Theoretical study and simulation analysis of distributed vibration de-icing technology for medium voltage overhead lines

MV overhead line refers to the overhead line in the power system that transmits medium voltage range, generally ranging from 1 kV to 69 kV. MV overhead line is usually made of conventional aluminum alloy bare conductor (ALFe) without any external insulating material cover, so it has the advantages of low installation cost, easy maintenance, good heat dissipation, etc., and is widely used in the medium voltage transportation environment [1–3]. However, due to the direct exposure of bare wire conductors to the external environment, ALFe bare wire overhead lines are susceptible to phase failures caused by severe weather and surrounding flora and fauna, which can lead to power supply failures [4–6]. Ice cover is a common natural phenomenon, the formation of which is due to the condensation of supercooled water in the air onto objects with temperatures below the freezing point. Cable ice cover is affected by factors such as meteorology, terrain environment, transmission line itself, altitude and cable alignment [7–9]. Transmission lines are widely distributed geographically, and the terrain and climatic conditions of the regions through which they pass are complex, so it is difficult to avoid ground line ice-covering has become one of the common natural disasters that jeopardize the safety of overhead transmission lines. Overhead transmission lines are damaged by ice cover for a variety of reasons, which can be mainly categorized into four types, namely, mechanical overload, ice dance, de-icing jumps and ice flashover [10–12]. Power safety accidents on overhead transmission lines due to icing problems are common in the international arena, and according to relevant statistics, thousands of icing accidents have occurred on transmission lines. Therefore, de-icing of medium voltage overhead lines is necessary to ensure the normal operation of transmission lines [13–15]. The overhead lines do not bear power transmission and have no thermal effect, thus the icing problem is more serious compared to transmission cables. In the snowstorm in southern China in 2008, a large number of cables in the southern power grid were interrupted, among which, 212 fiber optic cables (a kind of ground cable) were interrupted, accounting for 18% of the total number of fiber optic cables, so it is imperative to study the de-icing technology of medium-voltage overhead lines [16–19].

This paper proposes an overhead line de-icing method based on resonance, which is the basis for the design of an overhead line de-icing system. The method utilizes a driving force that consumes less energy to make the transmission line vibrate within the same frequency as the vibrating motor in cold climatic conditions, which ensures that the de-icing work is carried out smoothly, thus preventing the ice from persistently adhering to the transmission line. The attachment rate of supercooled raindrops is weakened, thus achieving the effect of preventing icing. The de-icing system design of this paper is verified by finite element simulation experiments in the de-icing effect under different vibration modes and frequencies, which provides a reliable basis for the engineering of coupled resonance de-icing of medium-voltage transmission lines.

2

De-icing system for power overhead line based on resonance principle

2.1

Overhead line de-icing principle based on resonance principle

The vibration of an object under the action of an external periodic force is called forced vibration, and its frequency is equal to the frequency of the external periodic force. When the frequency of the external periodic force is close to the intrinsic frequency of the object, the object will produce an obvious vibration intensification phenomenon. In the initial and developmental stages of line ice cover. If you can give the transmission line with a continuous high-frequency vibration, so that the vibration frequency reaches or close to the intrinsic frequency of the ice, then the accumulated energy is enough to make the ice collapse, so as to achieve the purpose of eliminating the ice.

The intrinsic frequency of ice-covering is determined by its hardness, quality, shape, and size, and these parameters are dynamically changing in the actual environment, making the process of calculating its intrinsic frequency complex. The intrinsic frequency of the ice is generally MHz, high-power mechanical vibration frequency by the technical conditions are not likely to reach this level, so the practical application of only need to take the vibration frequency of the excitation and the intrinsic frequency of the ice is an odd number of times can be. De-icing method based on the principle of vibration does not strictly rely on the principle of resonance, the conductor is particularly serious harm to the overlying ice for the mixing of freezing, but in fact in the mixing of freezing in the early stage of the emergence of the conductor appears to be any higher-frequency vibration on the shaking of the ice crystals or the over-cooling of the rain droplets are effective.

The vibration of an object under the continuous action of a periodic external force is called forced vibration [20], and this periodic external force is called the driving force [21]. For convenience, let the driving force be: 1 $F = F_{0} \cos ω t$

Where F₀ is the amplitude of the driving force and ω is the angular frequency of the driving force. The equation of motion of the object under the action of the elastic force and the driving force is: 2 $m \frac{d^{2} x}{d t^{2}} = - k x - g \frac{d x}{d t} + F_{0} \cos ω t$

Let: $\frac{k}{m} = ω_{i}^{2}$ , $\frac{g}{m} = 2 β$ , then equation (2) can be rewritten as: 3 $\frac{d^{2} x}{d t^{2}} + 2 β \frac{d x}{d t} + ω_{0}^{2} x = \frac{F_{0}}{m} \cos ω t$

When damping is small, the forced vibration reaches a steady state of equal amplitude vibration can be solved by equation (3): 4 $x = A \cos (ω_{t} + ϕ_{0})$

Based on theoretical calculations, the amplitude is obtained as: 5 $A = \frac{F_{0}}{m \sqrt{{(ω_{0}^{2} - ω^{2})}^{2} + 4 β^{2} ω^{2}}}$

A certain vibration system, if the amplitude of the driving force is certain, the amplitude of the forced vibration steady state changes with the frequency of the driving force.

When the frequency of the driving force is close to the intrinsic frequency of the system ω₀, the amplitude of the resonance displacement is maximum.

The phenomenon of resonance is extremely common and exists in the fields of sound, light, radio, atomic physics, and engineering technology. In this paper, this principle is utilized for de-icing experiments, and the basic idea is to use an amplifier to drive a loudspeaker array to output an acoustic driving force to an overhead power line, which, by adjusting the frequency, causes a mechanical resonance of the overhead line, thus eliminating the overlying ice.

2.2

Power overhead line de-icing system design

2.2.1

Vibration motor structure

The vibration motor is installed at the left and right ends of the eccentric block. The vibration motor’s excitation force increases, and the two eccentric blocks’ angle decreases, resulting in the largest vibration. On the contrary, the vibration motor excitation force decreases, while the eccentric blocks between the angles increase. Figure 1 shows the eccentric block angle and excitation force schematic.

2.2.2

Principle of operation of vibration motors

Vibration motors are devices that can convert electrical energy into mechanical energy, all in accordance with the following formula. 6 $e = B L v$

Where e - induced electromotive force.

L - Length of the conductor.

B - Magnetic induction intensity [22].

v - The speed of the conductor cutting the magnetic induction. 7 $F = I B L$

Where F - Ampere force.

I - current.

B - Magnetic induction strength.

L - length of the conductor.

There are many types of vibration motors, but the principle of conversion of electrical and mechanical energy is the same. Vibration motor to be able to realize the normal energy on the conversion, must meet the above laws, in addition to the energy conversion of the motor.

Excitation force, by the following formula to calculate: 8 $F = m r ω^{3}$

Where F - Excitation force.

m - Mass of the eccentric block, N.

r - synthetic eccentricity, m.

ω - Angular velocity of rotation, rad/s.

Eccentricity moment is: 9 $M_{g} = m g r$

Where M_g - Eccentricity moment.

m - Mass of the eccentric block, kg.

g - Acceleration of gravity.

r - Eccentricity distance, m.

Vibration motor power size according to the following formula: 10 $p_{0} = \sum m_{0} ϖ^{2} R$

Where p₀ - biased inertia force.

ϖ - Operating frequency.

m₀ - Motor mass.

R - Radius of rotation of the motor. 11 $A = f p_{0} π d$

Where A - consumed friction work.

f - Journal friction coefficient.

d - Diameter of main journal (m). 12 $N = K \frac{A n}{60 \times 120} (K W)$

Where N - Vibration motor power.

n - motor speed (r min).

K - other power consumption reserve factor.

Through the above formula, the power of the motor can be finally calculated, and the appropriate vibration motor can be selected according to the actual need.

2.2.3

Resonance of vibrating motors with transmission lines

The ice-covered snow on the medium-voltage transmission line produces forced vibration under the action of the uninterrupted periodic external force of the vibration motor, and the periodic external force produced by the rotation of the vibration motor is the driving force, which can be set as: 13 $F = F_{0} \cos ω t$

Where F₀ - Amplitude of driving force.

ω - Angular frequency of the driving force.

Under the driving force, the equation of motion is: 14 $m \frac{d^{2} x}{d t^{2}} = - k x - \frac{d x}{d t} + F_{0} \cos ω t$

Let $\frac{k}{m} = ω_{0}^{2}$ , $\bar{m} = 2 β$ , then by Eq: 15 $\frac{d^{2} x}{d t^{2}} + 2 β \frac{d x}{d t} + ω_{0}^{2} x = \frac{F_{0}}{m} \cos ω t$

Equal amplitude vibration, from Eq. (15): 16 $x = A \cos (ω t + ϕ 0)$

Based on theoretical calculations, the amplitude is obtained as: 17 $A = \frac{F_{0}}{m \sqrt{{(ω_{0}^{2} - ω^{2})}^{2} + 4 β^{2} ω^{2}}}$

The medium voltage transmission line de-icing device utilizes the principle of resonance, and the basic idea is: 1)

A driving force is output to the MV transmission line through a vibration motor.

2)

Subsequently determine the MV transmission line vibration frequency.

3)

Adjust the vibration motor frequency, so that it and the transmission line within the same frequency.

4)

The vibration motor resonates with the transmission line for de-icing.

2.3

Principle Prototype Dynamics Simulation

Virtual prototyping technology is used to simulate the dynamics of a downsized de-icer and evaluate whether the excitation force generated during de-icer operation is consistent with the design requirements. When using virtual prototype technology to simulate the dynamics of the de-icer, small parts such as bolts, spacers and pins are small in size and light in weight compared to the de-icer as a whole, and do not affect the motion of the de-icer, so their impact on the dynamics simulation results is extremely small. And these small parts are small in size but relatively large in number, which affects the efficiency of establishing the virtual prototype of the de-icer. Therefore, these small parts are removed. After removing the small parts from the de-icer, the CAD model is converted into x_t format that can be recognized by ADAMS. After importing the model, the material of each part is set and the constraints for each part are established according to the structural design. These constraints can be categorized into three types: fixed, rotary and contact. The constraints between the wire clamp and the earth, between each plate and between the bearing housing and the pallet in the de-icer are fixed constraints, and these constraints prevent the two constrained parts from generating relative motion. The rotational constraints between the shaft parts and the housing make it possible for the shaft to rotate around the bearing center of the housing, but not move in the axial direction. Gears are limited by their contact with each other.

The drive function 2 × pi × 15.383 is set to drive the main wheel connected to the motor at a constant speed. The analysis duration is set to 0.25s and the number of steps is 100 in total. Figure 2 shows the force and moment of the two line clamps when the de-icer is working. Figures 2(a), 2(b), 2(c) and 2(d) show the filtered results of the branch reaction force at the two line clamps, the component of the branch reaction force along the direction of the three axes at line clamp 1, the component of the branch reaction force along the Y-direction at line clamp 1, and the filtered results of the branch reaction moment at line clamp 1, respectively.

Based on the observation of Fig. 2(a), it can be seen that the branch reaction force at the two wire clamps is basically the same. Thus, it is possible to analyze only one of the wire clamps (selecting wire clamp 1 for analysis). Fig. 2(b) demonstrates the branching force along the three coordinate axis directions of the branching force at wire clamp 1. The branching force in the X-axis direction and the Z-axis direction are smaller, and the branching force in the Y-axis direction is larger and varies in a simple harmonic manner, with a peak value of 125 N. In Fig. 2(c), the branching force along the Y-axis direction is demonstrated after filtered processing, and the trend of its variation is close to that of the image of the function y = 18.5sin(8π)30, which is in line with the design expectation of consistent with the design expectation. Fig. 2(d) shows the moment at wire clamp 1, oriented in the X-axis direction, with a peak moment of about 0.051 Nm and a short peak time, thus its effect on the principle prototype is negligible.

3

Finite Element Simulation of Distributed Vibratory Deicing for Medium Voltage Overhead Lines

3.1

Finite element modeling of MV overhead conductor

Medium-voltage transmission lines in China generally use steel-core aluminum stranded wire, according to which this paper is modeled, the type of wire and its geometric parameters are shown in Table 1. Ice-covered conductor is a three-composite material, the type of ice cover taken in this paper is the common and the highest intensity of freezing rain-type ice cover in the southern power grid, and the physical parameters of each material are shown in Table 2.

Table 1.

Mechanical parameters of the conductor

Parameter	LGJ-70/10	LGJ-400/65
(aluminum/steel) root number/root	6/1	26/7
(aluminum/steel) diameter/mm	3.80/3.80	4.12/3.45
Outer diameter d/mm	11.50	29.00

Table 2.

Physical parameters of the conductor

Material	Elastic modulus/pa	Poisson ratio	Density/(g*cm⁻³)
steel	2.06×10¹¹	0.3	7.9
aluminium	7.17×10¹⁰	0.33	2.7
rime	3×10⁸	0.3	0.9

The conductor modeling of steel-core aluminum stranded wire structure is more complex, involving a lot of line contact relationship problems, which needs to consider the main factors affecting the analysis results, so as to simplify the less influential secondary factors, and take into account the accuracy of the theoretical calculations. In this paper, for the structural characteristics of the ice-covered conductor, the cylindrical freezing rain ice-covered model of LGJ-70/10 and LGJ-400/65 is established. According to the relationship between the long half-axis a of the freezing rain elliptic cross-section and the outer diameter D of the conductor, the elliptic (a=D and a=1.5D) ice-covering model of LGJ-70/10 is established. According to the relationship between the radius R of the freezing rain fan and the diameter D of the conductor, the fan-shaped (R=D and R=1.5D) ice-covering model of LGJ-70/10 is established.

In the process of solving ANSYS finite element analysis for modal frequencies, Lanczos method is a very effective method, whose mathematical idea is to approximate the symmetric matrix to a tridiagonal matrix by a matrix composed of orthogonal vectors, which in turn transforms the problem into solving for the eigenvalues of the tridiagonal matrix. The modal frequencies of different ice-covered conductors with different rain shapes are shown in Table 3. Due to the symmetry of the cylindrical ice-covered conductor model, the same-order modal frequencies and vibration patterns of the ice-covered conductor in the y-direction and z-direction are almost the same, which are 814 Hz and 815 Hz, respectively.

Table 3.

Modal frequency of iced LGJ-70/10

Cylinder mode frequency/Hz	Elliptical pattern frequency/Hz(a=D)	Elliptical pattern frequency/Hz(a=1.5D)	The modal frequency of the fan/Hz(a=D)	The modal frequency of the fan/Hz(a=1.5D)	Vibration characteristic
814	956	925	887	865	Horizontal first order vibration type, z direction
815	9510	945	894	882	Horizontal first order vibration, y direction
2566	4192	3985	3191	3198	Reverse stage 1
2175	2568	2459	2371	2286	Horizontal stage 2, z direction
2184	2584	2556	2390	2311	Horizontal stage 2, y direction

3.2

Finite Element Analysis of Distributed Vibratory Deicing of Medium Voltage Overhead Lines

The displacement curves of two displacement measurement points on conductors A and B were selected for analysis, and 1 sec was set as the start-up time for the vibration machine. Figures 3 and 4 show the displacement curves of measurement points 1 and 2 on conductor A, and Figures 5 and 6 show the displacement curves of measurement points 3 and 4 on conductor B. The results of the finite element numerical simulation are also presented for comparison with the test results. From Fig. 3, Fig. 4, Fig. 5 and Fig. 6, it can be seen that the simulated displacement curves of each measurement point are basically in line with the results of the test, and the largest error is 6.75% for measurement point 1 when the experimental time is 6.1 s. The maximum error is only 6.75%.

In order to deeply analyze the de-icing effect of the two vibration de-icing methods, we simulate the de-icing dynamic response of the wire under the two vibration de-icing methods. In the simulation process, the ice cover is equivalent to the same quality of freezing rain, and its own material properties were used in two ways. As this paper uses the simulation of de-icing method for the equivalent density method, the equivalent of the ice cover to the same quality of freezing rain will not affect the transmission line in the equivalent density of the ice cover, so the two simulation methods established by the transmission line model is the same. It can be seen that the cohesive strength of 0.2g/cm³ ice overlay is 0.03Mpa, the cohesive strength of 0.9g/cm³ ice overlay is 13.42Mpa, the shedding acceleration of real ice overlay is 6675.92m/s², and the shedding acceleration of equivalent freezing rain is 18658m/s².

The acceleration amplitude of each node of the wire under the two vibration de-icing modes are extracted respectively, and the simulation results of the ice-covered shedding length of conductor A and B are shown in Fig. 7 and Fig. 8, respectively. By comparing the acceleration amplitude of each node of the wire under its own parameter simulation condition with the critical acceleration of ice-covered shedding, we can get the simulation results of the ice-covered shedding length of conductor A to be 72 m, and the error of the experimental results to be 1.6%, and the simulation results of ice-covered shedding length of conductor B to be 42 m, and the error of the experimental results to be 4.7%. The simulation result of ice cover shedding length of conductor B is 42m, and the error of the test result is 4.7%. By using the equivalent of freezing rain simulation method of working condition results can be seen, due to the freezing rain shedding acceleration is very great, only the detonation position of the overlying ice to reach the shedding acceleration, while the rest of the position acceleration can not reach the de-icing conditions, so compared to the equivalent of freezing rain way to use their own parameters to simulate the study has a higher degree of accuracy. By analyzing the size of the acceleration amplitude of each node can be seen, the use of segmented vibration wire generated by the maximum acceleration is less than the maximum acceleration of the whole vibration, which is due to the instantaneous release of segmented vibration of the energy is less than the whole vibration, so the use of segmented vibration de-icing than the whole vibration de-icing has a better safety.

In order to study the de-icing effect of ice-covered transmission lines after different impact methods, the de-icing jump height and de-icing rate of ice-covered transmission lines under two loading methods of single impact and continuous impact are synthesized. The time course diagram of the de-icing jump height of the transmission line under two impact loading methods is shown in Fig. 9, and the other parameters of the control calculation model are the same, and the de-icing jump height of the conductor under different loading methods is studied, and it can be seen in Fig. 9 that the trend of the curve diagrams of the two loading methods is the same, and the maximum de-icing jump height is 8.2m, which is within the permissible range, and the application of the impact loads does not pose a threat to the structure. Compared with the application of a single impact load, the vibration response of the de-icing of the ice-covered transmission line is more intense after the continuous impact load, and the value of the de-icing jump height is large.

The de-icing rate of transmission conductor under different loading methods is shown in Table 4. Compared with the loading mode of single impact, the de-icing of conductor under continuous impact load is more optimistic, when the number of de-icing gears is 4, the de-icing rate of conductor under continuous impact load is 27.5%, which is 10.1% higher than that under the loading mode of single impact. Therefore, the choice of continuous impact load de-icing can better ensure the de-icing effect, but the moment of applying a large continuous impact load, the transmission line will undergo a drastic change in the dynamic response and dynamic process, it is very likely that the transmission tower line system damage, in order to ensure the safe operation of the transmission line, the transmission line should be real-time monitoring of ice-covered conditions, in the line ice-covered thickness of the line when the completion of the de-icing work.

Table 4.

The transmission wire removes the ice rate in different loading modes

Loading mode	Ice rate(%)
Loading mode	First gear	Second gear	Third gear	Fourth gear	Fifth gear
Impact load	23.6	11.6	67.8	17.4	32.6
Continuous shock load	29.5	18.5	74.6	27.5	40.7

4

Conclusion

In this project, for the de-icing needs of medium-voltage power overhead lines, the theoretical research on the design scheme of the principle de-icing system based on resonance is carried out, and the de-icing device is developed and simulation experiments are conducted. 1)

The branch reaction force at line clamp 1 has a large component force along the Y-axis direction and changes in simple harmonic, with a peak value of 125 N. After filtering treatment, the component force along the Y-axis direction has a trend that is close to the image of the function y=18.5sin(8π)30, which is in line with the design expectation. The moment direction at wire clip 1 is in the X-axis direction, and the peak moment is about 0.051Nm, and the peak time is very short, and its effect on the principle prototype is negligible. This confirms the rationality of the principle prototype design.

2)

The displacement time curve of each measurement point obtained from the simulation experiment is basically consistent with the results of the test, and the largest error is 6.75% when the experimental time of measurement point 1 is 6.1s. It shows that the method presented in this paper can effectively reduce the jump amplitude of the wire, leading to higher safety performance.

3)

The de-icing of the conductor under continuous impact loading is more effective than that under single impact loading, when the number of de-icing gears is 4, the de-icing rate of the conductor under continuous impact loading is 10.1% higher than that under single impact loading. And the continuous impact load under the action of the lowest de-icing rate of 18.5%, far more efficient than the artificial de-icing, indicating that the choice of continuous impact load de-icing is more to ensure the de-icing effect. The de-icing system design in this paper is highly efficient, but to ensure the safe operation of transmission lines, it should also implement real-time monitoring of transmission line ice-covering conditions.

Lingua:: Inglese

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Theoretical study and simulation analysis of distributed vibration de-icing technology for medium voltage overhead lines

Xingping He

Yuan Ma

Ke Wang

Chengmeng Liu

Pubblicato online: 19 mar 2025

Ricevuto: 31 ott 2024

Accettato: 16 feb 2025

DOI: https://doi.org/10.2478/amns-2025-0465

Parole chiaveResonance principle, Overhead line de-icing, Vibration frequency, Finite element analysis

© 2025 Xingping He et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
Resonance principle, Overhead line de-icing, Vibration frequency, Finite element analysis