Design of a New Busbar for VFTO Suppression and Analysis of the Suppression Effect

Abstract

Very fast transient overvoltage (VFTO) is characterized by short wavefront time, high amplitude and wide frequency. VFTO poses a threat to the safe operation of power equipment. In order to suppress the harmful effects of VFTO transmission on power equipment, a new type of busbar based on the structure of “inductance + resistance” has been designed, which is called a “damping busbar”. In this study, the equivalent circuit of a damping bus including spurious parameters was developed. These stray parameters are formed between the GIS enclosure and the damping bus, and between the disk insulators and the damping bus. A damping bus simulation model was established based on the equivalent circuit to carry out analysis of the relationship between the structural parameters of the damping bus and the inductance generated by the damping bus. The simulation results showed that the number of turns plays a decisive role in bus inductance, and the relationship between the number of turns and inductance is approximately linear. Comparative analysis of multiple waveforms was carried out before and after the addition of damping buses to the GIS on a 550 kV test rig. The test data showed that the average amplitude of VFTO decreased by 20.36% after the installation of the damping bus, the number of breakdowns decreased by about 66.7%, and there was no obvious high frequency in the measured waveform after installation. In short, the damping busbar had a good suppression effect on the amplitude and frequency of VFTO, and reduced the number of breakdowns. This technique provides a novel solution for VFTO suppression.

1. Introduction

VFTO is a phenomenon of voltage fluctuation in power systems within very short time periods, usually occurring during the operation of gas-insulated switchgear (GIS). VFTOs have extremely short rise times, typically in the nanosecond range, and can reach hundreds of MHz or even GHz. This overvoltage is caused when a circuit breaker or disconnect switch in the GIS is operated. Arc reignition and multiple breakdowns occur during operation, leading to rapid voltage changes and reflection and superposition of electromagnetic waves, resulting in the formation of VFTO. The amplitude of the VFTO is usually high, and can be several times the rated system voltage or even higher. This is the reason VFTOs pose a threat to the insulation of electrical equipment [1,2,3,4,5].

Several of the hazards that VFTOs produce on a power system may be identified as follows:

• The high amplitude and rapid rise time of VFTO can cause impacts on the insulation system of electrical equipment, leading to insulation deterioration and even breakdown [6,7,8].
• The high-frequency component of VFTO generates strong electromagnetic interference (EMI) in the power system, which affects the operation status of secondary equipment [9,10,11].
• Transformer windings are deformed or damaged due to mechanical stress on the transformer windings caused by VFTO [12,13].

The above hazards not only increase the maintenance cost of the power system, but also may cause large-scale power outages, affecting the safe operation of the power system.

The following methods are currently the conventional means of suppressing VFTOs:

• VFTO generation and propagation is reduced by optimizing the design of GIS equipment; for example, by using low inductance bus structures, increasing damping resistors, etc. [14,15,16].
• The VFTO amplitude is suppressed by metal oxide arresters (MOAs) [17,18,19,20].
• The wavefront steepness of the VFTO is flattened by the capacitance which is generated by the overhead line [21,22,23,24].

However, these methods still have limitations in practical application. For example, although the method of optimizing the design of GIS equipment can effectively reduce the generation of VFTOs, it is costly and difficult to retrofit existing equipment. Although an MOA can limit the amplitude of VFTO, its response speed is limited and it cannot completely suppress the high-frequency part of VFTO. The steepness of VFTO is suppressed by overhead lines to some extent, but the transient attenuation is weakened beyond a certain length, and the decline tends to level off. A comparison of the common VFTO suppression methods mentioned above is shown in

Table 1. Comparison of common VFTO suppression methods.

Method	Advantage	Disadvantage
Damping resistance Method	Principle is simple and the inhibitory effect is good	Increases the complexity of the isolation switch structure and makes it expensive
Magnetic ring schemes	Good inhibitory effect	Easy to saturate
Lightning arrester method	Low cost, no need to change the GIS structure	The amplitude suppression effect is significant, but the wavefront steepness suppression effect is not significant, and the protection range is limited

.

In response to the shortcomings of the existing VFTO suppression methods, a new type of busbar with an “inductor + resistor” structure has been designed, which is called a “damped busbar”. A damping busbar utilizes the characteristic that the busbar itself is an inductor, and the suppression of VFTO propagation is achieved by mechanical processing on the basis of a conventional busbar and the addition of a non-inductive resistor. In this study, an equivalent analytical model of a damping bus with stray parameters was established based on the structural characteristics of the damping bus. Relying on the equivalent analytical model, damping bus parameters were calculated, and a damping bus simulation model built. The current throughput capacity and insulation properties of the damped busbar were analyzed based on simulation modeling. Finally, the damping busbar’s effect on VFTO suppression was verified on a 550 kV GIS test rig.

2. Analysis of Damping Busbar Design and Suppression Mechanism

2.1. Structure Design

The structure of the damping bus is shown in Figure 1. The conventional busbar is machined into a spiral shape, as shown in Figure 1a [25,26]. The processed busbar tube forms a multi-turn inductive coil state. The circular spiral hollow on the busbar reduces its mechanical strength. Therefore, an epoxy support member is added inside the busbar to enhance the mechanical strength of the damping busbar, and a number of radial grooves are provided around it. Multiple non-inductive damping resistors are mounted in the grooves of the epoxy supports. The purpose of installing a non-inductive resistor is to allow the resistor to absorb energy and thus achieve suppression of the VFTO amplitude. The epoxy supports and resistors are shown in Figure 1b.

The damping busbar is hollowed out into a skeletonized slot by a spiral method, and the slot gap that is hollowed out becomes a discharge gap, so it exhibits strong inductive characteristics under high frequency conditions. The schematic cross-section of the damping busbar spiral is shown in Figure 2. The distance of the discharge gap near the outer side of the spiral tube is much larger than the inner gap distance. The insulation capability of the GIS duct enclosure is enhanced by this design. Because this design ensures that the gas discharge channel for the turn-to-turn breakdown of the overvoltage through the damping busbar is on the inside of the spiral tube, the effect of sparks on the outside of the damping busbar is minimized.

2.2. Suppression Mechanism

Installation of resistance, inductance or capacitance are the three most common means of suppressing overvoltage. A damping busbar utilizes the inductance of the wire itself to achieve overvoltage suppression. In this section, we analyze the working mechanism by which a damping busbar suppresses VFTO, based on traveling wave theory.

Figure 3 shows a schematic of a traveling wave through an inductor. The busbar itself has an inductance, so the busbar in Figure 3 is represented by Z₁, and Z₂ represents the load. According to Peterson’s law, when an infinitely long right-angle voltage $u_1^{\prime }$ traveling wave passes through an inductor, its voltage $u_2^{\prime }$ for the amplitude can be expressed as:

$$u_2^{\prime }=i_2^{\prime }{Z}_2={\displaystyle \frac{2Z_2}{Z_1+Z_2}}{u}_1^{\prime }(1-e^{-{\displaystyle \frac{t}{{\tau }_L}}})=a{u}_1^{\prime }(1-e^{-{\displaystyle \frac{t}{{\tau }_L}}})$$

(1)

In Equation (1), ${\tau }_L$ represents the time constant of the loop as $L/(Z_1+Z_2)$, and a represents the voltage refraction coefficient in the absence of inductance as $2Z_2/(Z_1+Z_2)$. The wavefront steepness changes from that of an infinitely long right-angle wave, so that:

$$a={\displaystyle \frac{d{u}_2^{\prime }}{dt}}={\displaystyle \frac{2Z_2}{Z_1+Z_2}}{u}_1^{\prime }{\displaystyle \frac{1}{{\tau }_t}}{e}^{-{\displaystyle \frac{t}{{\tau }_L}}}={\displaystyle \frac{2Z_2{u}_1^{\prime }}{L}}{e}^{-{\displaystyle \frac{t}{{\tau }_L}}}$$

(2)

The equivalent circuit of the VFTO wave as it passes through the damping bus is shown in Figure 4.

In Figure 4, u₁ represents the input VFTO wave, u₂ represents the voltage at node A, and i_L and i₂ represent the incident currents flowing through L and Z₂, respectively. R and L represent the damping resistance and inductance, respectively, of the damping bus. Z₁ represents the wave impedance of the line between the isolation switch and the damping bus. Z₂ represents the wave impedance of the line after the damping bus. Z₁ and Z₂ are formed by equating the distributed parameters of wave propagation to the centralized parameters to form an impedance, and they are real numbers. According to the previous analysis of the wave through the inductance, it can be seen that the equivalent impedance Z outside the inductance L can be expressed as:

$$Z=(z_1+z_2)//R={\displaystyle \frac{R(z_1+z_2)}{R+z_1+z_2}}$$

(3)

$$\tau ={\displaystyle \frac{L}{Z}}={\displaystyle \frac{L(R+z_1+z_2)}{R(z_1+z_2)}}$$

(4)

We then solve for the current flowing through the inductor, as follows:

$$i_L(t)={\displaystyle \frac{2u_1^{\prime }}{z_1+z_2}}(1-e^{-{\displaystyle \frac{t}{\tau }}})$$

(5)

After the VFTO wave passes through the damping bus, the current and voltage across the impedance Z₂ are expressed as:

$$\begin{array}{l}{i}_2^{\prime }(t)=i_L+{\displaystyle \frac{L}{R}}{\displaystyle \frac{d{i}_L}{dt}}={\displaystyle \frac{2u_1^{\prime }}{z_1+z_2}}(1-{\displaystyle \frac{R}{R+z_1+z_2}}{e}^{-{\displaystyle \frac{t}{\tau }}})\\ ={\displaystyle \frac{2z_1}{z_1+z_2}}{i}_1^{\prime }(1-{\displaystyle \frac{R}{R+z_1+z_2}}{e}^{-{\displaystyle \frac{t}{\tau }}})\end{array}$$

(6)

$$u_2^{\prime }(t)=i_2^{\prime }{z}_2={\displaystyle \frac{2u_1^{\prime }{Z}_2}{Z_1+Z_2}}(1-{\displaystyle \frac{R}{R+z_1+z_2}}{e}^{-{\displaystyle \frac{t}{\tau }}})$$

(7)

The steepness of the voltage wave is expressed as:

$$a={\displaystyle \frac{d{u}_2^{\prime }}{dt}}={\displaystyle \frac{2u_1^{\prime }{R}^2{z}_2}{L{(R+z_1+z_2)}^2}}{e}^{-{\displaystyle \frac{t}{\tau }}}$$

(8)

The maximum steepness of the VFTO across the inductor is:

$$a_{\max }={\displaystyle \frac{d{u}_2^{\prime }}{dt}}{|}_{t=0}={\displaystyle \frac{2u_1^{\prime }{R}^2{z}_2}{L{(R+z_1+z_2)}^2}}(kv/us)$$

(9)

The wave impedance of a coaxial GIS bus is calculated by the following equation:

$$Z={\displaystyle \frac{\sqrt{\mu /\epsilon }}{2\pi }}\ln ({\displaystyle \frac{r_2}{r_1}})$$

(10)

In Equation (10), $r_1$ and $r_2$ represent the inner and outer radii, respectively, of the GIS bus conductor. As the voltage levels are the same, the voltage on impedance Z₂ after passing through the damped bus is:

$$u_2^{\prime }(t)=i_2^{\prime }{z}_2=(1-{\displaystyle \frac{R}{R+z_1+z_2}}{e}^{-{\displaystyle \frac{t}{\tau }}})u_1^{\prime }$$

(11)

The SF₆ is used as an insulating medium for GIS, and its magnetic permeability is approximately equal to the vacuum magnetic permeability, as μ ≈ μ₀ = 4π × 10⁻⁷ H/m. Taking the 550 kV GIS bus wave impedance of 120 Ω as an example, the voltage and steepness behind the bus after the addition of the damping bus can be expressed as:

$$a={\displaystyle \frac{2u_1^{\prime }{R}^2{z}_2}{L{(R+z_1+z_2)}^2}}{e}^{-{\displaystyle \frac{t}{\tau }}}={\displaystyle \frac{240R^2}{L{(R+240)}^2}}{u}_1^{\prime }{e}^{-t/\tau }$$

(12)

$$\tau ={\displaystyle \frac{L}{Z}}={\displaystyle \frac{L(R+240)}{240R}}={\displaystyle \frac{L}{240}}+{\displaystyle \frac{L}{R}}$$

(13)

It can be seen from Figure 4 that both the magnitude and steepness of VFTO decrease with an increase in inductance, and the effect of resistance on the magnitude and steepness of VFTO exhibits a non-monotonic influence property. This means that an interval of values exists within which VFTO amplitude and steepness suppression may be optimized. A resistance interval of (0–300) Ω is used for the calculations in this paper. The calculations showed that the VFTO is optimally suppressed at a resistance value of (100–120) Ω.

Next, analysis of the effect of damping bus resistance and inductance on VFTO amplitude suppression and steepness suppression is carried out using the separated variable method. Substituting different inductors and resistors into Equations (11) and (12) to analyze the variation of node voltage and wavefront steepness, the trend is obtained, as shown in Figure 5.

2.3. Equivalent Circuit Parameter Analysis

Next, the damping busbar is installed in the GIS. Considering the existence of stray inductance and capacitance between the GIS shell and the damping busbar, and between the damping busbar and the tub insulator, the equivalent circuit of the damping busbar is established as shown in Figure 6.

In Figure 6, L_e represents the equivalent inductance per turn of the coil. R_e represents the parallel resistance per turn of the coil. Each turn of the damping busbar coil is uniformly machined so that the turn inductances are all equal, that is, L_e0 = L_e1 = … = L_em. C_σm and L_σm represent the turn-to-turn stray capacitance and stray inductance, respectively. Because the inductance at the two ends of the damping busbar connecting the pot insulator portion is not equal in magnitude to the uniform spiral tubular turn-to-turn inductance in the center, it is denoted by L_e0 and L_em. C_σe0 and C_σem represent the stray inductance between the ends of the damping bus and the housing. R_g represents the gap breakdown impedance. The gap breakdown impedance is shown as a dashed line in Figure 5, as the gap breakdown of the damped bus under VFTO conditions is uncertain.

Capacitance is defined as $C=Q/(V_1-V_2)$, for n conductors, by the potential superposition theorem:

$$\left(\begin{array}{c}{Q}_1\\ Q_2\\ \dots \\ Q_n\end{array}\right)=C\left(\begin{array}{c}{V}_1\\ V_2\\ \dots \\ V_n\end{array}\right)=\left[\begin{array}{cccc}{C}_{11}& C_{12}& \dots & C_{n1}\\ C_{12}& C_{22}& \dots & C_{n2}\\ \dots & \dots & \dots & \dots \\ C_{1n}& C_{2n}& \dots & C_{nn}\end{array}\right]\left(\begin{array}{c}{V}_1\\ V_2\\ \dots \\ V_n\end{array}\right)$$

(14)

In Equation (14), Q_i denotes the charge of the i-th conductor, and C is the Maxwell capacitance matrix, which describes the relationship between the charge of the i-th conductor and the voltages of all the conductors in the system. For n conductors, the Maxwell capacitance matrix can be expressed as:

$$C=\left[\begin{array}{cccc}{\displaystyle {\sum }_{i=1}^n{C}_{m1i}}& -C_{m12}& \dots & -C_{m1n}\\ -C_{m21}& {\displaystyle {\sum }_{i=1}^n{C}_{m2i}}& \dots & -C_{m2n}\\ \dots & \dots & \dots & \dots \\ -C_{mn1}& -C_{mn2}& \dots & {\displaystyle {\sum }_{i=1}^n{C}_{mni}}\end{array}\right]$$

(15)

In Equation (15), C_mni is the stray capacitance resulting from the charge accumulation of the n-conductor and the i-conductor. The Maxwell’s capacitance matrix is used to solve for the relationship between the stray capacitances of the damping buses.

Neglecting the non-uniformity of the current distribution in the cross-section of the conductor under low-frequency conditions, the value of inductance at this time can be expressed as:

$$L={\displaystyle \frac{1}{i}}{\displaystyle \int \frac{1}{s}({\displaystyle \int Bds})ds}$$

(16)

Under very high frequency conditions, the current is almost entirely concentrated in the surface layer of the conductor, when the skinning depth can be expressed as:

$${\delta }_{sd}=\sqrt{{\displaystyle \frac{1}{\pi f\mu \sigma }}}$$

(17)

In Equation (17), ${\delta }_{sd}$ indicates the skinning depth in m. f is the excitation frequency in Hz. μ is the magnetic permeability in H/m. σ is the electrical conductivity in S/m. Because of the skinning effect, Equation (17) cannot be calculated directly; however, the effective cross section of the current can be calculated by approximation of the skinning depth, which is then brought into Equation (18):

$$L={\displaystyle \frac{2\pi (a+1)}{i^2}}{\displaystyle \int ({\displaystyle \int B\frac{1}{\sqrt{\pi f\mu \sigma }}}dr)di}$$

(18)

From the above equation, it can be seen that the inductance L of the damping bus under high frequency conditions is not only related to the conductor structure but is also affected by the excitation characteristics, and inductance decreases with the increase in current frequency.

Due to the extremely short time of VFTO action, the gap SF₆ breakdown process can be viewed as an arc discharge process. An exponential model is used to describe the change in resistance when the damped bus gap is undergoing breakdown, as in the following equation:

$$R_v=R_0{e}^{-\left({\displaystyle \raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{${\tau }_g$}\right.}\right)}+R_a, t\ge t_0$$

(19)

In Equation (19), R_a = 0.5 Ω for static arc resistance, and R₀ = 10¹² Ω for isolation switch gap insulation when in a high resistance state. τ_g denotes the breakdown time of the gap. The SF₆ breakdown time is very short, usually at the ns level, so τ_g is also very small. During SF₆ gas breakdown, gas gap resistance can take the value of 0.5 Ω. In this paper, a 550 kV voltage level is used as an example to calculate the internal damping busbar parameters of GIS. Assuming that the damping bus processing involves 25 turns, the specific calculation parameters are shown in

Table 2. Parameters of the damping busbar for 550 kV GIS.

Parameter	Lσ0	Le0 (μH)	Lσ1 = ……Lσ24	Cσ0	Cσe0	Cσ1 = ……Cσ24	Re	Rg
Amplitude	18.46	40.28	0.432	0.18	0.187	5.2	4	0.5

Note: Inductance units not listed in the table are μH, the unit of capacitance nF, and the unit of resistance Ω. R_g is the resistance of the gap after breakdown. According to the calculation results, the 1st, 5th, 19th, 23rd and 25th gaps have undergone breakdown.

.

3. Structural Optimization Design of Damping Busbar

In this paper, an aluminum busbar for GIS at a 550 kV voltage level is used as an object to analyze the effect of variations in turn spacing and numbers of turns on the inductance value of a damped busbar at a certain length (1451 mm).

3.1. Analysis of the Effect of Turn Spacing on Inductance

A spiral cutting surface is made symmetrically from the geometric center of the damping busbar to both sides to form one turn spiral, constituting a single-turn damping busbar as shown in Figure 7.

Keeping the shape of the spiral skeletonized cross-section constant, the turn spacing is continuously increased, as shown in Figure 8. Finite element modeling for various different turn spacings is included, as follows:

• Small increase in turn spacing between 0 and 200 mm.
• Wide range of turn spacing between 200 and 800 mm.

Next, keeping all other conditions constant, finite element inductance calculations are carried out.

(1)

Inductance variation within 0~200 mm turns spacing

The model of the unprocessed bus is defined when the turn spacing is 0 mm. A single-turn damped bus model is then constructed with a small range of turn spacings by increasing the turn spacing by 10 mm each time from 0 to 200 mm. The inductance distribution curves of each model at industrial frequency and high frequency are shown in Figure 9.

It can be seen from Figure 9 that a small increase in the single-turn spacing has no effect on the inductance values of the damping busbar at IF or HF in the range of 0 to 200 mm. The inductance value floats around 0.833 μH at industrial frequency and 0.79 μH at high frequency. The inductance increases, but not significantly, when conventional busbars are machined into single-turn damped busbars.

(2)

Inductance Variation within 0~800 mm Turn Pitch

Damping busbars can be machined in the middle section of a busbar with a length of 1451 mm, increasing the range of single-turn helical machining by 100 mm per turn in the range of 0 to 800 mm. The same finite element method inductance calculations as above were performed for the damping bus for a large turn spacing range, and the results are shown in Figure 10. After increasing the turn spacing variation, the inductance of the damping bus remains almost unchanged for both the IF and HF inductances.

Comparison of the curves in Figure 10 reveals that the effect of single-turn processing on inductance is small for both turn spacing variations. The single-turn construction of the busbar does not change the path of the transmitted current on the busbar, and the inductive effect is not significant. Although single-turn spacing variations have a small effect on busbar inductance, the number of turns and the amount of turn spacing are inversely proportional over a fixed machinable length. Damping busbars can be processed with reduced turn spacing to obtain more turns, thus increasing the inductive effect of the busbars.

3.2. Analysis of the Effect of the Number of Turns on Inductance

Next, the damping busbar turn spacing is set to 50 mm and the number of turns is increased from 1 to 25. The same excitation imposition, meshing, and solution setup as above is used. The busbar material is aluminum (conductivity 3.8 × 10⁷ S/m), and the change of inductance of the busbar under industrial frequency and high frequency conditions is shown in

Table 3. Inductance of busbar at 50 mm turn spacing.

Piral Processed Turns	Inductance (μH) 50 Hz	Inductance (μH) 50 Hz	Spiral Processed Turns	Inductance (μH) 50 Hz	Inductance (μH) 50 Hz
1	0.83906	0.79384	15	9.1246	6.5351
3	1.2405	0.91169	17	10.567	7.4277
5	2.1894	1.2157	19	11.912	8.6756
7	3.4927	2.0156	21	13.445	10.069
9	4.785	2.7401	23	15.234	11.583
11	6.2028	3.6758	25	16.347	12.888
13	7.3524	4.9515

.

According to the data in Table 3, it can be seen that with same amount of turn spacing and number of turns, the value of inductance under industrial-frequency excitation is greater than that under high-frequency excitation, and with an increase in busbar turns, the inductance of the busbar increases under both industrial frequency and high frequency conditions. In addition, regardless of whether there is industrial- or high-frequency excitation, the damping bus inductance shows a linear increase with the number of turns, and the inductance of the traditional spiral coil increases linearly with the number of turns of the coil, similar to the law. On this occasion, the damping bus can be seen as a large-size, high-current capacity of the coil.

4. Analysis of Damping Busbar Effect on VFTO Suppression

The appearance of the damping busbar for 550 kV GIS obtained by actual processing is shown in Figure 11.

The electrical principle of the 550 kV verification test circuit is shown in Figure 12. In Figure 12, each piece of equipment is connected or enclosed in a GIS pipe, and AC stands for alternating-current power supply, which provides power for the whole test circuit and is used to simulate the generation of high-frequency over-voltage. BG1 and BG2 stand for GIS bushings, and DS1, DS2 and DS3 stand for disconnecting switches. The GIS pipe is used to simulate the branching of busbars, and the length of the pipe can be adjusted and dismantled. In addition, the test circuit includes grounding switches, busbars and other components. The length of the tubing between DS1 and DS2 is 9 m, and the length of the tubing between DS2 and BG1 is 14 m. Photographs of the validation test platform are shown in Figure 13.

The VFTO measurement system is mainly composed of three parts: a VFTO measurement sensor; a synchronized trigger device; and a waveform acquisition device with remote measurement and control computer (waveform recording.) The VFTO measurement adopts a window-type sensor based on the principle of capacitive voltage division, with measurement bandwidth ranging from 10 Hz to 204 MHz and a sampling accuracy of 0.05%, which meets the needs of VFTO measurement. The measurement system uses a synchronized trigger device to ensure the stability and synchronization of the measurement system. The synchronous trigger is 1 pps. The high-frequency radiation signal during the VFTO generation process controls the synchronous trigger device to generate a trigger signal, which is transmitted through optical fiber, converted optically and electrically, and recorded at each measurement point of the stable synchronous trigger oscilloscope. Waveform recording includes on-site recording and remote computer reading. The on-site acquisition device is placed in a shielded box, powered by an independent power supply, with strong anti-interference capability. A DLM2054 oscilloscope was used to record the field waveforms. The sampling frequency of the oscilloscope was set to 125 MHz, the length of the recorded waveforms was 1 s, and the accuracy of this oscilloscope was 0.05%. The computer controls the oscilloscope through a fiber optic transmission channel and remotely reads the waveforms stored in the oscilloscope, thus improving the efficiency and safety of testing.

The test first measured the VFTO appearing on the conventional GIS. Testing was then carried out again under the same working condition at the same observation point after adding the damping bus, to observe the damping bus’s suppression effect on the VFTO, and read the recorded VFTO waveforms with Xviewer software V1.0. Due to the large number of measured data, only the measured data of the isolating switch tripping operation are selected here to analyze the damping busbar’s suppression effect on VFTO. Figure 14 shows the VFTO full waveforms before and after the addition of the damping bus.

Figure 15 shows a comparison of breakdown times before and after the installation of the damping bus. Comparison of Figure 14 and Figure 15 shows that the amplitude and breakdown times of the VFTO are obviously suppressed after the installation of the damping bus. The specific data are shown in

Table 4. Statistical table of suppression effect before and after adding damping busbar.

Installation Status	Amplitude	Number of Breakdowns
Before installation	1.57 p.u.	18
After installation	1.19 p.u.	6

.

The single breakdown pulse waveforms before and after the addition of the damping bus are shown in Figure 16. Comparing Figure 16a,b, it can be seen that the amplitude of the single breakdown pulse waveform is significantly suppressed after the addition of the damping bus.

Figure 16c shows the spectral comparison of the single breakdown VFTO before and after the addition of the damping busbar. From the figure, it can be seen that the frequency of the VFTO is significantly reduced after the installation of the damping busbar. The data are shown in

Table 5. Statistical results of the main frequency of the waveform before and after installing the damping busbar.

Main Frequency (MHz)
Before Adding Damping Busbar	After Adding Damping Busbar
0–7.5, 46.5	0–5

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From the data in Table 5, it can be seen that the number of breakdowns and the amplitude of oscillations are reduced before and after the addition of the damping busbar, and the attenuation of the single and overall transient processes is accelerated. The high-frequency components of the VFTO are mainly 7.5 MHz, 14.5 MHz and 46.5 MHz before the addition of the damping busbar, while there is no significant high frequency after the installation of the damping busbar. It can be seen that the damping buses flatten the high-frequency component heads and tails of the VFTO wave as it passes through by enhancing the inductive effect, and the amplitude is reduced.

Plots of the test statistics for the suppression effect of VFTO under the condition of multiple tripping operations are shown in Figure 17. The effect of the number of test tripping operations on the VFTO suppression effect is random, and the suppression effect does not become more significant with the increase in the number of operations. According to the data in Figure 17, the amplitude of VFTO after the damping busbar is installed is significantly lower than that in the uninstalled state. The average amplitude of VFTO before installation is 1.67 p.u., and the average amplitude of VFTO after installation decreases to 1.33 p.u. After analyzing the ANOVA using independent samples t-test, the p-value is less than 0.001 and the difference in means is very significant; excluding the effect of randomness of VFTO amplitude on the statistical results, the damping busbar causes a 20.36% reduction in the average amplitude of the VFTO. The results are shown in

Table 6. Statistical results of VFTO amplitude suppression before and after adding damping busbar.

Installed State	Average Amplitude of VFTO (p.u.)	Standard Deviation	F-Value for t-Test	Degree of Reduction in the Average Value of the Amplitude (%)
Before installation	1.67	0.135	4.207 **	20.36%
After installation	1.33	0.067

Note: ** represents p < 0.01.

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5. Conclusions

In this paper, a new type of busbar is designed for VFTO suppression, which is called a “damped busbar”. A damped busbar is a traditional busbar hollowed out into a spiral-tube hollow coil to increase inductance, in which the hollow wire inside each turn of the coil is matched with the corresponding resistance, composed of “inductance + resistance” structure. In this work, we established a damped bus circuit model, carried out an analysis of the structural constraints of the damped bus, and finally conducted a test on the damped bus suppression effect. The following conclusions were obtained:

• As ordinary busbar using 550 kV GIS platform was processed into a spiral damping busbar. After processing, its stray inductance was about 0.4 μH and its stray capacitance was about 0.18 nF.
• The structural parameter that plays a decisive role in the inductance of the damping busbar is the number of turns. Whether under industrial-frequency or high-frequency excitation, when the length of the damping bus is certain, the higher the number of turns, the greater the bus inductance. The value of inductance under industrial-frequency excitation is greater than that under high-frequency excitation. Damping bus inductance increases approximately linearly with the number of turns, similar to the linear increase in inductance with the number of turns of a conventional helical coil.
• The VFTO suppression effect of the damping busbar was systematically verified using a combination of simulation calculation and experimental verification. The test data showed that the average amplitude of VFTO decreased by 20.36% after addition of the damping busbar, the number of breakdowns decreased by about 66.7%, and there was no obvious high frequency after the installation of the damping busbar. These data show that the damping busbar has a good suppression effect on the amplitude and frequency of VFTO, and reduces the number of breakdowns.

The damped bus technique proposed in this paper can be used for other voltage systems (e.g., 220 kV or 1000 kV), but the following key parameters need to be adjusted. First, the inductance and resistance values of the damping bus need to be recalculated based on the wave impedance of the new system to ensure that they meet the amplitude and steepness suppression requirements expressed in Equations (5)–(8). Second, the number of turns and the spiral structure dimensions of the damping bus need to be optimized to accommodate the spurious parameters at different voltage levels. This is because the spurious parameters generated between the damping bus and the GIS enclosure are different within the system at different voltage levels, and the spurious parameters will affect the suppression effect of the damping bus on VFTO. In addition, it is necessary to consider adjusting the design of the mechanical strength support member to cope with the size and force changes of busbars of different voltage levels. In conclusion, the versatility of the damping busbar relies on its parametric customized design, which is based on matching the electrical characteristics and structural requirements of the target system.