## 3 Case Study and Results Analysis  
### Data Selection  
Transmission line icing is affected by many factors, which mainly include wind direction, light intensity, air pressure, altitude, condensation level, terrain, alignments, wires hanging height, wire stiffness, wire diameter, load current and so on. However, the necessary meteorological conditions are: (1) the relative air humidity must be above 85%; (2) the wind speed should be greater than 1 m/s; (3) the temperature needs to reach 0 \({}^{\circ}\)C and below. In addition, the impact factors, which have the greater correlations with the line icing, mainly include: wind direction, light intensity and air pressure, _etc._ In general, when the wind direction is parallel to the wire or the angle between the wire and the wire is less than 45, the extent of line icing is lighter; when the wind direction is vertical to the wire or the angle between the wire and the wire is more than 45, the extent of line icing is more severe. Similarly, the lower the light intensity is, the more severe the line icing is.  
In this paper, three power transmission lines, named \"Qianpingxian-95\", \"Fusha-I-xian\" and \"Yangtongxian\" in PingXi, ChangSha and ZhaoYang of Hunan province, respectively, are selected as the case studies to demonstrate the effectiveness, feasibility and robustness of the proposed method. The data from the above mentioned three transmission lines are provided by Key Laboratory of Disaster Prevention and Mitigation of Power Transmission and Transformation Equipment (Changsha, China).  
As is known, a large freezing disaster occurred in the south of China, which caused huge damage to the power grid system. Hunan province, located in the southern part of China, was one of the most serious areas affected by this disaster. During the disaster period, one third of 500 and 200 kV substations were out of action in the Hunan power grid. According to the statistics, there were 481 line breakages of 500 kV transmission lines, 673 line breakages of 200 kV transmission lines, 142 tower  
Figure 1: The flowchart of the quantum fireworks algorithm (QFA)-w-SVM (wavelet Support Vector Machine) model.  
collapses of 500 kV AC and DC transmission lines, 633 tower collapses of 220 kV transmission lines, and 1203 tower collapses of 110 kV transmission lines. Moreover, in the Hunan area, which suffered from the influence of topography, it is easy to form the stationary front due to the mountains block, when cold air enters the area. Therefore, it is due to their certain typicality that we select those three transmission lines in Hunan province as cases to verify the validity and robustness of the proposed method.  
Case 1: the data on \"Qianpingxian-95\" are from 10 January 2008 to 15 February 2008, which has 221 data groups for the training and testing in total. The former 180 data groups are regarded as a training set and the last 41 groups of data are a testing set. The input vectors of SVM are average temperature, relative humidity, wind speed, wind direction, and sunlight intensity, and the output vector is ice thickness. The sample data are shown in Figure 2.  
Case 2: the data of \"Fusha-I-xian\" are from 12 January 2008 to 25 February 2008, which has 287 data groups. The former 240 groups are taken as a training set and the remaining 47 groups as a testing set. The input vectors are same as that of _Case 1_. The sample data are shown in Figure 3.  
Case 3: the data of \"Yangtongxian\" are from 8 January 2008 to 24 February 2008, whose data groups total up to 329. The former 289 groups are taken as a training set and the remaining 40 groups as a testing set. The input vectors are still same as that of Case 1. The sample data are shown in Figure 4.  
Figure 3: Original data of “Fusha-I-xian”.  
Figure 2: The original sample data charts.