## 3 Numerical Simulation Method for Ice Shedding
### Finite Element Model (FEM) of Transmission Line  
With reference to the actual parameters of a transmission line section, and ignoring the influence of the transmission tower, this paper established a three-span \"conductor-insulator\" finite element model including LGJ-630/45 conductor, FC7P/146 glass insulators, and a 400 m span distance. The self-weight of the LGJ-630/45 conductor was 20 N/m. The upper suspension point of the insulator string was fixed, and the connecting wire end could swing freely. To further analyze the risk of ice shedding response, it was assumed that the phase conductors on the transmission line were horizontally or vertically arranged, while the ground wire were arranged above the conductors. The finite element model of the designed transmission line had three spans. The spacing of each span was 400 m. The ice shedding position was the middle span, with a shedding rate of 100%. Icing is uniformly distributed at the same moment, without considering the height difference of the insulator suspension points. The shapes of the designed non-circular iced conductors include fan-shaped, D-shaped, elliptical, and crescent-shaped. The equivalent icing thickness was 15 mm, and according to Equation (1), the equivalent ice load was calculated as 20 N/m. The airflow velocity conditions were set to 10 m/s and 20 m/s, with wind angles of attack at 45\({}^{\circ}\), 90\({}^{\circ}\), and 180\({}^{\circ}\). Calculation of Lift and Resistance for Iced Conductors with Different Icing Shapes  
Before analyzing the dynamic response of ice shedding on overhead conductors under strong wind conditions, it is necessary to calculate the lift and resistance of the airflow received by the iced conductor before and after ice shedding. In order to simplify the calculation, in this paper, the definition in Figure 1 shows the shape of the icing for a 0\({}^{\circ}\) wind attack angle (the wind direction is from left to right), and the shaped icing clockwise rotation angle was defined as the wind attack angle, as shown in Figure 2.  
Assuming that the equivalent ice thickness on the LGJ-630/45 wire was 15 mm and the equivalent icing load was 20 N/m, the resistance and lifting force of the crescent-shaped, fan-shaped, D-shaped and elliptical-shaped iced conductors at different wind attack angles are shown in Figure 4 when the air velocity was 10 m/s. Among them, at a wind attack angle of 180\({}^{\circ}\), the fan-shaped and D-shaped icing had a sharp curvature change and the maximum windward surface, so the obstruction to the airflow was the strongest. At this time, the resistance of the iced conductor was 13.5 N/m and 19.2 N/m, is more than 10 times that of the elliptic-shaped and crescent-shaped iced conductors. In addition, the crescent-shaped and elliptical-shaped icing at 90\({}^{\circ}\) and 270\({}^{\circ}\) angles of attack have relatively large wind attack areas, and the formation of two have obvious extreme maximum points. Figure 4: Lifting force and resistance of iced conductors under a 10 m/s wind speed. (**a**) Resistance of the iced conductor; (**b**) lifting force of the iced conductor. Lifting force is the vertically upward force that air currents create on an iced conductor, which changes the elastic potential energy caused by the weight of the conductor and icing. The crescent-shaped and elliptical-shaped icing were more streamlined, and they generally experienced much less lift than the other two shapes. Due to the unique shape of the D-shaped icing, its lift was positive at 0-180\({}^{\circ}\) wind attack angles, and the maximum value reached 6.5 N/m at approximately 135\({}^{\circ}\), reaching 1/3 of the icing load, while at 180-360\({}^{\circ}\) wind attack angles, the lift formed by the airflow was negative, and the lift curve formed a centrosymmetric shape at 180\({}^{\circ}\) wind attack angles. Furthermore, the lift and drag acting on the iced conductor varied rapidly with wind speed, as shown in Equation (2).