## 4 Simulations
### Voltage Stability Analysis  
As the access number of distributed generation and electric vehicle is increasing, it will have a great impact on the stability of the network voltage. Therefore, it is necessary to analyze the effects on the network voltage distribution under different access modes of distributed generation and electric vehicle.  
In Figure 7a-c, the dark blue curve in the figure corresponds to V\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G, define as the initial voltage distribution of the network without distributed generation and electric vehicle. The red and green curves correspond to V\({}_{\text{\_}}\)KELM\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G and V\({}_{\text{\_}}\)SVM\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G, respectively define as the voltage distribution of the network when only distributed generation are connected, where n = [1, 2, 3] representing case1, case2, case3 respectively. The light blue and purple curves correspond to V\({}_{\text{\_}}\)KELM\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G&EV and V\({}_{\text{\_}}\)SVM\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G&EV respectively define as the voltage distribution when distributed generation and electric vehicles are connected at the same time.  
Figure 7a-c, shows the change of the voltage gained by the kernel extreme learning machine and support vector machine methods, with different distributed generation access modes and with or without electric vehicle. The voltage amplitude increases with the distributed generation access capacity. This indicates that the access of the distributed generation is beneficial for increasing the network voltage level. Meanwhile, by comparing the results obtained by the support vector machine, the voltage distribution curve given by kernel extreme learning machine is better.  
On the other hand, when considering the electric vehicle access, by comparing the voltage distribution curves before and after electric vehicle access, shown in Figure 7d. After distributed generation and electric vehicle access, the voltage distribution is better than the original voltage level (V\({}_{\text{\_}}\)nD\({}_{\text{\_}}\)G&EV). So the distributed generation and electric vehicle access is helpful to improve the voltage stability.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node Number** & _I\(\_\)_rese\_o_ & _I\(\_\)_rese\_case1\(\&\)_I\(\_\)_rese\_case2\(\&\)_I\(\_\)_rese\_case3\(\}\) \\ \hline Node 5 & 0.06707 & 0.06392 & 0.06374 & 0.06294 \\ Node 17 & 0.001802 & 0.001635 & 0.001629 & 0.001604 \\ Node 27 & 0.0543 & 0.0498 & 0.0496 & 0.0486 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Index value of _I\(\_\)_rese_ without electric vehicle.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Node Number** & _I\(\_\)_rese\_o_ & _I\(\_\)_rese\_case1\(\&\)_I\(\_\)_rese\_case2\(\&\)_I\(\_\)_rese\_case3\(\}\) \\ \hline Node 5 & 0.06707 & 0.06392 & 0.06374 & 0.06294 \\ Node 17 & 0.001802 & 0.001635 & 0.001629 & 0.001604 \\ Node 27 & 0.0543 & 0.0498 & 0.0496 & 0.0486 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Index value of _I\(\_\)_rese_ with electric vehicle.  
Figure 6: The voltage stability evaluation index (_I\(\_\)_rese_) initial value without DG. (DG: distributed generation).