# Wind Turbine Power Curve Modelling with Logistic Functions Based on Quantile Regression
## 4 Case Study
### Experimental Results
#### 4.3.2 Results for Outlier Filtering  
Similar to Section 4.3.1, three wind turbines in WF3 are selected to verify the effectiveness of the outlier filtering method based on QRLF. The scatter plots of wind speed and power output before and after outlier filtering are shown in Figure 7.  
Before outlier filtering, we can clearly observe the stacked outliers caused by wind curtailment from WT08 and WT10, and few sparse outliers in the scatter plot of WT02. After outlier filtering, both sparse and stacked outliers are eliminated, while most normal data points are reserved. Among them, outliers caused by zero power output are filtered by using the monitoring parameters of the SCADA system (the f  
Figure 6: The values of quantile regression (QR) cost function optimized by particle swarm optimization (PSO), whale optimization algorithm (WOA) and Adam algorithms during the training process.  
Figure 7: Scatter plots of wind speed and power output of WT02, WT08 and WT10., where the black points are the raw data of power outputs, and the orange points are the power outputs after outlier filtering.  
outlier filtering method), and then the remaining outliers are eliminated via the iterative calculations based on 5P-QRLF (step 2 to step 4). The proposed method has a certain adaptive processing capability, which can determine the number of iterations according to the number of outliers. As shown in Figure 7, after seven iterations, the outlier filtering algorithm of WT08 reaches the end condition, but for WT02, only one iteration is needed. This feature can significantly reduce the computing cost, e.g., under the same conditions, the computing time of WT08 is 181.7 s; this is more than seven times of that of WT02, i.e., 23.8 s.  
For in-depth analysis, both GP based and DBSCAN based outlier filtering methods are selected to make comparative studies with the proposed method. The former one filters the outliers through removing the measurements that deviate from the expected value by more than a certain \(\sigma\)-dependent threshold [15], and the latter one eliminates the outliers by clustering [32]. Before filtering, we first use the same data preprocessing method (listed in Table 1) for all filtering methods to be tested to reduce the interference of other factors. Then, the model parameters are fine-tuned through cross validation in order to achieve the best filtering effect. Figure 8 shows the filtering results of one of the test wind turbines under wind curtailment.  
In Figure 8, the threshold of GP based filtering method (GP-Filter) is set to 3\(\sigma\); the eps and the sample numbers [32] of DBSCAN based filtering method (DBSCAN-Filter) are set to 1.2 and 20, respectively. The results show that GP-Filter is not able to effectively eliminate the stacked outliers caused by wind curtailment. Although DBSCAN-Filter can filter the abnormal power points, the filtering results are sensitive to the setting of model parameters, and it is difficult to be deployed in actual wind farm, e.g., we should fine tune the eps and sample numbers for each wind turbine (even for the same wind turbine in different time periods) to obtain the correct filtering results. Compared with DBSCAN, the proposed QRLF-Filter only has one hyperparameter \(\lambda\) that needs to be adjusted. The filtering results of QRLF-Filter are more robust than that of DBSCAN. Once \(\lambda\) is determined, we can use the same value of \(\lambda\) in the whole wind farm.