# A Data-Driven Approach for Generating Synthetic Load Profiles with GANs
## 3 Results
### Evaluation and Comparison
#### 3.2.3 Visual Methods for Evaluation of the Synthetic Data
The Conv1D-WGAN-GP model delivers a moderately improved approximation with a broader spread and less central bias compared to Vanilla-GAN and Conv1D-GAN. However, it still fails to reproduce the sharp spike near the upper end of the real, similar to the other models. While this reflects improved balance across mid-range values, the advantage is less visually pronounced than in other cases. Lastly, the WGAN-GP model struggles the most. It significantly overestimates the frequency of low-load values and fails to model both the mid-range and high-end values with any fidelity. The synthetic distribution is skewed heavily toward the lower range, creating a pronounced mismatch with the real data. This indicates a weakness in the model's ability to learn from the full range of real data, particularly when it comes to representing more extreme values. Based on the histogram visualization of the Industrial dataset (Figure 19), an interesting case that should be further examined is the 6 th hour. Therefore, the 6 th hour is chosen for the histograms in Figure 6. The Conv1D-GAN model shows a reasonable match in the central range of the distribution (roughly between 0.15 and 0.6). However, the synthetic data overrepresents the low-load region (around 0.1 to 0.3), while it underrepresents values in the higher range (above 0.6). The real data display a noticeable peak near 0.65 and scattered values beyond that, which the synthetic  
Figure 19: Histograms of the 6 th hour for the Industrial dataset using Vanilla-GAN (**a**), WGAN-GP (**b**), Conv1D-GAN (**c**), and Conv1D-WGAN-GP (**d**). data fail to replicate accurately. Overall, the model captures the distribution's general shape but misses details, particularly in the higher-load tail. The Vanilla-GAN model continues to produce a smooth, bell-like synthetic distribution centered in the 0.2-0.5 range. While the match is acceptable in the middle of the range, the model again fails to capture the peaks in the higher-load portion of the real distribution. It also appears to generate an excessive number of mid-range values while not representing the lower and higher extremes well. This results in a distribution that is less realistic and biased toward average load levels. The Conv1D-WGAN-GP model performs slightly better in representing the overall variability of the real data. It captures values across the full range and appears more aligned with the real distribution in both shape and spread. However, there are still mismatches, particularly around 0.6, where the real data have stronger peaks. Despite some misalignment in frequency, this model seems to offer a more balanced approximation with a diverse synthetic output. The WGAN-GP model, similar to its Conv1D-enhanced counterpart, succeeds in spreading synthetic values across the full domain. It replicates the general bimodal nature of the real data reasonably well, although the heights of the peaks differ. It still underrepresents some of the more prominent clusters in the real data, especially beyond 0.6. Nevertheless, among all models, it appears to generate the most evenly distributed synthetic data, though not necessarily the most accurate in terms of matching specific distribution features. In general, when talking about households and their consumption, the time around the 18 th hour is considered important, as there are expected peaks in the loads. Therefore, this is the hour represented in Figure 20 as its real distribution presents a challenge due to its steep skew and dominant low values. Figure 20: Histograms of the 18 th hour for the Household dataset using Vanilla-GAN (**a**), WGAN-GP (**b**), Conv1D-GAN (**c**), and Conv1D-WGAN-GP (**d**). The Conv1D-GAN shows a partial match with the real data. It captures the overall decreasing trend of the distribution, with a prominent spike near zero. However, the real data display a much sharper and higher peak at the lowest load values, which the synthetic distribution underestimates.