# Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Analyzing the Complex Conditions of Iced Conductors

#### 2.1. Icing Shape and Icing Load

^{3}; $D$ is the diameter of the conductor, mm; ${b}_{1}$ is the equivalent thickness of icing, mm; g is the acceleration of gravity; L is the conductor length, m; and n is the number of nodes divided.

#### 2.2. Wind Load at Different Wind Attack Angles

## 3. Numerical Simulation Method for Ice Shedding

#### 3.1. Analysis Method for Ice Shedding on Overhead Transmission Lines under Complex Conditions

#### 3.2. Finite Element Calculation Procedure

#### 3.3. Calculation of Wind Loads Based on Aerodynamic Parameters

#### 3.4. Finite Element Model (FEM) of Transmission Line

#### Calculation of Lift and Resistance for Iced Conductors with Different Icing Shapes

## 4. Analysis of Ice Shedding Response of Overhead Conductors under Strong Winds

#### 4.1. Influence of Ice Morphology on the Ice Shedding Response of Transmission Lines

#### 4.2. Effect of Wind Attack Angle on the Ice Shedding Response of Transmission Lines

#### 4.3. The Effect of Wind Speed on the Ice Shedding Response of Transmission Lines

**Figure 7.**Effect of wind speed on ice shedding bouncing process. (

**a**) round-shaped; (

**b**) crescent-shaped; (

**c**) elliptical-shaped; (

**d**) fan-shaped; (

**e**) D-shaped.

## 5. Discussion

- (1)
- The calculation of lift and drag forces on the iced conductor is fundamental for understanding the dynamic response of conductors during ice shedding under strong wind conditions. Additionally, the stability of conductor galloping was assessed based on Den Hartog’s vertical vibration theory and Nigol’s torsional vibration theory, both of which rely on the concept of negative damping. In this study, finite element methods were utilized to compute the lift and drag forces on iced conductors under different conditions. It was found that fan-shaped and D-shaped ice covers exhibited sharp changes in curvature and planarity, with the strongest hindrance to airflow occurring at a 180° attack angle, resulting in the highest drag force on iced conductors. At this angle, the drag force on D-shaped ice covers could exceed ten times that of the elliptical and crescent-shaped samples. The unique shape of D-shaped icing resulted in positive lift between 0–180°, peaking around 135°. These results closely match those observed in wind tunnel experiments [24]. At a wind angle of 225°, the airflow increased the directional additional load by one-third, leading to an increase in the conductor’s elastic potential energy.
- (2)
- Due to variations in meteorological conditions and conductor characteristics, natural icing can exhibit significant differences in morphology, resulting in shapes such as circular, crescent, D-shaped, fan-shaped, and elliptical. Under the same icing mass (volume) and wind speed conditions, the dynamic response process of conductors after ice shedding becomes highly complex. Under the combined influence of airflow and icing, conductors possess both longitudinal and lateral elastic potential energy. Generally, iced conductors with circular, crescent, and elliptical shapes have smooth outer curves, resulting in minimal lateral displacement under wind forces. At a wind speed of 10 m/s, their maximum vertical bounce heights were 9.94 m, 10.6 m, and 10.07 m, respectively. The maximum lateral bounce heights were only 0.31 m, 1.16 m, and 1.36 m, indicating minimal differences from the no-wind condition. The maximum longitudinal displacement was approximately 1.62 times the difference in longitudinal positions before and after ice shedding, slightly smaller than the value of 1.8 reported in the literature [14], but with minimal differences from the literature [25]. Except for the crescent-shaped ice cover at a 45° wind angle, corresponding to the minimum bounce condition, the maximum lateral displacement was approximately 1.56 times the difference in lateral positions before and after ice shedding.

## 6. Conclusions

- (1)
- The resistance mainly affects the initial ice shedding position of the overhead conductors and leads to significant differences in the lateral oscillation of the conductor after ice shedding.
- (2)
- The outer curves of crescent, and elliptical iced conductors are smooth, with less lateral displacement under wind force, and their risk of ice shedding response is mainly in the vertical direction.
- (3)
- When the wind attack angle approaches 180°, the airflow resistance of the fan-shaped and D-shaped icing conductors significantly increases. In the process of ice shedding response of transmission lines, the lateral amplitude may exceed 20 m, which has a high possibility of causing phase–phase and phase–ground discharge.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Huang, G.; Yan, B.; Wen, N.; Wu, C.; Li, Q. Study on jump height of transmission lines after ice-shedding by reduced-scale modeling test. Cold Reg. Sci. Technol.
**2019**, 165, 102781. [Google Scholar] [CrossRef] - Ji, K.; Rui, X.; Li, L.; Yang, F.; McClure, G. Dynamic response of iced overhead electric transmission lines following cable rupture shock and induced ice shedding. IEEE Trans. Power Deliv.
**2016**, 31, 2215–2222. [Google Scholar] [CrossRef] - Ji, K.; Liu, B.; Zhang, Y.; Chen, J.; Li, Y.; Li, X.; Lu, R. Analysis of Ice-shedding induced flashover accident on a transmission line in mountainous terrain. J. Phys. Conf. Ser.
**2024**, 2703, 012094. [Google Scholar] [CrossRef] - Abdollahzadeh, H. A distance protection approach for untransposed parallel transmission lines in case of phase-phase-ground inter-circuit faults. Int. J. Electr. Power Energy Syst.
**2023**, 145, 108623. [Google Scholar] [CrossRef] - Zhu, Y.; Zhou, R.; Zhang, Y.; Dong, X.; Huang, X. Review on flashover risk prediction method of iced insulator based on icing monitoring technology. Cold Reg. Sci. Technol.
**2021**, 185, 103252. [Google Scholar] [CrossRef] - Rui, X.; Ji, K.; Li, L.; McClure, G. Dynamic response of overhead transmission lines with eccentric ice deposits following shock loads. IEEE Trans. Power Deliv.
**2017**, 32, 1287–1294. [Google Scholar] [CrossRef] - Huang, G.; Yan, B.; Guo, Y.; Zhang, B.; Wu, G. Experimental study on dynamic response characteristics of isolated-span transmission lines after ice-shedding. High Volt.
**2023**, 8, 2397–7264. [Google Scholar] [CrossRef] - Jamaleddine, A. Simulation of ice-shedding on electrical transmission line using ADINA. Comput. Struct.
**1993**, 47, 523–536. [Google Scholar] [CrossRef] - Roshan Fekr, M.; Mcclure, G. Numerical modeling of the dynamic rensponse of ice shedding on electrical transmission lines. Atmos. Res.
**1998**, 46, 1–11. [Google Scholar] [CrossRef] - Kollar, L.E.; Farzaneh, M. Vibration of Bundled Conductors Following Ice Shedding. IEEE Trans. Power Deliv.
**2008**, 23, 1097–1104. [Google Scholar] [CrossRef] - Kalman, T.; Farzaneh, M.; Mcclure, G. Numerical analysis of the dynamic effects of shock-load-induced ice shedding on overhead groundwires. Comput. Struct.
**2007**, 85, 375–384. [Google Scholar] [CrossRef] - Barbieri, R.; Barbieri, N.; De Souza Junior, O.H. Dynamical analysis of transmission line cables. Part 3-Nonlinear theory. Mech. Syst. Signal Process.
**2008**, 22, 992–1007. [Google Scholar] [CrossRef] - Murín, J.; Hrabovský, J.; Gogola, R.; Janíček, F. Dynamic Analysis of Overhead Power Lines after Ice-Shedding Using Finite Element Method. J. Electr. Eng.
**2016**, 67, 421–426. [Google Scholar] [CrossRef] - Yan, B.; Chen, K.; Guo, Y.; Liang, M.; Yuan, Q. Numerical simulation study on jump height of iced transmission lines after ice shedding. IEEE Trans. Power Deliv.
**2013**, 28, 216–225. [Google Scholar] [CrossRef] - Meng, X.; Hou, L.; Wang, L.; MacAlpine, M.; Fu, G.; Sun, B.; Guan, Z.; Hu, W.; Chen, Y. Oscillation of conductors following ice-shedding on UHV transmission lines. Mech. Syst. Signal Process.
**2012**, 30, 393–406. [Google Scholar] [CrossRef] - Xie, X.; Wu, Y.; Liang, K.; Liu, S.; Peng, J. Experiment Study on Dynamic Effects of Tower-Line Systems Induced by Ice Shedding. Adv. Civ. Eng.
**2020**, 2020, 6241789. [Google Scholar] [CrossRef] - Wen, Y.; Chen, Y.; Wu, J.; Mao, X.; Huang, H.; Yang, L. Research on Risk Assessment and Suppression Measures for Ice-Shedding on 500 kV Compact Overhead Lines. Energies
**2022**, 15, 8005. [Google Scholar] [CrossRef] - Zhang, M.; Zhao, G.; Wang, L.; Li, J. Wind-Induced Coupling Vibration Effects of High-Voltage Transmission Tower-Line Systems. Shock Vib.
**2017**, 34, 1205976. [Google Scholar] [CrossRef] - Jiang, Q.; Zhu, B. Influence on Ice Shedding of Overhead Power Transmission Line Conductor by Wind Speed. Guangdong Electr. Power
**2015**, 28, 127–130. (In Chinese) [Google Scholar] - Zhang, Z.; Zhou, T.; Jiang, X.; Hu, J. Influence of Wind Loads on Transmission Lines Under Typical Ice Shapes. Power Syst. Technol.
**2023**, 47, 5247–5255. (In Chinese) [Google Scholar] - Zhu, Y.-C.; Huang, X.-B.; Zhao, L.; Tian, Y.; Mu, J.-Y.; Gao, H. Thermodynamic model of critical ice-melting current on iced transmission lines. Therm. Sci.
**2019**, 137, 3187–3198. [Google Scholar] [CrossRef] - Bian, R.; Zhang, Y.; Liu, W.; Chen, K.; Lou, W. Influence of Wind Load on Jump Height of Conductorin Transmission Lines after Ice Shedding. Electr. Eng.
**2020**, 7, 44–47+52. (In Chinese) [Google Scholar] - Li, M.Z.; Cai, Q. Theoretical algorithm for maximum jump height of the conductor after ice-shedding considering elevation angle and nonlinearity. Cold Reg. Sci. Technol.
**2024**, 218, 104088. [Google Scholar] [CrossRef] - Lou, W.; Luo, G.; Yang, X.; Lu, M. Fluctuating aerodynamic characteristics and wind-induced swing response of typical iced conductors. J. Zhejiang Univ. Eng. Sci.
**2017**, 51, 1988–1995. (In Chinese) [Google Scholar] - Zhang, D. Design Manual of High Voltage Transmission Lines for Electric Engineering, 2nd ed.; Electric Power Press: Beijing, China, 2003. (In Chinese) [Google Scholar]

**Figure 1.**Schematic diagram of the cross-sectional shapes of iced conductors. (

**a**) circular-shaped; (

**b**) crescent-shaped; (

**c**) fan-shaped; (

**d**) D-shaped; (

**e**) elliptical-shaped.

**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.

**Figure 5.**Effect of different icing morphologies on ice-shedding bouncing process of transmission lines, and the red and yellow lines represent the projections of curves on different planes, respectively. (

**a**) Round-shaped; (

**b**) elliptical-shaped; (

**c**) crescent-shaped; (

**d**) fan-shaped; (

**e**) D-shaped.

**Figure 6.**Effect of wind attack angle on the ice shedding bouncing process of transmission lines, and the red and yellow lines represent the projections of curves on different planes, respectively. (

**a**) Crescent, 45°; (

**b**) crescent, 90°; (

**c**) crescent, 180°; (

**d**) D-shaped, 45°; (

**e**) D-shaped, 90°; (

**f**) D-shaped, 180°.

**Table 1.**The coordinates of the span midpoint before ice shedding, and the maximum coordinates during the bouncing process.

Wind Attack Angle | Ice-Covered Landscape | Round-Shaped | Crescent-Shaped | D-Shaped |
---|---|---|---|---|

45° | initial coordinate | (1.12 m, −3.09 m) | (1.27 m, −3.04 m) | (1.57 m, −1.6 m) |

maximum horizontal coordinate | (1.44 m, 2.86 m) | (1.4 m, 2.44 m) | (1.57 m, −1.6 m) | |

maximum vertical coordinate | (1.35 m, 6.84 m) | (1.27 m, 6.81 m) | (1.13 m, 5.89 m) | |

90° | initial coordinate | (1.12 m, −3.09 m) | (1.9 m, −3.5 m) | (0.52 m, 3.01 m) |

maximum horizontal coordinate | (1.44 m, 2.86 m) | (1.9 m, −3.5 m) | (1.74 m, 3.05 m) | |

maximum vertical coordinate | (1.35 m, 6.84 m) | (0.93 m, 7.10 m) | (1.74 m, 3.05 m) | |

180° | initial coordinate | (1.12 m, −3.09 m) | (0.52 m, −3.09 m) | (8.82 m, 3.6 m) |

maximum horizontal coordinate | (1.44 m, 2.86 m) | (1.68 m, 6.47 m) | (8.82 m, 3.6 m) | |

maximum vertical coordinate | (1.35 m, 6.84 m) | (1.68 m, 6.84 m) | (8.70 m, 3.59 m) |

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**MDPI and ACS Style**

Dong, X.; Zhao, M.; Li, M.; Zhu, Y.
Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions. *Appl. Sci.* **2024**, *14*, 4285.
https://doi.org/10.3390/app14104285

**AMA Style**

Dong X, Zhao M, Li M, Zhu Y.
Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions. *Applied Sciences*. 2024; 14(10):4285.
https://doi.org/10.3390/app14104285

**Chicago/Turabian Style**

Dong, Xinsheng, Mingguan Zhao, Meng Li, and Yongcan Zhu.
2024. "Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions" *Applied Sciences* 14, no. 10: 4285.
https://doi.org/10.3390/app14104285