## 5 Simulation and Numerical Results
#### Case 2  
The optimal performance of the MCMG system in the presence of several technologies is examined in this case, considering both environmental and economic perspectives. As discussed, the proposed model is formulated as a multi-objective problem to minimize  
Figure 8: Load demand before and after leveraging DRP in case 1.  
Figure 9: Comparison of power purchased before and after DRP.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **CAES** & **CAES and P2G** & **Integrated CAES, P2G, and DRP** \\ \hline Cost (\$) & 7296.25 & 7048.16 & 6912.73 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Effects of the integrated technology on the economic saving for case 1.  
both objectives. To this end, the weighted sum technique is used to find Pareto solutions to reduce the daily emission and operation cost in the proposed multi-objective model. Pareto solutions are given in Table 4. According to the obtained Pareto solutions, the min-max fuzzy technique is implemented to normalize \(OF_{1}\) and \(OF_{2}\) in addition to presenting the tradeoff between two objective functions. Besides, the obtained solutions are studied in Figure 10. According to the obtained solutions in Table 4 and Figure 10, iteration number 5 is selected as an optimal solution based on the fuzzy approach. The selected solution (iteration number 5) is given as $7456.81 and 9656.11 kg, respectively, for the system's operation cost and emission pollution in case 2.  
In case 2, the CAES scheme is shown in Figure 11. The results denote that the CAES operates in the simple-cycle mode when there is an increase in loads, e.g., hours 13 and 14. Purchasing intense-carbonized power from the grid is the dominant reason for utilizing the CAES fed by lower carbonized natural gas. In other words, the operator tends to generate power by the CAES in simple-cycle mode instead of purchasing power, contributing to environmental and economic goals.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Iteration** & \(K_{1}\) & \(K_{2}\) & \(OF_{1}\)(5) & \(OF_{2}\)(kg) & \(OF_{1}^{m}\) & \(OF_{2}^{m}\) & \(min\{f_{1}^{m},f_{2}^{m}\}\) \\ \hline
1 & 1 & 0 & 6912.73 & 9976.45 & 1 & 0 & 0 \\
2 & 0.9 & 0.1 & 6989.05 & 9865.02 & 0.914 & 0.146 & 0.146 \\
3 & 0.8 & 0.2 & 7047.31 & 9815.96 & 0.849 & 0.212 & 0.212 \\
4 & 0.7 & 0.3 & 7107.95 & 9752.41 & 0.7811 & 0.294 & 0.294 \\
5 & 0.6 & 0.4 & 7456.81 & 9656.11 & 0.39 & 0.421 & 0.39 \\
6 & 0.5 & 0.5 & 7497.44 & 9604.14 & 0.344 & 0.489 & 0.344 \\
7 & 0.4 & 0.6 & 7600.06 & 9547.02 & 0.229 & 0.564 & 0.229 \\
8 & 0.3 & 0.7 & 7659.35 & 9405.3 & 0.162 & 0.75 & 0.162 \\
9 & 0.2 & 0.8 & 7783.13 & 9374.25 & 0.04 & 0.791 & 0.04 \\
10 & 0.1 & 0.9 & 7792.52 & 9281.91 & 0.013 & 0.912 & 0.013 \\
11 & 0 & 1 & 7804.67 & 9215.55 & 0 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Pareto solution for the model in case 2.  
Figure 10: The Pareto optimal front for the bi-objective problem in case 2.  
P2G has impressive effects on CO\({}_{2}\) capturing as given in objective function Equation (4). P2G facilitates the integration of wind power in the system. In this way, the surplus power is converted into natural gas and injected into the system in gas peak hours. As given in objective function (4), natural gas is one of the main emission pollution resources. Meanwhile, the P2G captures the CO\({}_{2}\) gas and mixes it with the produced hydrogen. In this way, the CH\({}_{4}\) is produced and injected into the system. Thus, P2G technology has a unique role in emission pollution minimization. The effects of CAES, P2G, and DRP integration on the system's operation cost and emission pollution under the multi-objective framework are shown in Table 5. In case 2, the integration of CAES, P2G, and DRP would result in cost and pollution reduction of up to 14.2% and 9.6%. This table proves the advantages of the integrated energy system from emission reduction and cost improvement.