Analysis of the correlation between GIS partial discharge current waveform and charge quantity with UHF signals

The Ultra-High Frequency (UHF) method, as a crucial technology for online GIS monitoring, struggles with the issue of being unable to accurately reflect the number of partial discharges, which poses a significant challenge for this technique. To examine the relationship between partial discharge waveforms, charge quantity, and UHF signals, a physical field model of partial discharge is developed using finite element simulation software, allowing a comparison of the peak-to-peak values of UHF signals with the parameters of the partial discharge current. Research demonstrates a roughly linear relationship between the peak-to-peak values of UHF signals and the magnitude of the partial discharge current but no definitive connection with the discharge quantity. These significant findings guide the quantitative detection of partial discharges in electrical equipment using the UHF method.


Introduction
Gas-insulated switchgear (GIS), with its excellent insulation performance, small footprint, and high operational reliability, has become essential to high-voltage power transmission and transformation systems.However, the level of manufacturing technology affects the insulation defects that may exist within GIS during long-term operation, distorting the surrounding electric field, which in turn leads to partial discharge (PD).The continuous presence of PD can exacerbate insulation deterioration, jeopardizing the safe operation of the equipment and even leading to power outage accidents [1][2][3].Therefore, online monitoring of GIS partial discharge is of significant importance for assessing the condition of the equipment.The ultra-high frequency (UHF) method is a mature monitoring technique that does not alter the operation of the equipment and can be used for continuous energized monitoring of GIS [4].It has been widely applied in the online monitoring of GIS.
In recent years, scholars have dedicated significant research to GIS partial discharge detection via the UHF method, focusing on sensor antenna design and defect diagnosis [5][6][7].However, studies on the correlation between UHF signals and the level of GIS partial discharge are less common.Discharge measurement is critical for assessing insulation integrity and severity of discharges in electrical equipment.The impulse current method is the only standardized technique for quantitatively measuring high-voltage equipment discharges.Still, it suffers from poor electromagnetic interference resistance, rendering it unsuitable for on-site monitoring.Thus, it is necessary to investigate further the inherent relationship between discharge volume and UHF signals for GIS online monitoring.Several studies have explored this area.Tang et al. [8] demonstrated a linear and quadratic correlation between UHF signal peak voltage, cumulative energy, and apparent discharge volume, respectively.Zhang et al. [9] concluded a linear correlation between UHF signal energy and the square of the discharge quantity by the impulse current method.Wang et al. [10] inferred a linear relation between discharge volume and UHF signal voltage integration using a virtual model and fault inversion.
This article primarily simplifies the analysis of the waveguide modes inside a GIS, introducing the frequency domain relationship between various modal patterns of UHF-induced electromagnetic waves and partial discharge currents and investigating the relationship between UHF signals and partial discharge currents.

Analysis of GIS chamber waveguide mode
Based on the structural characteristics of GIS, it can be regarded as a coaxial waveguide.When a partial discharge occurs inside the GIS due to insulation defects, the duration of a single discharge is extremely short, generally a few nanoseconds to several tens of nanoseconds.This will generate a current pulse with a steep rising edge, which excites wideband electromagnetic waves, including TEM and highfrequency TE and TM waves.TEM waves and high-frequency TE and TM waves can propagate through the coaxial waveguide, with the TEM wave being the fundamental mode that is a nondispersive electromagnetic wave without a cutoff frequency, allowing it to propagate at any frequency without distortion.The mode field lines are shown in Figure 1, where solid lines indicate electric force lines and dashed lines indicate magnetic force lines.The electric field lines are distributed radially, which means the strongest radial component is in the coaxial waveguide.There are infinitely many modes for TM and TE, denoted as TMnm and TEnm, respectively.The cutoff frequencies for different TE and TM wave modes can be represented by the approximate Formulas (1) and ( 2 ) where a represents the radius of the inner conductor, b represents the radius of the outer conductor, and c is the speed of propagation of the electromagnetic waves.

Theoretical relationship between electromagnetic waves and partial discharge source currents in GIS
From the text above, it is known that at the inner wall of the GIS, the radial component of the electric field, E r , is the strongest, whereas E Φ and E z are close to zero based on the boundary conditions of the coaxial waveguide [11].Therefore, this paper primarily investigates the relationship between the discharge current and the radial field strength E r of the induced electromagnetic wave.2, should the trajectory of the partial discharge current be a radial line stretching from (r 1 , 0, 0) to (r 2 , 0, 0), then the frequency-domain representation for the electric field intensity of modal electromagnetic waves at an arbitrary point (r, Φ, z) inside the GIS can be described as follows [12][13]: In Formulas (3) to (7), I(ω) represents the expression for partial discharge current in the frequency domain; Z 0 is the wave impedance of a plane wave in vacuum, which is 377 Ω; c is the speed of light in vacuum; J n denotes the Bessel function of the first kind of order n; q nm is the m-th root of J n =0; p nm is the m-th root of the derivative of J n , J n '=0; ω nm is the cutoff angular frequency for the nm-th mode wave.

Partial discharge source model
In GIS, the channels formed by partial discharge currents are very narrow, and the discharge paths are generally short, so partial discharge currents can be simulated using the elemental current model.An elemental current refers to a very short section of an antenna with a uniform current distribution along its length.In this paper, simulations are performed using a dipole antenna to approximate the elemental current model.The generation of partial discharge is simulated by applying a current excitation signal to the feeding point at the center of the dipole antenna.The model of the dipole antenna is shown in Figure 3.The pulse current of the partial discharge can be approximately expressed using a multi-order Gaussian function, as shown in Formula (8): where t represents time; I i represents the amplitude of the pulse current; t pi represents the peak position of the pulse wave; t wi is the time constant, which determines the width of the pulse current; n represents the number of different pulse functions superimposed.This paper uses a simple first-order Gaussian function to describe the partial discharge current.

GIS finite element model and boundary conditions
The finite element model of GIS and its dimensions are constructed in COMSOL, as shown in Figure 3.
To detect the electromagnetic waves induced after partial discharge, three sets of probe arrays are placed at 0°, 90°, and 180° on the inner wall of the GIS model.Each probe has an interval of 0.2 m; the specific positions are indicated in Figure 3.To reduce the simulation computation time, components made of metal, such as busbars and metal enclosures, are set as perfect electrical conductors, with the relevant material parameters shown in Table 1.The front and back cross-sections of the model are set as scattering boundary conditions to minimize the reflection of electromagnetic waves.2, in the UHF frequency range, there are multiple modes of TE and TM waves in the GIS chamber, in addition to TEM waves.

The relationship between partial discharge current waveform, charge quantity, and UHF signal
Taking the simulation results with a current peak t p located at 2 ns, pulse width t w of 1ns, and amplitude of 0.1 A as an example, Figure 4 shows the waveforms of the induced electromagnetic waves in all directions received by Probe 1 at 0° on the inner wall of the GIS, with a duration of 100 ns to obtain a relatively complete waveform.It is observed that the radial component is also much larger than the other components, consistent with the previous analysis results of the coaxial waveguide.A spectral analysis of the aforementioned radial component of the electromagnetic wave is shown in Figure 5, which reveals the presence of a rich spectrum of higher-order TE and TM modes in the electromagnetic waves induced by partial discharge.Therefore, in the following text, all electromagnetic wave studies will focus on the radial component.

The influence of the partial discharge current amplitude on UHF
The partial discharge source (dipole antenna) is placed radially directly above the busbar, and the parameters of the excitation current function and their corresponding images are shown in Table 3 and Figure 6, respectively.7 shows the relationship between the peak-to-peak value of the induced electromagnetic waves, E pp , and the position of the probe under the condition of a fixed current width for different current amplitudes, that is, the attenuation characteristics.According to Formulas (3) to ( 5), it is known that the propagation of the TEM wave inside the GIS does not depend on the angle Φ between the probe and the partial discharge source, while the TE and TM waves are related to Φ.This means that when Φ is 90°, and n is an odd number, the radial electric field components of the TE and TM waves are zero.Therefore, as shown in Figure 7, among the three directions, the E pp is smallest at all positions of the probe group at 90°.Specifically, in each figure, Figure 7 demonstrates similar attenuation characteristics for the seven probes of each directional probe group at different current amplitudes.As the current amplitude increases, the E pp experiences a greater attenuation at the same distance, with the relative attenuation degree (relative to the electric field strength at the first probe) being the same.Taking the 0° probe group as an example, when I 0 is 0.1 A, E pp attenuates by 4.1 V/m over the distance of 1.2 m from probe 1 to probe 7, which is a relative attenuation of 32.5%; when I 0 is 0.4 A, E pp attenuates by 16.5 V/m, with a relative attenuation of 36.9%; when I 0 is 0.7 A, E pp attenuates by 28.9 V/m, with a relative attenuation of 36.9%.The other four points also exhibit the same degree of relative attenuation.For the 90° and 180° probe groups, E pp shows a relative attenuation of 57.9% and 50.8%, respectively.Figure 8 shows the relationship between the peak-to-peak value of the induced electromagnetic waves E pp detected by the probe arrays in various directions and the magnitude of partial discharge current.It is observed that as the excitation current magnitude increases, E pp increases linearly with it, and the further the detection point is from the source of the partial discharge, the smaller the linear slope of E pp to the current magnitude becomes.

0° direction 90° direction 180° direction
The analysis above indicates that, under the condition of constant pulse width, the magnitude of the partial discharge current in GIS primarily affects the absolute attenuation degree of the electromagnetic wave's electric field intensity with the increase of the propagation distance but does not affect the relative attenuation degree.Moreover, it also affects the peak-to-peak value E pp of the induced electromagnetic waves in GIS.The greater the magnitude of the partial discharge current is, the higher the E pp will be.

The influence of partial discharge current width on UHF
We set the parameters and images of the excitation current function as shown in Table 4 and Figure 9, respectively.  .Epp attenuation characteristics.Figure 10 shows the relationship between the peak-to-peak electric field strength E pp of the induced electromagnetic wave and the probe position under the condition of a fixed current amplitude at different widths.Overall, the E pp at each probe in each direction still shows attenuation characteristics.However, both the absolute and relative attenuation values of E pp decrease with the increase in current amplitude at the same distance, which is different from the constant relative attenuation values of E pp when the current width was previously unchanged.After t w is greater than 2 ns, the 0° direction shows a phenomenon where E pp first attenuates and then rises; in the 90° direction, E pp hardly attenuates anymore and tends to the same E pp value.
Figure 11 shows the relationship between the E pp detected by the probe arrays in each direction and the width of the partial discharge current.Unlike the previous impact of current amplitude on E pp , it can be seen that with the increase in the width of the initial excitation current, the peak E pp of the induced electromagnetic wave, including the charge amount, exhibits a quasi-nonlinear decrease.

Conclusions
This paper constructs a GIS (Gas Insulated Switchgear) partial discharge finite element model to study the distance attenuation characteristics of the electromagnetic field strength induced by partial discharge at 0°, 90°, and 180° directions, as well as its relationship with the partial discharge current waveform.
The simulation results indicate that the strength of the electromagnetic field gradually decreases with increasing distance; the amplitude of the partial discharge current and its rate of change has a similar effect on the electromagnetic field strength, which is approximately a linear relationship with the field strength; when the amplitude of the partial discharge current remains constant, the electromagnetic field strength shows a nonlinear decrease as the current width increases.

r 2 r 1 iFigure 2 .
Figure 2. Path of local discharge inside GIS.As illustrated in Figure2, should the trajectory of the partial discharge current be a radial line stretching from (r 1 , 0, 0) to (r 2 , 0, 0), then the frequency-domain representation for the electric field intensity of modal electromagnetic waves at an arbitrary point (r, Φ, z) inside the GIS can be described as follows[12][13]:

Figure 3 .
Figure 3. Straight tube GIS finite element simulation model.

Figure 8 .
Figure 8.The relationship between Epp and the current magnitude.Figure8shows the relationship between the peak-to-peak value of the induced electromagnetic waves E pp detected by the probe arrays in various directions and the magnitude of partial discharge current.It is observed that as the excitation current magnitude increases, E pp increases linearly with it, and the further the detection point is from the source of the partial discharge, the smaller the linear slope of E pp to the current magnitude becomes.The analysis above indicates that, under the condition of constant pulse width, the magnitude of the partial discharge current in GIS primarily affects the absolute attenuation degree of the electromagnetic wave's electric field intensity with the increase of the propagation distance but does not affect the relative attenuation degree.Moreover, it also affects the peak-to-peak value E pp of the induced electromagnetic waves in GIS.The greater the magnitude of the partial discharge current is, the higher the E pp will be.

Figure 11 .
Figure 11.The relationship between Epp and current width.

Table 1 .
GIS Model Material Parameters.The cutoff frequencies for the different modes of TE and TM waves in the GIS chamber can be calculated using Formulas (1) and (2) based on the dimensions of the GIS:

Table 2 .
The cutoff frequency of the coaxial waveguide in the GIS chamber.