## 4 Case Study  
### Data Presentation and Analysis  
#### 4.1.1 Data Presentation and Evaluation Metrics  
A wind farm cluster in Jiangxi Province of China consists of 67 wind farms, with a total installed capacity of 5388.9 MW. The wind farms are distributed within the latitude range of 24\({}^{\circ}\) N to 30\({}^{\circ}\) N and the longitude range of 113\({}^{\circ}\) E to 118\({}^{\circ}\) E. The data span from 1 January 2021, to 30 December 2022, and include measured power, as well as NWP data for 100 m wind speed, 10 m wind speed, temperature, dew point temperature, and other relevant variables. All data were sampled at an interval of one hour. The power measurements are aggregated.  
Figure 9 shows the distribution of the duration and frequency of cold waves in a certain area over two years. The duration of most cold waves is concentrated between 1 and 10 h, and cold wave events lasting more than 30 h are rare. However, cold waves with longer durations can have a significant impact on the operation of wind turbines, particularly under extreme weather conditions, where turbine equipment may suffer from icing and unstable power output. These effects not only reduce the operational efficiency of wind turbines but also lead to a considerable decrease in the accuracy of wind power forecasts, which, in turn, affects grid scheduling and the stability of the energy supply. Therefore, accurately identifying cold waves and predicting their impact on wind farms is crucial for improving the accuracy of wind power forecasting and ensuring the safety of power systems.  
Based on the analysis of cold wave judgment criteria, cold wave events are primarily influenced by temperature and wind speed. Figure 10 presents the curves of power, wind speed, temperature, and dew point temperature during all cold wave periods.  
Figure 10: Power, wind speed, temperature, and dew point temperature curves during the cold wave period.  
Figure 9: The distribution of the duration and frequency of cold waves over two years in a certain region.  
Cold wave event recognition is performed using the improved U-Net model, Random Forest, K-Nearest Neighbors (KNNs), Multilayer Perceptron (MLP), Support Vector Machine (SVM), and Long Short-Term Memory (LSTM) models to classify the data. The dataset consists of 17,520 samples, with an 8:2 split between the training and test sets. Among the six classification models, accuracy, precision, recall, and the F1 score are used to evaluate the classification performance.  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{14}\]  
\[Precision=\frac{TP}{TP+FP} \tag{15}\]  
\[Recall=\frac{TP}{TP+FN} \tag{16}\]  
\[F_{1}=2\times\frac{Accuracy\times Precision}{Accuracy+Precision} \tag{17}\]  
where \(TP\) represents the number of samples correctly predicted as positive, \(TN\) represents the number of samples correctly predicted as negative, \(FP\) represents the number of samples incorrectly predicted as positive, and \(FN\) represents the number of samples incorrectly predicted as negative.  
The time scale for wind power forecasting is day-ahead forecasting. The forecasting method used is a combined approach, as cold wave events exhibit clear seasonality, primarily occurring in January, February, November, and December. Therefore, the data are divided into periods with cold wave occurrences and periods without cold wave occurrences. The division of the training and test sets is shown in Table 3.  
In this paper, the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are used to evaluate the forecasting results. The calculation formulas are as follows:  
\[N_{MAE}=\frac{1}{n}\cdot\sum_{i=1}^{n}\frac{\big{(}P_{i}-\hat{P_{i}}\big{)}}{ Cap} \tag{18}\]  
\[N_{RMSE}=\frac{1}{Cap}\sqrt{\frac{1}{n}\cdot\sum_{i=1}^{n}\big{(}P_{i}-\hat{P_ {i}}\big{)}^{2}} \tag{19}\]  
\(P_{i}\) represents the actual value, \(\hat{P_{i}}\) is the predicted value, and \(Cap\) is the rated installed capacity of the wind farm.