## 5 Simulation Results
### The Effect of Uncertainty on the Vulnerable Points of the Studied Case  
This part tries to express how the uncertainty effects can be significant on achieving over goals considered in this paper. On the other hand, concerning the uncertainty model for scheduling the energy management of the smart grid based on the proposed framework is a must. Moreover, it is needed to check how the uncertainty modeling can change the vulnerability rates of different areas within the grid. To realize this issue, we deploy the UT method based on uncertain parameters in the energy scheduling of the smart grid regarding the proposed framework. In addition, we provide the consequence related to uncertainty impacts on the different significant aspects including the power exchange between two the electrical grids, financial management of the smart grid and the vulnerability indices, which is the most important goal in this section. Hence, Figures 17-19 indicate the relevant results of uncertainty modeling. As it was mentioned before, the power exchange between the microgrid and the smart grid is determined concerning different criteria aiming to get the vulnerability rate reduction. Figure 17 shows the power injection of the microgrid to the smart grid for both deterministic and stochastic scenarios, respectively. According to Figure 17, altering energy exchange in the stochastic model compared to scenario one proves that it is necessary to think about the uncertainty modeling in scheduling to get effective and accurate energy management. The important facts about the various situations will be twigged by observing Figure 17a,b. The cumulative diagram of power exchange across 24 h between stochastic and normal manners have a lot of conflict with each other (Figure 17b), although the difference between them is insignificant for 24 h in a one by one manner (Figure 17a). It is inferred that we should watch out for failure in schedules if we ignore the impact of uncertainty. Hence, we try to indicate the results related to case I for uncertainty state as shown by Figures 20 and 21. In addition, the strategy's effectiveness proposed in part I in order to reduce the costs is obviously proven based on the uncertainty by Table 5. As a second goal, Figure 19 shows the comparison of the NGO and NLO indexes related to the study case in both uncertainty and deterministic scenarios. For instance, we assume that the outages of lines 22, 15, and the generation unit 15 happened within the smart grid and the relevant vulnerability indexes on a case-by-case basis are represented. The consequences indicate that the uncertainty model causes varied changes ranging from 2%, 3.5%, and 10% in the vulnerability rates of the smart grid compared to scenario one, respectively. This results in the microgrid's effectiveness at preventing the cascading events in the smart grid, which will be seen if the uncertainty effects are modeled using the UT method. Comparing the costs pertaining to microgrid and the smart grid in the uncertain condition with the normal one (refer to Figure 18), it is seen that the costs of microgrid, smart grid, and total cost take higher fluctuations, which are 2%, 23%, and 1.4%, respectively (see Figure 18). To sum, the smart grid is better to make use of the uncertainty framework to assess the vulnerable areas in the grid and to get effective scheduling in the bargaining power with the microgrid.  
Figure 17: _Cont._Figure 19: _Cont_.  
Figure 17: The comparison of power exchange: (**a**) the power transaction in 24 h, (**b**) cumulative changes across 24 h.  
Figure 18: The comparison of vulnerability indices.  
Figure 21: The vulnerability indices arising from generation unit outage in uncertainty condition.  
Figure 19: The operation costs of smart grid (**a**) and microgrid (**b**) in stochastic and normal conditions.  
Figure 20: The vulnerability indices arising from line outage in uncertainty condition.