# A Data-Driven Approach for Generating Synthetic Load Profiles with GANs
## 2 Materials and Methods
### Benchmark Models  
For evaluating the performance of the proposed model, several benchmark models are selected. Vanilla GANs represent the original formulation introduced by [PERSON] et al. in 2014 [23]. They serve as a foundational benchmark for evaluating generative models in numerous studies. Despite their simplicity, vanilla GANs can effectively capture the global distribution of real data and are a valuable baseline for comparison. However, they are notoriously unstable during training, especially when applied to complex or high-variance datasets such as electrical load profiles. These types of profiles exhibit strong temporal dependencies and varied behavioral patterns, which vanilla GANs often struggle to replicate accurately. Common issues include mode collapse, where the generator \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Threshold Values \({}^{*}\)** & \begin{tabular}{c} **The Metric’s Importance in This** \\ **Methodology** \\ \end{tabular} \\ \hline Average Wasserstein Distance [35] & \textless{}0.15 (Excellent), \textless{}0.25 (Good) & \begin{tabular}{c} Measures distribution alignment per hour. \\ Lower is better; high values indicate poor \\ matching of load shapes. \\ \end{tabular} \\ \hline Mean Difference [36] & \textless{}0.05 (Excellent), \textless{}0.10 (Acceptable) & \begin{tabular}{c} Ensures the synthetic data have the same \\ overall average load. \\ \end{tabular} \\ \hline STD Difference [36] & \textless{}0.1 (Excellent), \textless{}0.2 (Acceptable) & \begin{tabular}{c} Captures variability; essential for \\ representing diversity in users’ behavior. \\ \end{tabular} \\ \hline Classifier Accuracy (logistic regression) & \(\leq\)0.6 (Ideal), \(\leq\)0.65 (Tolerable) & \begin{tabular}{c} If a simple model cannot easily distinguish \\ real from synthetic, it indicates high realism. \\ \end{tabular} \\ \hline JS Divergence (overall) & \textless{}0.05 (Excellent), \textless{}0.1 (Good) & \
\begin{tabular}{c} A symmetric version of KL. Easier to \\ interpret; 0 = identical, 1 = total difference. \\ \end{tabular} \\ \hline RMSE (per profile and overall) & \textless{}0.1 (Excellent), \textless{}0.2 (Acceptable) &
\begin{tabular}{c} Penalizes large point-wise errors. It should \\ be small if the curves are aligned. \\ \end{tabular} \\ \hline \hline \end{tabular}  
* The threshold values in Table 1 are established based on a combination of existing literature and empirical validation. Specifically, the thresholds for JS divergence, Wasserstein distance, and classifier accuracy draw on precedent from prior studies evaluating GAN-generated time-series data [12; 33; 35]. However, due to the absence of universal standards for synthetic electrical load profile generation, these values were further refined using the authors’ benchmark experiments. Acceptable and excellent ranges were defined by evaluating the performance of multiple GAN architectures across datasets of varying sizes and comparing synthetic versus real profile fidelity through statistical and downstream task metrics. As such, the thresholds serve as practically motivated heuristics, rather than rigid universal standards, and provide a consistent evaluation framework across experiments in this study.  
\end{table} 
Table 1: A summary of the evaluation metrics adopted in this study. produces repetitive or limited variations in outputs, and non-informative loss curves, where discriminator and generator losses do not reflect true learning progress. Still, vanilla GANs remain important for benchmarking. They allow for assessing the baseline performance of adversarial training and provide a reference point against which improvements from more advanced models, such as WGAN-GP or recurrent GANs, can be measured. In the context of electrical load profile generation, they can be used to test whether the network can approximate daily usage patterns under perfect-like conditions and whether minimal architectures can capture essential characteristics like peak load times and average consumption levels.