Parameter Optimization of Electric Pulse Deicer for Overhead Ground Wire Based on Finite Element Method

Because it is difficult to implement short-circuit deicing, overhead ground wire deicing has always been a difficult problem in power grid ice prevention and disaster reduction. In this paper, the working principle of the overhead ground wire electric pulse deicing device is introduced. Then the electric pulse force calculation model of the overhead ground wire is established. The validity of the model is verified by comparing the model-calculated values of coil inductance and resistance with the experimentally measured values. The effect of coil turns, multiplier thickness, and the side length of the multiplier on the pulse force peak and impulse are analyzed. Finally, the electric pulse deicing test of the short-size ground wire is carried out in the artificial climate chamber. The results show that with the increase in the number of turns of the coil, the peak value of the pulse force decreases gradually, the impulse increases gradually, but the growth rate slows down. With the increase of the thickness of the multiplier, the peak value and impulse of the pulse force increase almost unchanged near the skin depth. With the increase of the side length of the multiplier, the peak value and impulse of the pulse force gradually increase until the area of the multiplier is close to the area of the coil. The electric pulse deicing test shows that the deicing length increases with the increase of the number of coil turns, and the deicing efficiency of the 60-turn coil deicing device is 90%.


Introduction
The occurrence of icing flashover accidents on transmission lines poses a threat to the safe operation of transmission lines [1][2].Due to the fact that the ground wire does not undertake the task of power transmission, there is no Joule heating effect on the ground wire, resulting in a more difficult icing situation on the ground wire.At present, thermal ice melting technology is commonly used to remove ground wire icing, but this method consumes a lot of energy and has a high cost [3][4][5][6].
The mechanical deicing method has low energy consumption and low cost, and relevant scholars have conducted research on this method.Montambault et al. [7] developed an ROV remote control deicing device, but its communication distance is short, and its terrain adaptability is poor.Karman and Karman et al. [8,9] studied the DAC deicing device and analyzed the impact load properties on deicing.However, the installation process of this device is relatively cumbersome and has a significant impact on the stability of transmission lines.Egbert et al. [10] proposed the concept of ground wire electromagnetic pulse deicing and conducted relevant experiments, achieving certain results.However, due to the technical conditions at that time, this method was not promoted.
To sum up, the installation process of the existing ground wire mechanical deicing device is cumbersome, which affects the safe operation of the line.Therefore, this article proposes an electric pulse deicing method for overhead ground wires and designs an electric pulse deicer.It analyzes the influence of different parameters on the peak and impulse of electric pulse force through the finite element method.It obtains the optimization results of the deicer parameters and conducts deicing experiments to verify the correctness of the optimization plan.

Working principle of overhead ground wire electric pulse deicer
The ground wire electric pulse deicer mainly includes an energy harvesting coil, a multiplier, an energy storage device, a pulse coil, and a limiter, as shown in Figure 1.The working principle is shown in Figure 2. When the circuit is not covered with ice, the energy coil takes power from the circuit and stores the energy in the energy storage device through the rectification circuit.When the icing reaches a certain level, the deicer acts, and the energy storage element discharges into the pulse coil, generating a large current i 1 in the coil.According to Faraday's law of electromagnetic induction, an induced eddy current i 2 is generated on the multiplier, and a reverse magnetic field is generated.Due to the opposite direction between the induced eddy current and the excitation current, a high amplitude instantaneous pulse force is generated between the multiplier and the pulse coil.Under this pulse force, the ground wire generates a high acceleration vibration that propagates along the axis, during which the ice layer on the ground wire falls off. Figure 2. Operating principle of the electromagnetic pulse coil.

Pulse circuit analysis
The electromagnetic pulse deicing system circuit is based on the principle of pulse discharge, and its equivalent circuit is shown in Figure 3.The thyristor is turned on under the deicing signal, and the circuit is equivalent to an RLC circuit.When the voltage at both ends of the freewheeling diode changes from negative to positive, the freewheeling diode conducts, and the pulse discharge circuit is an RL circuit.U 0 is the initial voltage of the capacitor, R K and L K are the equivalent inductance and resistance of the coil considering the coupling coefficient, C is the capacitance value, L A is the equivalent inductance of the multiplier, and R A is the equivalent resistance of the multiplier.
In order to simplify the research, the nonlinear circuit characteristics of devices in the circuit are ignored, and the influence of the freewheeling diode is considered.When R< 2/ K LC , the system is in an underdamped state, and its current synthesis expression [11] among them, R is the equivalent resistance of the pulse system, α is the attenuation coefficient, ω is the attenuation angle frequency, Im is the peak current, ti,max is the time when the current first reaches its peak.According to Faraday's law of electromagnetic induction, the induced electromotive force E, induced eddy current i2, and pulse force on the multiplier of the distance coil ra are calculated [12]: among them, Z is the equivalent impedance of the multiplier, φ is the impedance angle.

Parameter optimization analysis of pulse coil and actuator multiplier
According to Equation ( 2), the electromagnetic pulse force is related to parameters such as coil inductance and multiplier resistance.The pulse coil and multiplier are the core parts of the electric pulse deicer, and it is necessary to analyze the influence of their structural parameters on the electric pulse force.
The coil of the deicer is a flat coil.When the number of turns of the coil is less than 30, a single-layer circular coil is wound.When the number of turns of the coil is greater than 30, a double-layer circular coil is used.
The single-layer coil inductance L S can be expressed as [13]: among them, the vacuum permeability  0 =4π10 -7 , n is the number of turns in a single layer coil, d is the wire diameter, w is the wire turn spacing, d in is the inner diameter of the coil, d out is the outer diameter of the coil, and d avg is the average radius, ρ Is the filling rate.Due to the need to consider mutual inductance between double-layer coils, their inductance L S can be expressed as: 22 among them, L U and L D represent the coil self-inductance of the upper and lower layers, and K C represents the coupling coefficient.According to Equations ( 3) and ( 4), the coil inductance is related to the wire diameter d, turn spacing w, layer spacing x, and coil inner diameter d in .The resistance of the multiplier is related to the Conductivity of Multipliers σ, the side length l of the multiplier, and the thickness h of the multiplier.
The amplitude and duration of the electric pulse force have an impact on the vibration effect of the ground wire.Therefore, it is necessary to calculate the peak force F and impulse J of the electromagnetic pulse.

Benchmark model
A 3D simulation model is established using Comsol Physics multi-physical field finite element software.Due to the distance between the steel core aluminum stranded wire and the coil, the induced current on the wire is not considered.Given the unbounded nature of the magnetic field, the air domain is divided into two layers, with the outer layer set as an infinite element domain, as shown in Figure 4a.Since the current frequency is high, up to thousands of hertz, the skin effect needs to be considered.When meshing, set the boundary layer grid for the multiplier, as shown in Figure 4b.The multiplier in the model is a square multiplier, and the settings of the multiplier and coil reference parameters are shown in Table 1.
Table 1.Parameters of coil and aluminum plate.

Solution steps
The resistance R K and inductance L K after coupling the coil and multiplier in the frequency domain are calculated.The obtained results are used as input to the circuit module.The coil excitation current i is calculated by the circuit module, and i is used as the input of the transient electromagnetic module.
According to Maxwell's electromagnetic induction law, the induced eddy current of the multiplier is solved, and the electromagnetic force F on the multiplier is solved.The pulse force impulse J can be obtained by integrating the electromagnetic pulse force with time.The calculation process is shown in Figure 5.

Simulation model validation
Based on the above analysis, it can be concluded that the uncoupled inductance L S , resistance R S , coupled inductance L K , resistance R K , and excitation current i of the coils can all be calculated and measured by simulation models and experiments.By comparing and analyzing the experimental and simulation results, the effectiveness of the simulation model can be verified.Under the same other conditions in Table 1, coil 20, 30, 40, 50, and 60 turns, respectively, and measure L K and R K .Compare the simulation results, as shown in Figure 6.At a pulse voltage of 500 V, the capacitor capacitance is 470 μF.Under the condition of a multiplier thickness of 3 mm, the current waveform of a 20-turn coil was measured using a Roche coil and compared with the current waveform calculated by a numerical model, as shown in Figure 7.
As shown in Figure 6, as the number of coils turns increases, the equivalent inductance L K and resistance R K of the system show an increasing trend.The error between the numerical calculation model results and the experimental measurement results is less than 10%.As shown in Figure 7, the average error between the pulse current calculated by the numerical model and the pulse current measured by the experiment is 4%.The error is within an acceptable range, proving the effectiveness of the simulation model.

Analysis of factors affecting the peak and impulse of electromagnetic pulse force
This chapter mainly studies the influence of coil turns n, multiplier side length l, and multiplier thickness h.The Control variates are used to study the influence of n, l, h on F and J [14].

Number of coils turns
According to the calculation process in Figure 5, while keeping the other parameters in Table 1 unchanged, the effect of the number of turns n on the peak electromagnetic force and impulse is calculated, as shown in Figure 8.
Figure 8.The variation of the peak value of pulse force and its impulse with the number of coils turns.
According to Figure 8, the electromagnetic force F of the coil decreases with the increase of coil turns.In contrast, the electromagnetic force impulse J of the coil increases to saturation with the increase of coil turns.The reason is that as the number of coils turns increases, the uncoupled inductance L S and R S of the coil increase; the coupled inductance L K and resistance R K increase; the peak electromagnetic force F of the coil continuously decreases; and the attenuation angle frequency ω gradually decreases; the duration of electromagnetic force increases; the impulse of electromagnetic force continues to increase.

Multiplier thickness
Due to the skin effect, the peak value and impulse of the electromagnetic force will be affected by the thickness of the multiplier to a certain extent δ for: among them, ω 1 is the angular frequency of magnetic field change, μ Is the magnetic permeability, and σ Is the conductivity of the multiplier.According to Equation ( 5), the skin depth of the 30-turn coil is calculated to be 2.4 mm.The variation trend of peak electromagnetic force F and impulse J with the thickness h of the multiplier is shown in Figure 9.
As shown in Figure 10, as the thickness of the multiplier is less than the skin depth, the peak electromagnetic force F and impulse J rapidly increase with the increase of the multiplier thickness, reaching their maximum values when the thickness approaches the skin depth.When the thickness of the multiplier exceeds the skin depth, the peak value of electromagnetic force F slowly decreases, and the rate of change slows down, while the impulse J remains almost unchanged.Therefore, when the thickness of the multiplier approaches the skin depth, the peak electromagnetic force and impulse reach their maximum values.

Multiplier side length
The side length of the multiplier determines the size of the deicer.To reduce the weight of the device, it is necessary to choose an appropriate side length for the multiplier.The variation of peak electromagnetic force and impulse with the side length of the multiplier is shown in Figure 10.By analyzing Figure 10, it can be seen that the peak value of pulse force F and impulse J gradually decrease with the increase of the side length of the multiplier.When the multiplier area is close to the coil area, the peak pulse force and impulse reach their maximum values.The reason is that the distribution of induced eddy currents is mainly concentrated in areas close to the coil area, as shown in Figure 11.When the side length of the multiplier is less than the coil diameter, the force area of the multiplier decreases.When the side length of the multiplier is greater than the coil diameter, the force on the multiplier remains almost unchanged.Therefore, the area of the multiplier should be close to the area of the coil, where the peak pulse force and impulse both reach their maximum values.

Ground wire electromagnetic pulse experiment
To investigate the deicing effect of an electric pulse deicer and verify the correctness of the pulse force calculation of the above simulation model, this paper conducted ground wire electric pulse deicing experiments with different coil turns in an artificial climate chamber.

Experimental setup
A scaled ground wire electromagnetic pulse deicing test platform was built in an artificial climate chamber, as shown in Figure 12.The ground wire model is GJ-50, with a length of 3.2 meters, and is fixed at both ends through tension sensors.The pulse device is arranged in the middle of the ground wire.By controlling the icing temperature and wind speed of the artificial climate chamber, mixed glaze icing was obtained.The icing thickness of the ground wire was measured at different positions of the ground wire, and the average value was taken as the icing thickness of the ground wire.The icing thickness of the ground wire under different turns of coils was obtained to be 3 mm.

Deicing effect of electric pulse deicer
Under the condition of a pulse voltage of 1300 V and multiplier thickness of 5 mm, the number of turns of the deicer coil is changed to conduct five deicing tests on the mixed glaze with an icing thickness of 3 mm on the steel strand GJ-50.The deicing test process is shown in Figure 13, and the deicing length of each time is recorded as shown in Figure 14.
From Figure 13 and Figure 14, it can be seen that when the number of coils turns remains constant, the deicing distance continues to increase with the increase of deicing times.After three rounds of deicing, the trend of increasing the deicing distance slows down.As the number of coils turns increases, the length of ground wire detachment increases under each electric pulse, and the increasing trend is the same as the peak acceleration changing with the number of coils turns.For a 60-turn flat plate deicer, under five electric pulses, the length of ground wire deicing is 286 cm, and the deicing efficiency is 90%.

Conclusion
This article analyzes the equivalent circuit of an electric pulse deicer.It establishes a numerical calculation model for the pulse force of the electric pulse deicer and analyzes the influence of coil and multiplier parameters on the peak and impulse of the pulse force.An electromagnetic pulse deicing experiment was conducted in a multifunctional artificial climate laboratory.The main conclusions are as follows: 1.The peak value of pulse force decreases with the increase of coil turns and increases with the increase of multiplier thickness and side length.The thickness of the multiplier is greater than the skin depth, and when the side length of the multiplier is greater than the coil diameter, the peak value of pulse force changes less.
2. The impulse of the pulse force increases with the increase of coil turns and also increases with the thickness and side length of the multiplier.When the thickness of the multiplier is greater than the skin depth, and the side length of the multiplier is greater than the coil diameter, the impulse of the pulse force remains unchanged.
3. This article conducts a mixed glaze deicing test on GJ-50 ground wire.The deicing length increases with the number of turns of the deicer coil, and the deicing efficiency of the 60-turn coil is 90%.
4. The electric pulse deicing method proposed in this article can effectively achieve the goal of shortsize ground wire deicing.However, for the deicing needs of long-span transmission lines, research on multi-pulse system collaborative deicing experiments is needed.

Figure 3 .
Figure 3. Circuit schematic diagram of electromagnetic pulse system.

Figure 4 .
Figure 4. Finite element calculation model of electromagnetic coil system.

Figure 6 .
Figure 6.Test and calculation of equivalent inductance and resistance of deicer.

Figure 7 .
Figure 7. Test and calculation of pulse current of deicer.

Figure 9 .
Figure 9. Variation of peak value and impulse of pulse force with the thickness of multiplier.

Figure 10 .
Figure 10.Variation of peak value and impulse of pulse force with side length of multiplier.

Figure 11 .
Figure 11.Distribution diagram of induced eddy current along the side length of aluminum plate.
(a) Schematic diagram of electric pulse deicing test platform (b) Physical diagram of electric pulse deicing test platform Figure 12.Ground wire electromagnetic pulse deicing test platform.