## 3 Case Study--The ANN Models for Load Forecasting
### Experiments and Results  
The ANN model's performances based on the number of data they have trained on and the inclusion of features, Univariable and Multivariable, are shown in Table 4.  
For example, when the models are trained on 30,000 data, the GRU univariable model has the Mean Absolute Error (MAE) of 0.00471, but as the training data increases to 120,000, the GRU model performance decreases significantly (with MAE 0.008551). Another interesting result is that when using 50% of the data (60,000), models with the same structures have the worst performance, as opposed to the assumption that as the number of training data increases, the performance of the ANN model increases as well. But overall, using the whole data set has the lowest error, and it confirms this assumption. AS, the LSTM model that has trained on the whole dataset with all features, multivariable, has the best performance. This confirms the fact that including more data and features increases the performance of LSTM models for the power prediction task. Also, it might be true for some models such as convolutional 2D and FCNmodels. But, this is not true for all models, as in some cases like that of BiLSTM, GRU, and Transformer, the univariable model performs better regardless of the number of data that the model is trained on. In some cases, convolutional 1D and ConvLSTM2D univariable models have a lower error in the smallest and biggest dataset, but in the middle, with 50% of the data, the multivariable model performs better. As can be seen from the behavior of the ANN models, there is no evidence that including more features such as temperature and so on will reduce the error in the prediction, as in many cases this is not true. As can be seen from Figure 16, there is not a significant change in the range of errors when models are trained on the smallest dataset. But, the range of errors increases as the amount of data increases, with the most in 50% of the dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**25\% of the Dataset**} & \multicolumn{2}{c}{**50\% of the Dataset**} & \multicolumn{2}{c}{**The Whole Dataset**} \\ \cline{2-6} \multicolumn{1}{c}{} & **Test** & **Validation** & **Test** & **Validation** & **Test** & **Validation** \\ \cline{2-6} \cline{10-6}  & **MAE** & **MAE** & **MAE** & **MAE** & **MAE** & **MAE** \\ \hline LSTM Multivariable & 0.00515 & 0.00490 & 0.01120 & 0.00400 & **0.004521** & 0.002426 \\ ConvLSTM2D Univariable & 0.00541 & 0.00467 & 0.01252 & 0.00317 & 0.00455 & 0.002653 \\  
The multivariable Transformer model is the only model that has an error of 0.01814, which is significantly more than the previous highest error, the BiLSTM multivariable model with an MAE of 0.00738, in 25% of the test data. By doubling the training data, the overall performance of models decreases, and there is more fluctuation in the range of error. Moreover, there are more models with higher errors (BiLSTM Multivariable, GRU Multivariable, FCN Univariable, LSTM Multivariable, Conv1D Univariable, FCN Multivariable, ConvLSTM2D Univariable, Transformer Multivariable), which have significantly more errors than that with the previous highest error, which is the Conv1D Multivariable model with an MAE of 0.00916. The models trained on the whole dataset have similar performance to when they are trained on 25% of the whole dataset with regard to the magnitude of errors with slightly lower values. For example, the MAE of the best model trained on the whole dataset, the LSTM multivariable, is 0.00019 less than the best model trained on 25% of the whole dataset, which is the GRU univariable. Moreover, to visualize the contribution of features in the prediction of Shapely values for the LSTM multivariable, the best-performing model, is shown in Figure 17. Interestingly, the periodicity in the day (cosine of the day) is more important than the temperature in the LSTM multivariable model's performance.