Analysis of Ice-shedding induced flashover accident on a transmission line in mountainous terrain

Transmission lines are essential infrastructure for modern society. Large amplitude vibration of conductors due to ice shedding may cause electrical faults, resulting from insufficient clearance among different phases and phase conductors and ground wires. A flashover fault on a 500kV transmission line located in a mountainous area, which is caused by ice shedding, is analysed in this paper. The approximate reason and history of the flashover accident were restored by the nonlinear finite element method with the help of ANSYS software. The key physical parameters such as conductor ice thickness and amount of ice shedding at the moment of the accident were analysed. The study in this paper helps to gain a deeper understanding of the ice-shedding–induced disasters of transmission lines and provides important reference for the design of transmission structures.


Introduction
Transmission lines are essential infrastructure for modern society.In early 2008, a once-in-50-year period of freezing weather occurred in the southern provinces of China.The Hunan, Jiangxi, Hubei, Henan, Sichuan, and Chongqing power grids in Central China, as well as the Zhejiang, Fujian, Anhui, and Jiangsu power grids in East China, sustained severe damage due to the harsh weather conditions.Among them, the Hunan, Jiangxi, and Zhejiang power grids were the most severely affected, resulting in widespread pole collapses and wire breaks with local power grids being destroyed on a massive scale.A total of 506 towers collapses and 142 damages were found at 500 kV lines, with 799 wire breaks.Additionally, 819 towers collapses and 239 damages were discovered at 220 kV lines, with 1330 wire breaks.This icing disaster was triggered by the prolonged period of low temperature, snow, and freezing weather, which impacted multiple provinces within the company's system.The primary icing hazard manifested as overload due to icing, leading to numerous ground wire breaks, tower damage, and tower collapses, making it the most severe icing disaster in the company's system in recent years.
In recent years, with frequent occurrences of extreme weather, the ice-shedding faults of overhead power lines have increased, causing serious harm to the electric grid.Large amplitude vibration of conductors due to ice shedding may cause electrical faults, resulting from insufficient clearance among different phases and phase conductors and ground wires.Therefore, it is urgent to study the response characteristics of ice shedding.
The research on ice shedding mainly focuses on the displacement at key positions of conductors and the dynamic tension, mainly including physical test methods, theoretical analysis methods, and numerical simulation methods.Among them, the physical test method includes full-scale tests and reduced-size tests [1][2][3][4].The former directly uses real transmission lines to carry out experiments, and the results are closer to the ice-shedding reaction under real conditions, but the cost is high and the test is difficult [1][2].The reduced-size test, using a small size or scaled reduction model, can carry out a large number of tests [3][4].Because the ice-shedding process is a strong nonlinear movement, the reduced-size test is based on linear theory, so there are certain limitations in the test results.The theoretical analytical method is based on the theory of mechanics, and the analytical formula of conductor displacement and tension is derived through reasonable simplification [5].With the development of computer technology, numerical simulation methods based on finite element simulation, due to their efficient modeling capabilities, have become the mainstream method, which can model complex ice shedding conditions, the tower-line coupling systems, and the joint effect of wind on ice shedding.The numerical modeling methods have successively gone through the stages of the concentrated mass method, the density changing method, the "composite-like" element method, and the induced ice-shedding method, which provides important support for the research of ice shedding [6][7][8][9].
A typical flashover fault on a 500 kV overhead line due to severe ice shedding was analysed in this study.A nonlinear finite element model of the accident line was established.The finite element method was used to calculate the conductor height following ice shedding when the ice thickness and ice shedding amount changed.The occurrence location of the flashover accident was reproduced by analysing the electric distance during the icing and ice-shedding processes.

Information on the studied case
The 500 kV line is located in a mountainous area in North China, with five spans and a total length of 2713 m, as shown in Figure . 1 and Figure .2. The conductor span lengths are respectively 346 m (Span 1), 410 m (Span 2), 697 m (Span 3), 348 m (Span 4), and 912 m (Span 5), and the height differences are respectively 42.9 m, 0.1 m, 7.1 m, -32.8 m, and -89.9 m, with two tension towers and the ends and suspension towers in the middle.The physical parameters are listed in Table 1.

Electrical fault details
Ice-accretion images from January 20-26, 2022 can be seen in

Finite element modeling method
The initial configuration of an electric cable with a small sag ratio can be described by Equation (1).
After considering the ice load, the nonlinear motion equation of a conductor can be expressed as: (2) where M and Cstr denote the conductor's mass matrix and damping matrix, respectively; F is the node load vector; Y is the conductor's vertical displacement vector; KT is the tangent stiffness matrix.
As shown in Equations ( 3) and ( 4), the Rayleigh damping model is used to consider the structural damping of the conductor, and the structural damping matrix Cstr is represented as a linear combination of the mass matrix M and the linear stiffness matrix KL: where ξ is the structural damping ratio, taken as 0.5%; ω1 and ω2 are the first two order natural frequencies, respectively.
Assuming that the conductor is uniformly ice-accreted across the span, the ice load is replaced by a concentrated force, and the conductor ice is equivalently simulated by applying a concentrated force at the conductor nodes.The conductor ice shedding is simulated by removing the concentrated force in a very short time.The ice load Fice on the conductor per unit length can be expressed as Equation ( 5): (2

Numerical simulation cases
Based on the flashover accident scenarios, 5 ice shedding conditions are verified in this paper, as detailed in Table 2.The ice thickness δ is chosen as 12.59 mm and 13.5 mm, respectively.The ice on the faulty 3rd span sheds uniformly, and the ice shedding rates β are 80%, 90%, and 100% respectively.

Cable motion trajectory following ice shedding
Figure .8 shows the motion trajectories under different cases in Table 2.It can be observed that when only the conductor ice sheds, the position of the ground wire remains unchanged, indicating that conductor ice shedding does not induce vibrations in the ground wire.The conductor's motion trajectory is nearly linear.Additionally, during the conductor vibration process after ice shedding, the electric distance changes in real time.The minimum and maximum clearances between the conductor and the ground wire after ice shedding are illustrated in Table 3.
To prevent flashover accidents, a certain clearance should be maintained between the transmission conductors and the ground wires.This minimum required clearance is referred to as the safety clearance, listed in Table 4.For the 500 kV transmission line discussed in this paper, the minimum electric distance should be no less than 2.20 m.In case 4, the minimum electric distance is 2.11 m, which is below the safety clearance (2.20 m) required for safe operation, leading to a flashover accident on the line.
In conclusion, the most likely scenario that matches the on-site flashover accident is Case 4, where the ground wire is covered with ice, and ice-shedding occurred in the 3rd span conductor section.Considering the difference in time between the on-site ice thickness measurement and the occurrence of the flashover accident, the ice might have partially melted, and the practical ice thickness at the time of the accident would be slightly greater than 12.59 mm, approximately 13.5 mm.To be noted that, apart from the need to prevent dynamic approach flashover of the ground wires and conductors caused by an uneven weight distribution resulting from conductor ice shedding at the centre of the span, the possibility of static approach flashover at the midpoint of the span due to the formation of an uneven load after conductor ice shedding should also be considered for vertically arranged ground wires and conductors.For double-circuit lines or compact lines with small phase spacing and low horizontal offset between conductors and ground wires, special attention needs to be paid to the issue of flashover caused by uneven icing or ice shedding as well.In vertically arranged ground conductors, an uneven load generated by conductor ice shedding can potentially lead to a static approach flashover of ground wires and conductors at the center of the span.This is because when ice accretion is shed from the conductor, its weight distribution may be non-uniform, resulting in uneven tension experienced by the conductor.If the difference in tension is significant, the risk of static approach flashover at the center of the span increases.Furthermore, for double-circuit lines or compact lines with small phase spacing and low horizontal offset between conductors and ground wires, uneven icing or ice shedding tends to occur more easily.If such cases are not properly attended to and controlled, potential flashover problems can still arise.
Therefore, appropriate measures need to be taken during the design and operation of vertically arranged ground conductors to prevent the impact of conductor ice shedding and uneven loads on ground wires and conductors.For instance, appropriate insulator string designs, increased intervals between conductors, and other insulation support measures can be employed to reduce the formation of an uneven load after conductor ice shedding.Regular patrols and maintenance can also help identify and address potential flashover issues in a timely manner, ensuring the stable operation of the overhead lines.

Conclusions
In this paper, a typical flashover fault on a 500 kV transmission line is analysed, which is induced by conductor ice shedding.The main conclusions can be conducted as follows: (1) An increase in ice thickness and shedding rate can lead to a significant increase in conductor jump height following ice shedding.
(2) Conductor ice shedding does not induce vibrations in the ground wire.The motion trajectory of the conductor following ice shedding is nearly linear.
(3) The most likely scenario that matches the on-site flashover accident is Case 4, where the ground wire is covered with ice, and ice-shedding occurred in the 3rd span conductor section.Considering the difference in time between the on-site ice thickness measurement and the occurrence of the flashover accident, the ice might have partially melted, and the practical ice thickness at the time of the accident would be slightly greater than 12.59 mm, approximately 13.5 mm.

Figure. 3 .Figure. 3 .Figure. 4 .
Figure. 3. Ice-accretion images during January 20-26, 2022.The flashover traces of the conductor and ground wire are shown in Figure.4 (a) and (b).After the flashover accident, the thickness of the fallen ice at the scene was immediately measured, as shown in Figure. 5.It is reported that the ice thickness was approximately 12.59 mm.

2
5) where ρ is the ice density; δ is the ice thickness; D is the outer diameter of the conductor.The numerical model of the faulty line (as shown in Figure.6)has been established, including conductors, ground wires, and insulator strings.

Figure. 6 .
Figure. 6. Numerical model of the transmission line.

Figure. 7 .
Figure. 7. Conductor jump height for the failure point of the 3rd span under different ice-shedding cases.

Table 1 .
Physical parameters of the line.

Table 3 .
The minimum and maximum clearances under different ice-shedding cases.

Table 4 .
The safety clearance between transmission conductors and ground wires.