# Phase Risk Analysis of Overhead Lines Under Complex Icing Conditions
## 4 Analysis of Discharge Risk Coefficients of Overhead Conductors Under Different Icing Conditions  
### Definition of the Risk Factor for Discharge of Overhead Conductors Under Ice-Covered Conditions  
The conductor-ground line safety distance is the minimum separation required in a power system to prevent flashover or breakdown between the conductor and the ground line. If the distance is exceeded, the overhead line is at risk of severe failure. According to the 110-750 kV overhead transmission line design technical regulations [15], a 500 kV line conductor discharges at a minimum gap of 1.3 m. Due to the formation of ice ridges on the surface of the ground wire caused by icing or other abnormal weather conditions, and considering that the calculation results of this model may be affected by factors such as the damping coefficient, it is important to avoid accidents in actual engineering. Therefore, to increase the margin of safety, the minimum distance is expanded to 2 m. This means that if the distance between the ground wire and other elements is less than or equal to 2 m, it is considered to be within the risk range. To simplify the analysis, this study assessed the risk of phase-to-ground discharge in overhead lines by comparing the minimum distance between the ground and conductor under de-icing conditions. The risk of phase-to-ground discharge is inversely proportional to the distance. The phase-to-ground discharge risk coefficient \(W\) of the line is calculated as follows:  
\[W=\frac{L_{1}}{D_{1}} \tag{11}\]  
where \(L_{1}\) represents the minimum safe distance of the conductor-ground line (m); \(D_{1}\) denotes the minimum distance of the conductor-ground line under the ice-covered load and de-icing condition (m). A larger value of \(W\) signifies a greater risk of phase-to-ground discharge. According to the study in [16], when the de-icing span count changes in mid-span, the constraint on both ends of the conductors in isolated spans is more uniformly sufficient. This results in significantly lower de-icing jump heights for isolated spans under icing conditions compared to continuous spans. As the number of continuous spans increases, the de-icing jump height gradually increases; however, when the span count exceeds five, the jump height almost no longer increases. Therefore, a continuous span configuration of five spans is more practical. Assuming a transmission line with five consecutive sections, where only the central section's conductor is de-iced, the conductor is LGJ-630/45 and the ground wire is OPGW-185, with a voltage level of 500 kV. The initial longitudinal distance without ice cover is 13 m, and the safety distance is 2 m. Model parameters include a de-icing section length of 400 m, divided into 400 grids, with no height difference and 100% de-icing. The conductor-ground line bounce diagram for a 30 mm ice cover is shown in Figure 6. The intersection of purple and green represents the scenario where the de-icing jump of the iced conductor occurs at the same vertical plane position as the iced ground wire. Due to the fact that the bouncing conductor and ground wires are not on the same vertical plane in spatial modeling (as shown in Figure 2), the minimum distance of 2 m between the ground wire and the conductor corresponds to a horizontal distance of 2 m. Therefore, when the vertical distance between the two wires coincides, it falls within the risk zone. For a continuously ice-covered overhead line with no height variation, experience indicates that the risk of phase-to-ground discharge is greatest at the midpoint of the span and decreases toward the endpoints. The phase-to-ground discharge risk coefficient \(W\) is highest at the midpoint. The risk area for phase-to-ground discharge can be determined by calculating \(W\) at each grid point.