## 5 Simulation Results
Changing the generation power percent related to each unit is dependent on the energy price and the relevant unit capacity at each hour as indicated in Figure 8. This topic needs to be opened up for economic discussion, the results of which are indicated in Table 3. Comparing the smart grid operation incorporating  
For the aforementioned reasons, we decide to accomplish such a scheduling framework aiming to dwindle the significant effects of the smart grid vulnerability. To prove this, there is a need to first carry out the vulnerability modeling of the grid to get the assessment and finding of the different vulnerable areas within the smart grid. To this end, we implement the formulation of vulnerability indices, which is defined in (1)-(13) and the relevant results are demonstrated in Figures 9 and 10. It is significant to say that the vulnerability rate pertaining to each piece of equipment is calculated for the condition in which all lines and generators are separately eradicated in the grid structure for any reason. Keeping this issue in mind, the vulnerability rate related to each generation unit named NGO index can be seen in Figure 9. Regarding the relevant consequence, the points marked by multiplication sign reply to the generation units taken at approximately high vulnerability rate arising from the outage of lines and generators compared to the other units. In other words, the NGO indices related to the G1, G2, G3, G4, and G10 take up to a level that has overtaken the threshold. This means that a failure in any area of the grid can have more effect on these areas identified as the more sensitive and vulnerable points than the other areas. In the same way, the NLO index indicating the vulnerability rate of each line is computed in accordance with Figure 10. As can be seen in this figure, some lines take more NLO index than the threshold, which is a compelling reason to highlight the vulnerable lines. Following the vulnerable areas of the smart grid, reducing the grid vulnerability with the use of the defined points can be guaranteed by the interconnected microgrid and smart-grid-based framework against unexpected events. In other words, such an energy management framework can be trustworthy to prevent cascading failures and blackouts with the use of injecting power at the proper times within the smart grid. To prove this proposition, we carry out the smart grid under different events considering the microgrid and compared to the scenario of ignoring the microgrid within the grid. By doing so, the comparative results for considering and ignoring the microgrid are provided in Figures 11-14. The outage of simulation shows that the microgrid leads to get a marked decline for the NGO indices ranging from 28% to 57% as represented in Figure 11. Similarly, for the generator outage, comparing the NLO indices for scenarios of ignoring and considering microgrid proves the microgrid's effectiveness at reducing the line vulnerability of the smart grid (see Figure 12). Moreover, Figures 13 and 14 show the comparison of the total cost of the smart grid for the relevant scenarios including the outage of all lines and generators, separately. As it can be seen, the total cost of the grid takes the least detriment using the proposed framework when occurring different events. \begin{table}
\begin{tabular}{c c c c} \hline
**Conditions/Costs (e)** & **Smart Grid** & **Microgrid** & **Total** \\ \hline With connection link & 2,197,716,343 & 11,228,799.15 & 2,208,945,142 \\ Without connection link & 7,007,211,265 & 80,185,404.84 & 7,087,396,670 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison among different conditions. Figure 11: The NGO indexes of generators for different scenarios. Figure 10: The NLO indexes of lines. Figure 9: The NGO indexes of generators. Figure 14: The total cost under the generation unit outage. Figure 12: The NLO indexes of lines for different scenarios. Figure 13: The total cost under the line outage.