# Data-Driven Prediction Method for Power Grid State Subjected to Heavy-Rain Hazards
## 6 Results  
The data range used for this study was from 2008 through to 2018; a historical dataset up to mid of 2016 was used to develop the prediction model and the remaining historical dataset was used to evaluate the performance of the prediction model. Furthermore, the parameters (kernel parameter (\(\alpha^{2}\)) and penalty coefficient (C)) of the SVM model were tuned using Bayesian optimization. In total, 30 trials were conducted to find the best combination of the parameters with a minimum classification error of 5-fold cross-validation. A search for the C log-scaled in the range between 1e-3 and 1e3 and \(\alpha^{2}\) log-scaled in the range between 1e-3 and 1e3 was performed to find the best parameters of SVM. The G-mean values were evaluated for each of the 10 available explanatory variables to identify the key explanatory variables as shown in Table 2.  
The complexity of the model may lead to overfitting and a computational burden and inadequate variables can decrease the performance of the model. Thus, in this study, variables were selected by adding variables sequentially and the model with the highest performance was selected as the final model. Moreover, the degree of misclassification cost was determined to obtain an appropriate separating boundary. First, this study applied the reference ratio of the cost, 0.618:1 (the golden standard), between minority classes and the majority classes, as follows:  
\[C=\left[ \begin{array}{cc}0&0.618/n\big{(}t_{j}\big{)}\\ 1/n(t_{i})&0\end{array} \right], \tag{7}\]  
where \(t_{j}\) and \(t_{i}\) are the minority and majority class, respectively. Twenty percent of the historical dataset was used to evaluate the performance of the proposed method. Based on the cost matrix \(C\), the SVM models with a combination of weather variables were \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable Name** & \\ \hline Average wind speed & \(x_{1}\) \\ Maximum wind speed & \(x_{2}\) \\ Minimum wind speed & \(x_{3}\) \\ Average wind direction & \(x_{4}\) \\ Maximum wind direction & \(x_{5}\) \\ Minimum wind direction & \(x_{6}\) \\ Average accumulated rainfall & \(x_{7}\) \\ Maximum accumulated rainfall & \(x_{8}\) \\ Minimum accumulated rainfall & \(x_{9}\) \\
12 h accumulated rainfall & \(x_{10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Available explanatory variables. developed and their G-mean values are summarized in Table 3. Based on the average accumulated rainfall, \(x_{7}\), other variables were added sequentially. In Table 3, the G-mean values tend to decrease with the addition of the wind direction-related variables, \(x_{5},x_{6}\). It implies that wind direction is not a substantial factor for power grid outage subjected to heavy rain hazards. Conversely, the G-man values tend to increase with the addition of the wind speed-related variable, \(x_{1},x_{2},x_{3}\). This means that wind speeds have a substantial impact on the power grid even under heavy-rain conditions. Consequently, the SVM model with \(x_{1},x_{2},x_{3},x_{7},x_{9}\) recorded the highest G-mean values. This model is not significantly different compared to the others; however, it is superior to other models. To further improve the SVM model performance and analyze the effect of misclassification cost, the costs were explored with the variables \(x_{1},x_{2},x_{3},x_{7},x_{9}\). A grid search for the misclassification costs c, {1, 1.5, 2, 0,..., 11, 11.5} was performed to find the optimal separating boundary that properly classifies the majority class and minority class. Figure 5 shows the G-mean values with cost values. As shown in this figure, when the cost value was 1, the G-mean value was recorded as 0. This implies the general SVM model without the cost matrix so that the separating boundary of the model was placed towards the minority class to obtain better classification accuracy. This results in the separating boundary being pushed toward the majority class by the high misclassification cost.