## 6 Experiment and Result Analysis
### Comparative Analysis of Data-Derived Models  
To verify the performance of SA-CTGAN, a box-type substation acquisition system was established for enterprise A, and a total of 700 different fault data and normal operation data were randomly selected from the database to form a small sample unbalanced data-set. The SMOTE model, CTGAN model, and SA-CTGAN model were used for data derivation experiments.  
For the above three data-sets, the number of nearest neighbors of the SMOTE model is set to five. The DE optimization algorithm was used to optimize the number of iterations, training batches, and learning rate in the CTGAN model and the SA-CTGAN model. The amount of the expanded data in all models is set to 1400.  
Select the original data and generated data of the fault type of the high-voltage circuit breaker and draw the heatmap of the raw data and the generated data, respectively, as shown in Figure 8, where (a), (b), (c), and (d) are the original data heatmap, the SMOTE- generated data heatmap, the CTGAN-generated data heatmap, and the SA-CTGAN-generated data heatmap, respectively.  
Based on the correlation coefficients shown in Figure 8, the correlation coefficient matrix of the data generated by SA-CTGAN is the closest to the original data. To quantitatively compare the data generation effects from the three derived models, four evaluation metrics  
Figure 8: Comparison of raw data and generated data heatmap: (**a**) original data distribution; (**b**) the generated data distribution of SMOTE; (**c**) the generated data distribution of CTGAN; (**d**) the generated data distribution of SA-CTGAN.  
constructed in Section 6.1 were used to evaluate the derived data of the three models. The evaluation results are shown in Table 3.  
By comparing the KL divergence and the mean cosine similarity, it is found that the CTGAN model and SA-CTGAN model are better than the SMOTE model in the similarity of data distribution. Comparing the cumulative deviation of correlation coefficient and the heatmap SSIM metric, the cumulative deviation of the correlation coefficient of the SA-CTGAN model is significantly lower than that of SMOTE and CTGAN, and the heatmap SSIM metric of the SA-CTGAN model is significantly higher than that of SMOTE and CTGAN. It is deduced that the SMOTE model and the CTGAN model are similar in the maintenance of data correlation, the data generated by the SA-CTGAN model with the introduction of the self-attention mechanism is significantly better than the other two models in terms of correlation similarity; that is, the self-attention mechanism can effectively maintain the correlation between different indicators.  
Furthermore, draw a distribution histogram, comparing the derived data results through the distribution of 24 indicators, as shown in Figure 9, where (a), (b), (c), and (d) are the distribution of original data, SMOTE-generated data, CTGAN-generated data, and generated data, respectively.  
Figure 9: Distribution comparison of original data with data generated: (**a**) original data distribution; (**b**) the generated data distribution of SMOTE; (**c**) the generated data distribution of CTGAN; (**d**) the generated data distribution of SA-CTGAN.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **SMOTE** & **CTGAN** & **SA-CTGAN** \\ \hline KL divergence & 0.0101 & 0.0042 & 0.0037 \\ Mean cosine similarity & 0.8494 & 0.8768 & 0.8996 \\ Cumulative deviation of the correlation coefficient & 11.9714 & 11.9682 & 9.8331 \\ Heatmap SSIM metric & 0.8365 & 0.8527 & 0.9135 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of model results.  
The distribution of the data generated by the three models is roughly similar to that of the original data. Among them, the SMOTE model has the worst generation effect, while the CTGAN model and SA-CTGAN model are better. This is because the SMOTE model can only generate edge data when generating data with positive samples distributed at the edge through sampling, which cannot solve the problem of distribution marginalization.