Study on Transmission Attenuation Characteristics of Abnormal Discharge Current in Transmission Lines

In order to analyze the transmission characteristics of abnormal discharge current in transmission lines, considering the frequency-dependent characteristics of line parameters, the transmission of abnormal discharge micro-current is studied theoretically and analyzed with examples. Then, ATP-EMTP is used to establish a hidden danger micro-current transmission model for the elevated line, and the micro-current transmission situation is simulated. The influence of frequency and different voltage levels on the hidden danger micro-current transmission characteristics is mainly considered. The results show that the higher the frequency of the initial signal, the larger the equivalent resistance and the smaller the equivalent inductance of the line. The frequency has little effect on capacitance and conductance. The attenuation constant of high-voltage class lines with multiple split wires is greater than that of low voltage class lines with single split wires, and the attenuation constant only increases slightly with the increase of split wires.


Introduction
Transmission line tripping is one of the frequent faults of the power grid.The fault tripping caused by natural factors such as lightning, mountain fire, pollution, and plant growth brings impact to the system every time, brings damage to the power grid equipment, and leaves security risks to the power grid.Most of the transmission lines are planned and distributed in sparsely populated areas, and the mountainous field environment makes it very difficult to find the fault of the transmission line.Therefore, in order to avoid the fault trip of the line, the abnormal discharge point of the line can be found timely and accurately, the discharge characteristics can be analyzed, and the abnormal discharge point of the line can be repaired to eliminate the hidden danger of the line.Avoiding circuit trip is the primary task of system operation and maintenance.
A lot of research has been done on the hidden fault analysis of transmission lines in China.Literature [1] analyzed the propagation characteristics of ultra-long lines similar to UHV halfwavelength lines, and theoretically studied the difference in wave speed between line-mode traveling wave and zero-mode traveling wave at different fault distances, considering the frequency dependent characteristics of line parameters.It is proposed that the zero mode travelling wave reflected from the fault point to both ends of the line contains part of the line mode travelling wave reflected from both ends of the line to the fault point, and the line mode travelling wave penetrating into the zero mode channel will make the calculated zero mode average wave speed approximate to the line mode average wave speed.Literature [2] analyzed the transmission characteristics of fault traveling wave in the distribution network, proposed the ranging method of distributing the traveling wave ranging device on the overhead lines of the distribution network, and conducted in-depth research on the optimization configuration of the traveling wave ranging device in the method and the design of the traveling wave ranging device applicable to the overhead lines of the distribution network.In literature [3], the detection function of signal singularity by wavelet transform is applied to the distance measurement of transmission lines.According to the mode maximum property of the mode component of the fault traveling wave current signal line, a new method is proposed which is not affected by the transition resistance, fault type and fault distance.The new fault location solution has high reliability and accuracy.
Firstly, this paper analyzes the transmission characteristics of abnormal discharge current from the aspects of theory and example, and then establishes the abnormal discharge model of overhead line.Based on this model, the influencing factors of abnormal discharge current are explored from the aspects of different frequency and different voltage levels.

Analysis of Abnormal Discharge Current Transmission Characteristics
Most of the transmission lines will produce weak abnormal discharge currents when there are hidden dangers.The main ways of these abnormal discharge currents are trees approaching wires, insulator fouling, bird damage and floating discharge.These hidden dangers gradually develop and eventually cause line tripping, so it is necessary to understand the characteristics of abnormal discharge current to judge the hidden dangers of abnormal discharge current in time by monitoring the abnormal discharge current.

Frequency Dependent Characteristics of Abnormal Discharge Current Transmission
When there is a hidden danger in an overhead transmission line, abnormal discharge will be generated, mainly for weak high-frequency pulse current.This process is equivalent to charging the line's capacitance to the ground and propagating along the line.In the process of propagation, these weak currents will generate transformed magnetic fields, and the changing magnetic fields will generate transformed electric fields, which all propagate along the transmission line at a certain speed.The current then travels in the form of a wave through an overhead transmission line.
In the actual transmission line, some energy-consuming factors such as the earth, corona phenomenon, wire to ground conductance and wire resistance will cause transmission line losses, there will be no lossless transmission lines, so in the process of abnormal discharge current transmission must produce different degrees of attenuation.
, Where γ is the propagation constant, α is the transmission line attenuation constant, Np/m; Beta is the phase coefficient of the transmission line, rad/m.However, considering that the hidden current is highfrequency current, the parameters of the overhead transmission line have frequency-dependent characteristics [4][5].The resistance, capacitance, conductance and inductance parameters of the overhead transmission line at different frequencies are different, so the propagation parameters can be rewritten as equation (1): Among the resistance, inductance, capacitance and conductance parameters of the line, resistance and inductance are greatly affected by frequency, and the influence of frequency on conductance and capacitance can be ignored.Therefore, the propagation equation of the forward wave can be obtained as follows: At this time, the attenuation coefficient and phase coefficient under the frequency-dependent characteristic are:

Example Analysis of Transmission Characteristics
Due to the complex impedance matrix of multi-wire transmission line and the skin effect between wire and earth, there is a functional relationship between impedance and current frequency, which makes the calculation more complicated.Some foreign scholars have derived some methods to calculate the impedance matrix of multi-wire transmission lines, including Carson formula, modified Carson formula, Dubanton formula, etc., Carson formula uses the distance between the conductor and its mirror image to calculate the impedance matrix of multi-wire transmission systems.The modified Carson formula simplifies the calculation of the original formula and improves the operation efficiency.The Dubanton formula is also a simplified version of Carson formula, and the influence of soil resistivity and permeability on the parameters of the overhead line is calculated by using the complex penetration distance method.The expression of Dubanton formula is simple, the calculation results are continuous, and the calculation accuracy is between Carson formula and Carson simplified formula.Dubanton formula and Carson formula are very close to each other when calculating overhead line parameters, with a difference of up to 9% in the frequency range of 100 Hz to 10 kHz.According to Dubanton formula, we can get: Where p is the complex penetration coefficient, σ is the soil conductivity, μ0 is the vacuum permeability, ω is the angular frequency of the signal, Zs is the self-impedance, Zm is the mutual impedance, h is the height of the wire from the ground, and d is the distance between the two wires.At the same time, when considering the frequency-dependent characteristics of the line parameters, the relationship between wave velocity and phase shift coefficient is as follows: Assuming the 110kV overhead line space model, the line is uniformly transposed, the line radius is 11.88mm, and the ground radius is 6.8mm, the general hidden current frequency is mostly concentrated between 100kHz and 200kHz, and the frequency is taken as 100kHz to calculate the potential length impedance matrix, as shown in figure 1: The unit length impedance at power frequency 50Hz can be obtained: It can be obtained at 100kHz frequency: It can be seen that the equivalent resistance per unit length of the line at 100kHz is much larger than the power frequency resistance, although the reactance per unit length at 100kHz is larger, the equivalent inductance is still gradually decreasing.The lightning-arrester line elimination process is carried out on equation (8), and the simplified three-phase parameter matrix is obtained.The specific calculation process is referred to the reference [6], which will not be repeated in this paper.
Through theoretical derivation, it can be obtained that the attenuation frequency at 100kHz is the attenuation constant at 50Hz, as shown in table 1 As can be seen from the above table, the attenuation frequency at 100kHz is far greater than that at 50Hz, indicating that the greater the frequency of the hidden current, the more difficult it is to carry out long-distance transmission, and the high frequency part of hidden current is easily consumed in the transmission process.

Simulation Model Construction
Taking the 110kV overhead line model in figure 1 as the parameter setting object, the simulation example in figure 2 is set up.In order to consider the variation of frequency characteristics, the line is set as Jmarti model, and two lightning arrester lines are set to simulate the real situation.

Simulation Result Analysis
Waveform data of current observation points at 0km, 2km and 4km are selected respectively, and the results are shown in figure 3: As can be seen from the figure, after the hidden current is injected into the wire from the injection point, it propagates to both sides of the wire, and the currents on both sides are equal, so the amplitude of the current on the side of the hidden danger is only 50mA.With the transmission of the traveling wave to 2km, it can be seen that the amplitude of the line decreases to 47.1mA compared with the starting point of the hidden danger, and when the traveling wave reaches 4km, the amplitude of the traveling wave decreases to 44.4mA.At the same time, since the traveling wave transmission takes time, the traveling wave speed can be calculated by the time difference between the arrival of the two traveling wave heads.The average interval time between the two traveling wave heads is 6.6768 microseconds, and the distance between the two current monitoring points is 2km.It can be obtained that the traveling wave transmission speed is , Compared with the attenuation constant calculated theoretically in table 1, the error is only 9.2%, so it can be considered that the simulation results have a certain accuracy.It can be seen from figure 4 that the error between the simulation attenuation and the attenuation constant obtained from the theoretical calculation is small, which confirms that the model has certain reference significance.However, it can be seen that there is a certain degree of deviation between the theoretical value and the simulation result at about 16km.Through the spectrum analysis of the current waveform monitored at 16km, it can be found that the waveform has a certain degree of distortion and a small amount of low-frequency component.Therefore, the attenuation rate is slower than the theoretical attenuation rate.

Influence of Different Factors on Hidden Current Transmission Characteristics
Generally speaking, due to the frequency dependent characteristics of the line, the equivalent line parameters at different frequencies are different, which has an impact on the transmission characteristics of the line.At the same time, the line structure, number of split wire, wire radius of lines with different voltage levels will also affect the transmission characteristics of the lines [7-9].Therefore, the modeling and simulation of 110kV lines at different frequencies and 110kV, 220kV and 500kV lines at 100kHz frequencies are carried out to analyze the influence of frequency and line grade on transmission characteristics.

Influence of Frequency on Transmission Characteristics.
Since the frequency of hidden current is mostly concentrated in the range of tens of kilohertz to several megahertz, another single frequency current source with the same amplitude of 50kHz and 500kHz frequency is taken as the hidden current source, and the current of the same position current monitoring point is taken for comparative analysis.The current amplitude table can be obtained through simulation calculation, as shown in table 3 It can be seen that the high-frequency part of the attenuation is very fast, and the higher the frequency, the faster the attenuation, at about 8km, the hidden current of 500kHz has almost decayed out, it is difficult to monitor the instrument, and the hidden current of 50kHz only loses less than 20% of the amplitude at 16km, basically no change.It can be seen that the 4 split wires of the 500kV voltage class decay the fastest, and those of the 110kV voltage class decay the slowest, because the split wires increase the line capacitance, and it can be seen from equation (3) that the line capacitance is a function of the attenuation constant, but on the whole, the difference between 220kV and 500kV lines is small.It shows that the influence of multiple split wires on the attenuation constant of the line gradually decreases.At the same time, due to the difference in line height, sag, line frequency resistance and other parameters, the final attenuation difference of different voltage levels is caused by the attenuation constant.It is precisely because the attenuation constant is related to all aspects of the line parameters, so it is difficult to analyze accurately.Through the analysis of the above two influencing factors, it can be concluded that the higher the frequency of hidden current, the faster the attenuation, so it is difficult for high-frequency signals to be transmitted over long distances, and different transmission levels of lines will also have a greater impact on the transmission characteristics of hidden current.In addition to the above two factors, there are many factors such as soil resistivity, tower grounding resistance, the relative position of power lines, etc, will have a certain degree of impact on the decay of hidden current, so it is generally to take an approximate model instead of the actual model, the approximation process will produce inevitable errors.When the high frequency content of a hidden current signal is mostly, it is difficult to detect its signal at a relatively long distance, resulting in the failure to eliminate hidden trouble in time, and a large number of hidden danger monitoring devices installed at close range will cause a lot of waste, so it is of great practical significance to investigate the hidden current transmission characteristics.

Conclusion
In this paper, the attenuation characteristics of transmission line abnormal discharge current are studied, and the effects of frequency and different voltage levels on the transmission characteristics are considered.The following conclusions were reached: (1) Due to the influence of the overhead ground line and the other two phases, the impedance matrix needs to be eliminated and decouped first in the process of theoretical calculation of transmission characteristics.
(2) Line parameters have frequency-dependent characteristics.The higher the frequency of the initial signal, the larger the equivalent resistance of the line and the smaller the equivalent inductance.The frequency has little effect on capacitance and conductance.
(3) High frequency hidden signal attenuation is faster, 500kHz hidden current almost decays at 8km; The low-frequency hidden signal is basically not attenuated, and the 50kHz hidden current attenuates less than 20% after 16km transmission.In addition, the attenuation constant of high voltage class lines with multiple split wires is greater than that of low voltage class lines with single split wires, and the attenuation constant only increases slightly with the increase of split wires.

Figure 1 .
Figure 1.Spatial distribution diagram of overhead line.

Figure 3 .
Figure 3. Current waveform at different positions.
Characteristics.Transmission lines of different line grades have different structures and transmission characteristics.In this paper, typical 220kV line 2 split wire 2×LGJ-185 and 500kV line 4 split wire 4×LGJQ-400 are selected as comparison references for modeling and simulation.The simulation model diagram is similar to figure 2. The hidden current source is a single frequency current source with amplitude of 100mA and frequency of 100kHz.Current waveform data can be obtained at the same current monitoring point, and the current amplitude

Table 1 .
. Attenuation frequency and attenuation constant at 100kHz and 50Hz.

Table 2 .
The simulation calculation of a line with a transmission distance of 16km is carried out, and its current amplitude and attenuation ratio are shown in table 2: Attenuation of current amplitude and frequency amplitude at different distances.According to the data in table 2, the attenuation constant obtained through theoretical calculation in table 1 can be compared, and the 100kHz theoretical and simulation attenuation diagram in figure4can be obtained: 6

Table 3 .
: Current amplitude at different frequencies.

Table 4 .
table can be obtained through simulation calculation, as shown in table 4: Current amplitude at different voltage levels.