## 4 Simulation Results
### Performance Analysis for Partially Cloudy Days  
In terms of partially cloudy days, the performance of the WT-ANFIS-HFPSO is compared with several forecasting models and the results are tabulated in Table 5. When the performance of the WT-ANFIS and ANFIS models are compared, the results obtained are similar to the results discussed in Section 4.1. The utilization of the WT with the ANFIS model has improved the performance of the forecasting model. This can be proven specifically when the MAE and RMSE values are lowered from 92.48 W in the ANFIS to 48.98 W in the WT-ANFIS and 109.28 W in the ANFIS to 61.58 W in the WT-ANFIS, respectively. Apart from that, the LCE value has been improved from 0.9221 in the ANFIS to 0.9334 in the WT-ANFIS. There is also an improvement in the WIA value as it increases from 0.9791 in the ANFIS to 0.9857 in the WT-ANFIS. Smaller values of the MAE and RMSE represent small \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Forecasting Model** & **MAE (W)** & **RMSE (W)** & **LCE** & **WIA** \\ \hline WT-ANFIS-HFPSO & 44.8471 & 56.4235 & 0.99427 & 0.99857 \\ WT-ANFIS-FF & 200.3330 & 234.1070 & 0.90366 & 0.96742 \\ WT-ANFIS-PSO & 53.5802 & 64.2567 & 0.99267 & 0.99813 \\ WT-ANFIS & 46.9559 & 58.6801 & 0.99395 & 0.99850 \\ ANFIS & 128.9838 & 153.3567 & 0.97631 & 0.99365 \\ \hline \hline \end{tabular} Note: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Legate* coefficient of efficiency (LCE) and Willmott’s index of agreement (WIA).  
\end{table} 
Table 4: Performance comparison of forecasting models on sunny days. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Condition of the Day** & **Sunny** & **Partially Cloudy** & **Cloudy** \\ \hline \multirow{3}{*}{**Date**} & 30 th September 2016 & 1 st October 2016 & 14 th November 2016 \\  & 15 th October 2016 & 16 th November 2016 & 1 st November 2016 \\  & 2 nd October 2016 & 10 th November 2016 & 17 th October 2016 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specified days for each condition of the day. differences that exist between the forecasted and actual solar power data. Meanwhile, a high value of the LCE and WIA signifies that the forecasted values of solar power are closer to the actual ones. Hence, the application of the WT as a denoising tool has helped improve the ANFIS model to forecast solar power on partially cloudy days. Furthermore, the combination result of the WT-ANFIS with the HFPSO algorithm is compared with the WT-ANFIS-FF and WT-ANFIS-PSO. Similar to the discussion made in Section 4.1, all of the performance metric values of the WT-ANFIS-HFPSO are superior to the WT-ANFIS-FF and WT-ANFIS-PSO. These results specify that the hybridization of the FF and PSO has the capability to improve the performance of the WT-ANFIS better than utilization of an individual FF and an individual PSO. In sum, the advantage of the WT to remove noisy data and the benefit of HFPSO to obtain the optimal values of premise parameters have increased the accuracy of the WT-ANFIS-HFPSO model to forecast solar power data. Figure 8 shows the behavior of forecasted solar power data for the WT-ANFIS-HFPSO on partially cloudy days. It can be found that the forecasted solar power data manages to capture the trend of the actual solar power data. Hence, it is obvious that the WT-ANFIS-HFPSO not only capable of forecasting solar power data on sunny days, but it manages to forecast solar power data on partially cloudy days with high precision and accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Forecasting Model** & **MAE (W)** & **RMSE (W)** & **LCE** & **WIA** \\ \hline WT-ANFIS-HFPSO & 37.5361 & 50.6254 & 0.94786 & 0.98905 \\ WT-ANFIS-FF & 79.5826 & 91.9239 & 0.88303 & 0.96935 \\ WT-ANFIS-PSO & 38.0304 & 51.4952 & 0.94318 & 0.98824 \\ WT-ANFIS & 48.9825 & 61.5801 & 0.93337 & 0.98569 \\ ANFIS & 92.4802 & 109.2813 & 0.92208 & 0.97913 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance comparison of forecasting models on partially cloudy days.