# A Data-Driven Approach for Generating Synthetic Load Profiles with GANs
## 3 Results
### Evaluation and Comparison
#### 3.2.1 Statistical Methods for Evaluation of the Synthetic Data  
The Wasserstein distance (W-Distance in Table 7) results across all datasets demonstrate that the Conv1D-WGAN-GP consistently achieves the lowest scores, indicating superior alignment between real and synthetic data distributions, as shown in Figure 9. For example, it records values as low as 0.0198 (ERGAN), 0.0239 (Industrial), 0.0329 (Household), and 0.0209 (Pig Farm)--all within the excellent threshold of <0.15 (as defined in Table 1). These results highlight the effectiveness of combining convolutional structures with gradient penalty regularization in capturing complex temporal dependencies and improving the stability of GAN training. In contrast, standard Conv1D-GAN and WGAN-GP models exhibit higher W-Distance values (often >0.05), suggesting less accurate distributional matching. And while those results are still within the 0.15 threshold, the results obtained by the Conv1D-WGAN-GP are preferable. Low Wasserstein distance values are particularly important, as they reflect how well the synthetic profiles mimic the hourly variations seen in the real data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Model** & **W-Distance** & **Mean Diff.** & **STD Diff. 1** & **Classifier Acc. 2** & **JS Div. 3** & **RMSE 4** \\ \hline \multirow{4}{*}{ERGAN} & Vanilla-GAN & 0.0263 & 0.0129 & 0.026 & 0.5972 & 0.0023 & 0.2669 \\  & WGAN-GP & 0.0369 & 0.0257 & 0.0356 & 0.8372 & 0.0091 & 0.2709 \\  & Conv1D-GAN & 0.0605 & 0.0484 & 0.0603 & 0.8419 & 0.0193 & 0.2633 \\  & Conv1D-WGAN-GP & 0.0198 & 0.0048 & 0.0153 & 0.5354 & 0.0176 & 0.2647 \\ \hline \multirow{4}{*}{Industrial} & Vanilla-GAN & 0.0599 & 0.0148 & 0.0263 & 0.5498 & 0.0329 & 0.2864 \\  & WGAN-GP & 0.0475 & 0.0365 & 0.0167 & 0.8557 & 0.0087 & 0.2893 \\  & Conv1D-GAN & 0.065 & 0.0568 & 0.0294 & 0.7973 & 0.017 & 0.2763 \\  & Conv1D-WGAN-GP & 0.0239 & 0.0124 & 0.0084 & 0.5567 & 0.0062 & 0.2716 \\ \hline \multirow{4}{*}{Household} & Vanilla-GAN & 0.0458 & 0.0332 & 0.0343 & 0.5586 & 0.0309 & 0.3109 \\  & WGAN-GP & 0.0507 & 0.0288 & 0.0293 & 0.8559 & 0.0348 & 0.3317 \\  & Conv1D-GAN & 0.0515 & 0.0276 & 0.0501 & 0.6126 & 0.0494 & 0.2871 \\  & Conv1D-WGAN-GP & 0.0329 & 0.0139 & 0.0078 & 0.5315 & 0.0341 & 0.3219 \\ \hline \multirow{4}{*}{Pig Farm} & Vanilla-GAN & 0.0326 & 0.0092 & 0.0161 & 0.5517 & 0.0162 & 0.2833 \\  & WGAN-GP & 0.0551 & 0.0415 & 0.0403 & 0.8483 & 0.0138 & 0.2549 \\ \cline{1-1}  & Conv1D-GAN & 0.1162 & 0.1142 & 0.051 & 0.869 & 0.0565 & 0.277 \\ \cline{1-1}  & Conv1D-WGAN-GP & 0.0209 & 0.0096 & 0.0081 & 0.5034 & 0.0078 & 0.2801 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results from training. Figure 9: Comparison between the Wasserstein distance metrics of the investigated algorithms using the ERGAN (**a**), Industrial (**b**), Household (**c**), and Pig Farm (**d**) datasets. It is worth noting that the Conv1D-GAN model records a significantly higher Wasserstein distance (0.1162) on the Pig Farm dataset compared to all other models. This deviation can be attributed to several factors. First, the Pig Farm dataset is relatively small (only 363 samples), making it highly prone to overfitting or mode collapse in unconstrained GANs like the Conv1D-GAN, which lack gradient penalty regularization. Second, Conv1D-GAN relies solely on adversarial loss with no explicit regularization or divergence control, which may cause the generator to fail in capturing the subtle and irregular temporal patterns present in the Pig Farm data. These limitations reinforce the need for regularization techniques, such as the gradient penalty used in Conv1D-WGAN-GP, to ensure stable training and improved performance, particularly on small and irregular datasets. The mean and STD difference metrics offer crucial insight into how well the synthetic data preserve the central tendency and variability of the original dataset (Figure 10).