## 4 Simulations
### Kernel Extreme Learning Machine Prediction Accuracy Verification  
Figure 5 shows the average root mean square error value of kernel extreme learning machine under different access modes. The abscissa represents the different access modes of the distributed generation (shows in Appendix A Table A2), and the ordinate represents the value of the root mean square error (_RMSE_). It can be seen that the _RMSE_ curve of the kernel extreme learning machine was relatively flat, and its average value is 0.04; the change of support vector machine is relatively large, and its average value is 0.062. A flatter curve corresponds to a smaller _RMSE_ value, indicating that the prediction accuracy is better. Therefore, the kernel extreme learning machine prediction was better than that of the support vector machine.  
To verify the feasibility and reasonability of kernel extreme learning machine, comparing the results of kernel extreme learning machine with and without electric vehicle. The calculation results of the kernel extreme learning machine without electric vehicle are given in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline
**DG Access Mode** & **Active Power Loss (kW)** & **Total Cost (Million RMB)** & **DG Capacity (MW)** \\ \hline Case 1(Wind) & 107.59 & 2274.74 & 2.87(5) \\ Case 2(Wind, 1 PV) & 108.22 & 2792.85 & 2.96(5); 0.53(18) \\ Case 3(Wind, 2 PV) & 108.61 & 3228.59 & 2.96(5); 0.55(18); 0.54(32) \\ \hline \end{tabular}
\end{table}
Table 1: Results of kernel extreme learning machine without electric vehicle; (DG: distributed generation).  
Figure 4: IEEE 33 distribution network structure.  
Figure 5: Changes of root mean square error (RMSE).  
It can be seen from Table 1 that as the number of distributed generation increases, the active power loss increases. As the distributed generation access location and capacity change, it will cause changes in network power flow. The larger the distributed generation access capacity, the greater the impact on the network power flow distribution. So the active loss increases with the access of distributed generation. The access node is listed behind the distributed generation capacity with brackets.  
Table 2 is the results with electric vehicle connecting, and the average capacity of the electric vehicle is 0.285 MW at node 32. For convenience of comparison, the electric vehicles are not included in the total investment cost.  
It can be seen from Table 2 that when electric vehicle access is taken into account, the capacity of wind and photovoltaic increases, while the active power loss decreases. So the electric vehicle access is beneficial to the access of distributed generation and helpful to reduce active power losses.  
On the other hand, the results of kernel extreme learning machine are compared with that of a support vector machine. With similar access capacities, the total investment costs are compared. The total investment cost obtained by the kernel extreme learning machine is reduced, with an average decrease of 0.8%, and the active loss was reduced by an average of 28%. In the calculation time, the support vector machine average calculation time was about 22.6 s, and the kernel extreme learning machine is about 16.9 s. Analyzing the reasons, in addition to the inherent calculation time required for the power flow calculation, the kernel extreme learning machine needs time on the millisecond level, while the support vector machine requires 3-5 s.  
The model mainly utilizes kernel extreme learning machine's non-linear approximation ability and generalization performance to approximate the non-linear relationship between the node voltage and the distributed generation power. The above analysis shows that the kernel extreme learning machine is better than the support vector machine in terms of calculation speed and prediction accuracy. And its calculation results are feasible and reasonable.