## 5 Case Studies and Discussions
### Impact Due to Congestion and Demand Response  
In this simulation, the impact due to congestion and demand response, with the same fuel price for all units, is adopted for investigation. Load shedding is added to avoid imbalance between load and generation. It is assumed that all NGFUs have an initial credit rank of 0.5, the entire scheduling time is for four days, and an hour is taken as a time step. The advantages of the proposed framework applied to daily scheduling for a few days are illustrated with the following case studies:  
Case 1: Decentralized and coordinated operation without natural gas pipelines congestion. Case 2: Decentralized and coordinated operation with natural gas pipelines congestion. Case 3: Decentralized and coordinated operation considering demand response (Based on Case 2). For Case 1, the natural gas supply capacity of the natural gas network to NGFUs is redundant. Because the gas consumption of NGFUs in ENO optimal scheduling is feasible for GNO, so the cost of ENO in DO is minimum and with no-load shedding. The hourly cost, total cost of ENO, and hourly generation of G1 are shown in Figure 9. It can be seen that DO hourly cost of the electricity network is less than CO for day 1, the main reason is due to the CR parameter is introduced in CO and has an initial credit rank of 0.5 at first day of optimization. CO has not reached the optimization. In Case 1, without natural gas pipelines congestion, the gas consumption in ENO optimization scheduling is feasible for GNO. Therefore, the cost of ENO in DO is the smallest. After updating the CR, DO total cost of the electricity network is same as that of CO, the scheduling results of the two coordinated operation methods are consistent. Table 4 shows the gap of the iteration process with various expansion points. SCP with initial point achieved by the penalty function is denoted as penalty function (PF) initial. Zero initial means SCP with zero initial points [56]. The gap of the proposed method reduces greatly, and the accuracy will converge 5 iterations later. The zero-point method will converge after 6 iterations. The proposed method has quicker convergence characteristics, while the zero-point method convergence is slower [57]. Figure 9: Hourly and total cost of ENO, hourly generation of G1. Case 2: According to steady-state natural gas flow model, the gas flow in pipelines depends on the first and last node pressure. To simplify the debugging process, we included the gas flow upper limit on pipeline 1 and pipeline 4 in this case. Pipeline congestion at hours 19-22 is a peak period for both electricity and gas networks in decentralized operation. Pipeline congestion creates the difference between expected generation and actual generation of NGFUs in DO. Figure 10 shows the output of gas-fired units with the optimal economic dispatch of the power grid and the discrete operation of the electricity-gas interconnection system. For the gas unit G1, under the condition of economic dispatch, the output has been kept at full capacity, but when considering the natural gas network constraints, in the discrete operation mode, due to the blockage of pipeline 1 during the period 19-22, G1 cannot get enough gas supply. The output is affected, and there is an imbalance in coupled scheduling. For gas-fired unit G3, in the discrete operation mode, pipeline 3 was blocked during the period 19-21. G3 could not get enough gas supply and there was also unbalanced coupling scheduling. This shows that in the case of natural gas network constraints, once the gas network pipeline is blocked, it will have a negative impact on the grid dispatching. The actual power generation is fewer than the expected one in hour 19-22, and part of the load is not satisfied in DO, so load shedding has to take place. CO total electricity cost is slightly higher than that in DO on the first day, but there is no load shedding. Electricity operation cost will be minimum on the next day in the proposed framework.