the optimized RES output power strategy. It can be seen that the output power decision of RES at all times is within the confidence interval of the RES output power within 24 h, and the optimal value of the RES output power in the periods 8-9 is the upper limit value of allowable output power. According to Figures 4-6, there are two factors that influence the optimal output to reach the upper limit: one is that the system power load is at the peak in the periods 8-9; the other is that the power price is at the peak in the periods 8-9.