# Adaptive Solar Power Forecasting based on Machine Learning Methods
## 5 Simulation Results
### Performance Evaluation of ASPF  
We now validate that our ASPF can adaptively revise the solar power which is predicted by NN. We randomly select 100 days of data from 1 January to 31 October 2016, and store the data as the initial database, which includes both predictive information and PV actual power. The data in the database gradually accumulates as the number of days increases in this system. Data from 1 November to 30 December 2016 are used to test the effectiveness of the ASPF. By comparing with the cluster centers \(C_{1}^{*}\) and \(C_{2}^{*}\), \(group\) 1 has 23 data points, and \(group\) 2 has 37. Here, \(d_{1}=1,2,\cdots,23\), \(d_{2}=1,2,\cdots,37\). For these 60 testing days, the ASPF results are in Table 6. \(NL\) is the number of days whose MxAE is smaller than \(\Delta_{2}\), and \(NB\) denotes the number of days whose MxAE is larger than \(\Delta_{2}\). Through Table 6, it can be observed that there are 8 times with similar day, and 15 times with no similar day in \(group\) 1. Due to the stored data in \(group\) 1 is less than in \(group\) 2, there are only 4 times that the historical actual value can be accepted as revised solar power. The non-similar day data are revised by our proposed BPNN, and the results are ideal as their MxAEs are less than \(\Delta_{2}\). Moreover, the similar day number of \(group\) 2 is more than that in group 1 because there are more data in \(group\) 2 in the database. There is also one non-similar day's result predicted by BPNN over the \(\Delta_{2}\), because the weather changes are more complex in non-sunny circumstances which lead to larger errors. However, the overall performance of our proposed methods is very stable and reliable. The comparisons between the proposed method and the historical data are shown in Figures 9 and 10. Here, \(P_{sdm}\) denotes the corresponding historical actual solar power if similar days exist. \(P_{ori}\) is the predicted solar power by original method. \(P_{act}\) represents the actual solar power of the day. Figure 9a shows the result when there is a similar day in \(group\) 1 and when \(d_{1}=1\), \(P_{sdm}\) is used as the revised PV power. In addition, at the night of the day, we can know the actual solar power \(P_{act}(d_{1})\) by EMS, the MxAE between the \(P_{sdm}\) and \(P_{act}(d_{1})\) will be gotten, here MxAE is 9.112, less than initial \(\Delta_{2}\), which is 9.476. In Figure 9b, there are 3 similar days, and the actual MxAE between \(P_{sdm}\) and \(P_{act}(13)\) is 8.351, larger than the current \(\Delta_{2}\). In Figure 9d, the data of the 13 rd day are used to \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\({}^{5}\)**Pattern**} & \multicolumn{3}{c}{**Similar Days**} & \multicolumn{3}{c}{**Non-Similar Day**} \\ \cline{2-7}  & **NT** & **NL** & **NB** & **NT** & **NL** & **NB** \\ \hline \(group\) 1 & 8 & 4 & 4 & 15 & 15 & 0 \\ \hline \(group\) 2 & 17 & 12 & 5 & 20 & 19 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The results of ASPF. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **RMSE (kW)** & **MAPE (\%)** & **MxAE (kW)** \\ \hline \(group\) 1 & 3.66 & 4.30 & 9.476 \\ \(NN\) & 9.31 & 16.42 & 22.34 \\ \hline \(group\) 2 & 1.74 & 7.04 & 8.33 \\ \(NN\) & 6.44 & 31.91 & 18.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of forecasting results in NN. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **RMSE (kW)** & **MAPE (\%)** & **MxAE (kW)** \\ \hline \(group\) 1 & 3.02 & 7.43 & 10.01 \\ \(MLR\) & 9.01 & 51.04 & 25.51 \\ \hline \(group\) 2 & 3.87 & 8.39 & 9.67 \\ \(MLR\) & 9.59 & 44.73 & 20.46 \\ \hline \(group\) 3 & 2.68 & 6.54 & 8.54 \\ \(MLR\) & 11.99 & 34.66 & 23.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of forecasting results in MLR. retain the BP neural network. When \(d_{1}=[2,3,4,5,6,8,9,10,11,12]\), there is no similar day, so BPNN is used to get the day-ahead revised solar power as shown in Table 7. And the MxAEs in these days are less than 9.476, so \(\Delta_{2}\) gradually reduces.