# Method for Wind-Solar-Load Extreme Scenario Generation Based on an Improved InfoGAN
## 4 Case Study
### Error Analysis of Different Models  
To assess the ability of the model described above to fit the historical data, wind, solar, and load data are used. The mean values of the Wasserstein distance measure for generating the set of extreme scenarios are given in Table 6, with smaller values indicating a higher accuracy of the model in fitting the historical data. The Wasserstein distance measures the difference between two probability distributions by calculating the minimum effort required to transform one into the other. In this model, a smaller Wasserstein distance indicates that the generated extreme scenarios closely resemble the historical data, reflecting a higher model accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Categories** & \multicolumn{2}{c}{**Wind Power**} & \multicolumn{2}{c}{**Solar Power**} & \multicolumn{2}{c}{**Load**} \\ \hline  & \(W\) & \(C\) & \(W\) & \(C\) & \(W\) & \(C\) \\ \hline Case 1 & 8.46 & 76.14 & 5.66 & 85.61 & 8.69 & 92.09 \\ Case 2 & 8.23 & 78.00 & 5.79 & 87.00 & 8.01 & 96.31 \\ Case 3 & 8.11 & 96.82 & 5. 28 & 92.65 & 6.14 & 98.82 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ensemble validity indexes of scenario sets under Cases 1–3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Categories** & **Wind Power** & **Solar Power** & **Load** \\ \hline Case 1 & 1.643 & 1.019 & 1.438 \\ Case 2 & 1.283 & 0.924 & 1.361 \\ Case 3 & 1.036 & 0.582 & 0.914 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Mean of Wasserstein distance of scenario sets under Cases 1–3.  
As shown in Table 5, Case 3, which is proposed in this paper, achieves a high accuracy improvement in the generation of wind, solar, and load scenarios. Compared with Case 1, the Wasserstein distance measure of the wind scenario obtained by Case 3 is reduced by 38.7%, that of the solar scenario is reduced by 45.1%, and that of the load scenario is reduced by 40.1%. Among the three scenarios, the model proposed in this paper has the greatest accuracy improvement in the generation of the solar scenario and the smallest accuracy improvement in the generation of the wind scenario. This is because the diurnal nature of solar power is reflected in the highest temporal correlation in the time series features, and the effect of using the improved InfoGAN model to extract data features is more obvious.  
Table 6 compares the error values of the test scenarios generated by the three cases, where two error metrics are considered, namely, MAPE (mean absolute percentage error, mean absolute percentage error) and RMSE (root mean square error, root mean square error); the formulae for each of the metrics are shown in Equations (24) and (25).  
\[MAPE=\frac{100\%}{\text{n}}\sum\limits_{i=1}^{n}\left|\frac{p_{i}^{Gen}-p_{i} ^{\text{Re}}}{p_{i}^{\text{Re}}}\right| \tag{24}\]  
\[RMSE=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\left(p_{i}^{Gen}-p_{i}^{\text{Re} }\right)^{2}} \tag{25}\]  
where \(p_{i}^{\text{Re}}\) and \(p_{i}^{Gen}\) denote the real scene power and the generated scene power, respectively.  
As shown in Table 6, it can be seen that the method proposed in this paper not only outperforms the traditional probabilistic generation method but also improves substantially over the traditional GAN model in Case 2. This can prove the effectiveness of the proposed model in wind, light, and load scene generation.