## 3 Results
### Experimental Results with the Subtractive Clustering Method  
Table 2 shows the results of modelling and prediction using the ANFIS subtractive clustering process. In addition, four ANFIS models using this approach are depicted in Figure 11a-d. The parameters used in these architectures are N, the number of inputs represented as in the previous method, the number of samples and the influence radius, IR, which gives the number of clusters, C. This type of ANFIS model differs from those obtained using the grid partition method. There are no very large numbers of neurons in layers 3 and 4, nor are there many rules. This ensures that the training time will not increase significantly.  
Figure 10: Regression coefficients for the training and testing phase for modelling with ANFIS grid partition method.  
Figure 9: The variation of the measured and predicted reactive power, and also of the error for modelling with ANFIS grid partition method for testing stage.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Crt.** \\ **No.** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Model Parameters** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Results** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Training** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Testing** \\ \end{tabular} } \\ \cline{2-10}  & **N** & **IR** & \
\begin{tabular}{c} **Training** \\ **Time** \\ \end{tabular} &
\begin{tabular}{c} **Rules** \\ **(Clusters)** \\ \end{tabular} & **MSE** & **RMSE** & **R** & **MSE** & **RMSE** &  
Analysing the modelling results, it can be concluded that the ANFIS architecture will not produce many rules in layer 3 using this method, subtractive clustering, unless the radius of influence is very small. When using this method, on the other hand, the smaller the radius of influence, the faster the number of fuzzy sets increases. The number of fuzzy sets in layer 2 does not increase beyond a certain radius of influence. Thus, over a radius of influence of 0.7, the ANFIS architecture is practically difficult to realize since it will result in less than two fuzzy sets, which is impossible. However, if the radius of influence is set to less than 0.1, the number of clusters, or fuzzy sets on each input, may increase. The training time increases with N = 5 and r = 0.05, as seen in Table 2, and the network architecture contains 65 clusters, or 65 fuzzy sets. However, there are practically not as many rules in this case as there are in ANFIS grid partition.  
The modelling and prediction results for the architecture in line 31 in Table 2 are shown in Figure 12a,b for the training and testing stages, respectively. As a result, in Figure 12a for training and Figure 12b for testing, the calculated active power and that obtained by training, as well as the errors, are shown. Figure 13 shows the regression coefficients for training and testing, respectively.  
Figure 11: Different architectures of the ANFIS models using subtractive clustering method; (a) N = 5, IR = 0.1; (b) N = 5, IR = 0.5; (c) N = 3, IR = 0.2; (d) N = 2, IR = 0.05.  
Figure 12: The variation in the measured and predicted reactive power and also of the error for modelling with ANFIS subtractive clustering method; (**a**) for training stage; (**b**) for testing stage.