## 5 Case Studies
### Simulation and Analysis of Results
As shown in Figure 5, there is a non-dispatched power during hours 5, 7, 9-10, 12-13, and 22-23 because of transmission-line-capacity limitations. However, utilizing free and green energy wind power is so important from both environmental and economic aspects. Thus, in this work, P2G technology is proposed and evaluated in Case 2, to solve this issue. In these two defined situations of gas limitations, the imported natural gas from the upstream gas network is clarified in Figure 6. As can be seen, the pattern of the purchased gas corresponds to the GFU's generation. This is because the GFU is the only gas demander in the system, so when the GFU is online, the required amount of gas is purchased from the market. The considerable point in this figure occurred at hours 15-17. In this period, the GFU wants to reach the maximum capacity because of the high electricity price, and, as a result, it requires more fuel, but the amount of purchased gas is limited due to the fuel limitations. Therefore, this limitation impacts the GFU generation and prevents it from reaching the maximum capacity. Figure 4: The generated power of GFU in Case 1 with two states. **Case 2. ** To solve the curtailed and non-dispatched power of WPU that has been occurred in Case 1, P2G conversion technology is applied as illustrated following figures. In reality, by this deployment, the GFU's gas-fuel limitation will be removed, and the hybrid energy system could obtain higher profit by selling power to the day-ahead energy market. Thus, in Figure 7, the comparison of the dispatched power of WPU for Case 1 and Case 2 is indicated. According to the figure, the amount of curtailed power owing to transmission-line capacity is dispatched in this case, using the P2G facility. During hours 5, 7, 9-10, and 12-13, wind power is converted to gas, as depicted in Figure 8. The GSS during these hours is charged, and, during the high-electricity-price period, i.e., hours 15-17, it is discharged to supply the GFU. In doing so, according to Figure 9, increasing the generated power of GFU resulted via the operation of discharged natural gas by GSS, and the gas-fuel restriction is eliminated, similar to Case 1, in the state of without gas limitation. Decreasing the GFU's generation at peak hours of the electricity price occurs due to the increasing wind power generation and the restriction of transmission line capacity. Figure 5: The forecasted and dispatched powers of WPU in Case 1. Figure 6: The imported natural gas from the upstream network in Case 1 with two states. Table 4, in the following, analyzes the all achieved profit and purchased natural gas values for two different case studies in the whole time horizon, i.e., 24 h ahead. Only the purchased natural gas in the status without gas-fuel limitation for the two cases besides reporting the related profits is provided in Table 4. As shown in Table 4, the hybrid energy system's maximum profit and the minimum purchased  
Figure 3:0 Charging and discharging status of the GSS. Figure 3:1 The comparison of dispatched power of WPU for Case 1 and Case 2. Figure 3:2 The generated power of GFU for each two cases. natural gas are constructed via Case 2. It is noticeable that the achieved profit in Case 2 is equal in the two statuses of with/without gas-fuel limitation. Equation  
At the end of this section, we applied the proposed robust approach to the bidding strategy of the hybrid energy system, and so the results are introduced as follows: For different uncertainty budgets of electricity market price, various day-ahead electricity price profiles are calculated, which are demonstrated in Figure 3:3 Applying robust optimization cause a reduction in the electricity price for the worst-case hours. In other words, whatever the uncertainty budget is increased, the optimization problem is moved through a pessimistic path and get a more robustness level in decisions. For instance, \(\Gamma=6\) means uncertainty is considered for six worst-case hours, i.e., t = 15-20, and during this period, electricity price is decreased.