# Deep-Learning Model Selection and Parameter Estimation from a Wind Power Farm in Taiwan +
## 5 Method Comparisons  
As shown in Figure 14a, the precision of four prediction models was increased by the decreased convergence error of the cost function in each iteration of the model training. More concisely, the descending speed of error convergence for the cost function was rapid with the increasing number of iterations (epochs). After 60 iterations, the loss function tended to be stable when TCN and GRU prediction models were applied (Figure 14b). However, the errors for the RNN and LSTM models did not converge slowly. Notably, the convergence error of the TCN model decreased more than that of the GRU model close to the fifteenth epoch, and the convergence error decreased steadily as the number of iterations increased. The experimental results revealed that the prediction error of the TCN model decreased the most steadily among the four models, followed by GRU and LSTM.  
To discriminate the performance of four prediction models in long-term prediction, different lengths of the prediction period based on the same amount of training data were tested. Notably, the experiment varied the lengths of the prediction periods set to examine the accuracy of the convergence error in practice; Table 12 lists the prediction error (i.e., MAPE), and the output results of the modules were sorted for a test set of distinct lengths of prediction periods with the same data size.  
Experimental results show that the prediction error increased as the length of the prediction period increased. In other words, the prediction error of wind power output increased with increasing length of prediction period. Particularly, the prediction error of the TCN-based model remained below 2% with increasing length of the prediction period, and the forecast errors for 72, 120, and 168 h were 0.07%, 1.71%, and 1.41%, respectively. In summary, the average prediction error of the proposed TCN-based model was approximately 1.063% based on 1-year historical data in three different predictive periods. In other words, the TCN model achieved highly precise prediction accuracy with consistent and stable results using selected parameters from the Q-learning algorithm.  
Figure 13: Experimental results for 168 h wind power forecasting.  
Compared to other studies in wind power forecasting, such as with LSTM [17], LSTM with grid search (LSTM-grid) [18], bidirectional LSTM with grid search (BiLSTM-grid) [18], GRU [17], TCN [17], and the ensemble learning-based AAA aggregation model [19], the detailed comparison information for distinct approaches is listed in Table 13. Notably, the project of the BSI electric power company used an AAA aggregation model based on an ensemble-based learning algorithm for 120 h forecasts by aggregating numerous deep learning models in different climate scenarios and reached approximately 2% prediction error in 2016. Overall, the proposed TCN-based model with Q-learning algorithm provides a lower prediction error with higher prediction accuracy than those of earlier deep learning schemes such as LSTM, BiLSTM, TCN and AAA aggregation models [32] in studies of wind power forecasting.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Period Performance** & **Excellent** & **Good** & **Medium** & **Bad** \\ \hline
72 h (3 days) & TCN (0.07\%) & LSTM (1.20\%) & GRU (1.46\%) & RNN (3.33\%) \\
120 h (5 days) & TCN (1.71\%) & GRU (4.01\%) & LSTM (7.75\%) & RNN (35.08\%) \\
168 h (7 days) & TCN (1.41\%) & GRU (3.72\%) & LSTM (6.99\%) & RNN (28.18\%) \\ \hline \hline \end{tabular}
\end{table}
Table 12: Performance comparison of four DNN models with prediction error for wind power forecasting.  
Figure 14: (**a**) Convergence error of the cost function for the RNN, LSTM, GRU and TCN models. (**b**) Partial enlarged image of (**a**).