Dispersion characteristics of switching transients from large‐scale experiments in a 1100 kV gas insulated switchgear circuit

Abstract

The switching operation of gas insulated switchgear (GIS) disconnector will produce multiple random spark discharges between the gas gaps of the disconnector. Each spark discharge can be affected by various random factors, such as trapped charge on the load side, the initial operating phase, gap distance and operating speed of the disconnector, leading to dispersion characteristics. At present, some studies have mentioned this dispersion, but its impact is still unclear due to the lack of experimental data, resulting in a deviation between the simulation results and the measured results. In this study, thousands of switching operations were carried out based on the 1100 kV full‐scale GIS circuit in Wuhan ultra‐high voltage alternating current Test Base. The maximal information coefficient analysis, linear regression fitting and other statistical methods were used to discuss the dispersion characteristics of very fast transient overvoltage (VFTO) and transient enclosure voltage (TEV) from large‐scale experimental data. The results show that the dispersion of VFTO and TEV in amplitude aspects both increase gradually as the breakdown voltage increases, with the maximum difference of five times of TEV amplitude at normalised breakdown voltage. In terms of frequency characteristics, the dispersion of different frequency components in TEV is always greater than that of VFTO, especially for the high‐frequency components. Moreover, by comparing the frequency characteristics of TEV at different positions, we notice that the dispersion is almost independent of the spatial position but only determined by the randomness of spark discharges. These discoveries reveal the importance of the dispersion in switching transients and make up for the lack of theoretical understanding of the correlation among them.

INTRODUCTION

Various electromagnetic transient phenomena, such as very fast transient overvoltage (VFTO) and transient enclosure voltage (TEV), are caused by switching operations of gas insulated switchgear (GIS) disconnector [1]. Very fast transient overvoltage is generated within GIS pipelines, which has the characteristics of high amplitude and large wavefront gradient, exerting pressure on the insulation of primary equipment [2, 3]. TEV is generated by transient waves propagating between the GIS enclosure and the earth, and it can easily interfere the secondary equipment, causing serious electromagnetic disturbance [4–8]. Hence, VFTO and TEV have always been the focus in the research of electromagnetic compatibility in ultra-high voltage (UHV) or extra-high voltage (EHV) GIS substations [9–12].

During one switching operation, multiple spark discharges will occur between the contact gaps of disconnector, and each discharge corresponds to a group of VFTO and TEV [13–16]. Therefore, the waveform characteristics of them should be closely related to the arc discharge process of spark discharge in theory [17]. S. Sugiyama et al. [18] and B. Lu et al. [19] both find from simulation results that the discharge gap length, gas pressure, electrode material and the initial electric field around the contacts of disconnector can affect the amplitude, wavefront rising rate and rising trend of the arc voltage. Z. Li et al. [20] carried out some discharge researches in a 252 kV GIS circuit and found that the wavefront rise time of VFTO are affected by the peak value of arc current, the trapped charge on the load side and gap distance. To sum up, the arc discharge can be affected by various random factors, such as trapped charge on the load side, the initial operating phase, gap distance, operating speed of disconnector, gas pressure, gas temperature, gas humidity, etc., which will inevitably affect the formation of VFTO and TEV.

Usually, the breakdown voltage, obtained from the VFTO waveform, is a key physical quantity in the transient study of switching operation, and it is used to characterise the dielectric strength of SF₆ gas in the gap of disconnector, which means that it represents the characteristics of spark discharge to a certain extent [3, 21, 22]. The relationship between breakdown voltage and the amplitude of switching transients have been mentioned in the electromagnetic transient research. Zhao et al. [23] found that the amplitude of TEV is not completely linearly with the breakdown voltage through several experiments, which indicates that there may exist a dispersion characteristic between them. Cai et al. [24] carried out several experiments during switching operations and found that the fluctuation range of TEV amplitude increases with the increase of breakdown voltage based on 320 groups of experimental data, which means there exactly exist the dispersion characteristics. However, due to the lack of experimental data, no systematic and accurate conclusions have been obtained.

Moreover, unclear understanding of dispersion characteristics will also affect the simulation of VFTO and TEV, resulting in inaccurate simulation results. One of the reasons behind this is that the step voltage or steep voltage with rise time of several nanoseconds are usually used as the input excitation in the simulation of VFTO and TEV, which will inevitably simplify the dynamic change process of arc voltage. The other reason is that mathematical models describing specific arc resistance $$r$$, such as $$r={R}_{\mathrm{constant}}\,(2\sim 5\,{\Omega })$$ or $$r(t)={R}_{0}{\mathrm{e}}^{-t/\tau }+{R}_{1}\,\left({R}_{0}={10}^{12}\,{\Omega },{R}_{1}=0.5\,{\Omega },\tau =1\,\mathrm{ns}\right)$$, cannot reflect the dispersion characteristics of spark discharge process, which make it impossible to account for the dispersion influence in VFTO and TEV simulations.

In this paper, we carried out large-scale experiments through switching operation on the full-scale 1100 kV GIS circuit to establish the statistical data of switching transients and clarify the characteristic of dispersion in VFTO and TEV. It should be noted that we have always kept the electrical structure of GIS circuit, the operating mode of disconnectors, the arrangement of the measurement system and other factors that may introduce random interference unchanged in the experiments. All statistical results were based on the breakdown voltage to discuss the dispersion characteristics of VFTO and TEV both in time-domain and frequency-domain from large-scale experimental data. Through maximal information coefficient (MIC) analysis, linear regression and other statistical methods, the characteristics of dispersion in VFTO and TEV are analysed, which is expected to make up for the lack of understanding of switch transient correlation.

This paper is organised as follows: Section 1 introduce the research status and existing problems of the dispersion characteristics in switching transients. In Section 2, the full-scale 1100 kV GIS test circuit and measurement equipment are developed. The arrangement of VFTO and TEV measurement system are also presented. In Section 3, we discuss the correlation between VFTO and TEV in terms of amplitude characteristics and frequency characteristics, as well as the regularity of their dispersion characteristics. Moreover, the spatial distributions of the dispersion characteristics of TEV amplitude and frequency are also explained. Finally, Section 4 offers final conclusions.

DEVELOPMENT OF GAS INSULATED SWITCHGEAR TEST CIRCUIT AND MEASUREMENT SYSTEM

Structure of the 1100 kV gas insulated switchgear circuit

In this research, we developed a full-scale 1100 kV GIS circuit, which can reflect the real physical processes of repeated spark discharges and can also be used to study various switching electromagnetic transients including VFTO and TEV.

This experimental circuit is improved based on the typical circuit for assessment of switching disconnector proposed in IEC 60129 standard [25]. It is composed of two disconnectors (DS1 and DS2), two bushings, a current transformer (CT), a potential transformer (PT) and several GIS pipelines, as shown in Figure 1. Among them, the DS1 is the main disconnector used to generate VFTO, and the DS2 is an auxiliary disconnector, which is used to pre-charge the no-load busbar between these two disconnectors. The bushing on alternating current (AC) side is used to introduce a power frequency supply with effective value of 635 kV for GIS circuit, and the bushing on DC side is used to pre charge the pipelines in load side of GIS circuit with DC voltage, which can be regarded as the initial trapped charge. Since the experiment of DC pre-charge is not involved in this study, the DS2 is always disconnected, and only the DS1 has been operated to connect and disconnect the no-load short bus between DS1 and DS2 generating switching transients.

[IMAGE OMITTED. SEE PDF]

Moreover, a branch bus structure is added between DS1 and the bushing on AC side to make the circuit more relevant to the actual engineering characteristics. To compare with the previous work of our research group [26], the influence of CT and PT equivalent models are considered on the design of the length of branch bus. According to the principle of port impedance equivalence, the formula between the equivalent lumped capacitance parameter of PT and the parameter of GIS pipeline is as follows: 1 $${-}\mathrm{j}{Z}_{0}/\tan \hspace*{.5em}\left(\frac{2{\uppi }{f}_{0}}{v}x\right)=-\mathrm{j}\frac{1}{2{\uppi }{f}_{0}C}$$ Where, $${Z}_{0}$$ is the GIS pipeline wave impedance; $${f}_{0}$$ is the resonant frequency with 6.8 MHz [3]; $$x$$ is the equivalent GIS pipeline length of PT; $$v$$ is the wave velocity; $$C$$ is the equivalent lumped capacitance of PT with 200 pF. Thus, the equivalent GIS pipeline length of PT is 4.8 m.

Furthermore, the CT is equivalent to a GIS pipeline with the length of 1.4 m. Therefore, the branch bus of this new GIS circuit should be reduced by 6.2 m in total, which means its length is about 2.8 m.

Measurement system

To accurately measure the switching electromagnetic transients inside and outside of the GIS pipelines, it is critical to develop suitable measurement systems. The overall structure of VFTO and TEV measurement systems are shown in Figure 2, which mainly include five parts: synchronous trigger device, electrical-optical signal converter, field acquisition oscilloscope, remote-control computer and various sensors for measuring different physical quantities. During the switching operation, the synchronous trigger device senses the change of the external electromagnetic field by a high-precision photosensitive module and generates a trigger signal with an amplitude of 5 V to provide to the oscilloscope. It was used to uniformly control the simultaneous sampling operation of each physical quantity, which ensures a coincident time scale between measured waveforms. The oscilloscope was powered by a lithium battery through a DC-AC inverter, and it communicated with a computer through the fibre-optic communication system to realise remote control. These devices were all installed in the shielding box to avoid the influence of transient disturbance during switching operations. As for the VFTO measurement sensor, it is composed of a port-hole-type capacitive divider and an impedance converter. The TEV measurement sensor was based on the Tek P6015A high-voltage probe with a high cutoff frequency of 75 MHz and a maximum measurement voltage of 40 kV. These measurement systems were all calibrated in the laboratory and verified by the field measurement performance to ensure the reliability and accuracy of them.

[IMAGE OMITTED. SEE PDF]

According to the structure of 1100 kV GIS circuit, we arranged the VFTO measurement system at the position numbered one, which is directly below the bushing on the AC side as shown in Figure 3. The TEV measurement systems are arranged at five different positions numbered 1–5, respectively, in the GIS enclosure circuit, see in Figure 1. Generally, the same measurement systems and method were used at different positions to ensure the consistency of measurement results, and no less than 200 groups (one opening and closing operation is one group) data were recorded at each measuring point to ensure the measurement results to be statistically significant.

[IMAGE OMITTED. SEE PDF]

Typical waveforms of switching electromagnetic transients

Thousands of VFTO waveforms and TEV waveforms were recorded during large-scale experiments of switching operations. Taking an opening operation as an example, the typical macro-pulses waveform and micro-pulse waveform of VFTO and TEV generated during the disconnecting operation are shown in Figure 4.

[IMAGE OMITTED. SEE PDF]

[IMAGE OMITTED. SEE PDF]

The whole waveform of VFTO is composed of a 50 Hz power frequency sine wave and dozens of high-frequency oscillation waves superimposed on the sine wave. In Figure 4a, $${V}_{\mathrm{b}}$$ is the breakdown voltage, which can be expressed by the difference between power frequency voltage at two adjacent breakdown times, $${V}_{\mathrm{o}\mathrm{s}}$$ is the overshoot voltage amplitude of a single pulse, and $${V}_{\mathrm{a}\mathrm{m}}$$ is the reverse overshoot voltage amplitude. From Figure 4b, the whole waveform of TEV is composed of dozens or even hundreds of pulses oscillating around zero. The TEV waveform is approximately symmetrical about the $$y=0$$ axis, which is not consistent with the change direction of the 50 Hz power frequency sine in the VFTO waveform. The $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ is the amplitude in the same direction as $${V}_{\mathrm{o}\mathrm{s}}$$, and $${V}_{\mathrm{t}\mathrm{a}\mathrm{m}}$$ is the amplitude in the opposite direction of this pulse in the TEV waveform. In addition, the typical micro-pulse waveform of VFTO and TEV are all damped oscillating waves, as shown in Figure 4. Among them, the VFTO micro-pulse oscillates around the power-side voltage, while the TEV micro-pulses oscillate around the zero point.

The VFTO frequency spectrum contains abundant frequency components, which can mainly be classified into three categories, as shown in Figure 5a. The first category consists of frequencies from a few hundred kHz to a few MHz, such as 300 kHz, 700 kHz and 1.1 MHz, which are determined by the parameters of arc current and inner structures of the GIS circuit. The second category consists of frequencies in the range of a few MHz, such as 4.5 MHz, 5.5 MHz and 7.7 MHz, which also constitute a part of the main frequency points in TEV waveforms, as shown in Figure 5b. These frequency components are decided by the external structures and the grounding structures of the GIS circuit. The last one consists of frequencies ranging from a dozen MHz to tens of MHz, such as 18.7 MHz, 24.5 MHz and 28.9 MHz, which are usually not obvious in the VFTO frequency spectrum but very prominent in the TEV frequency spectrum, as shown in Figure 5b. It can be concluded that these frequency components are caused by the effect of the resonant frequency point of supporting frames and grounding structures.

RESULTS AND DISCUSSION

Statistical data

To reflect the correlation between VFTO and TEV, it is necessary to determine the statistical data from their waveforms. As mentioned in Section 2, the amplitude of micro-pulse fast-oscillating waves can reflect the intensity of VFTO and TEV, and there should be a certain correlation between them. Therefore, the $${V}_{\mathrm{b}}$$, $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ were all recorded in the experimental data statistics.

According to the amplitude variation characteristics of these physical quantities in one operation of the disconnector, a counting rule was also defined to facilitate statistics. It means each breakdown process is recorded sequentially according to the time sequence of the gap distance from large to small, and each statistical physical quantity is brought into the lower subscript $$n$$. For example, during the closing operation, it specified the count of the first pulse as $$n=1$$, the count of the second pulse as $$n=2$$ and so on. For the opening operation process, the count $$n$$ is just opposite to the natural sequence of breakdown processes. Generally, only the breakdown occurrence with $${V}_{\mathrm{b}}$$ greater than 0.3 per unit (p.u.) is defined as effective occurrence and recorded in statistics, which means the breakdown occurrence with $$n\le 10$$ was counted in this study.

In data statistics, the MIC analysis method was used to analyse the statistical data. The reason behind this choice is that MIC belongs to the largest non-parametric exploration method based on information, and it has the basic characteristics of universality, fairness and symmetry with higher robustness, wider applicability and more accuracy than Pearson and Spearman statistical methods [27, 28]. Therefore, this method is more suitable for acquiring the feature of statistical data.

Generally, $${V}_{\mathrm{b}}$$, $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ can be written as random vectors, such as $${X}_{1}$$, $${X}_{2}$$ and $${X}_{3}$$, so the MIC c_MI is calculated as the following formula [25]: 2 $${c}_{\mathrm{MI}}\left({X}_{i};{X}_{j}\right)=\underset{ab< B}{\max }\hspace*{.5em}\frac{I\left({X}_{i};{X}_{j}\right)}{\log (\min (a,b))}$$ 3 $$I\left({X}_{i};{X}_{j}\right)=\sum\limits _{X,Y}p\left({X}_{i};{X}_{j}\right)\log \frac{p\left({X}_{i};{X}_{j}\right)}{p\left({X}_{i}\right)p\left({X}_{j}\right)}$$ Where $$p\left({X}_{i};{X}_{j}\right)$$ is the joint probability between random vectors $${X}_{i}$$ and $${X}_{j}$$ ($$i,j\in [1,2,3]$$); $$B$$ is usually equal to the 0.6 power of the amount of data; variables $$a$$ and $$b$$ represent the number of grids divided along the direction of $${X}_{i}$$ variable and $${X}_{j}$$ variable, respectively [25].

As for the frequency aspect, since the main frequency components of each micro-pulse in VFTO and TEV waveforms include 4.5 MHz, 5.5 MHz, 7.7 MHz, 18.7 and 24.5 MHz, the basic characteristics and variation regularities of these frequency components are also analysed in our study.

Statistical results of amplitude characteristics

The statistical results of $${V}_{\mathrm{b}}$$, $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ are presented in Figure 6a and Figure 6b, where the breakdown voltage is represented by the p.u. value, while the other physical quantities are standardised according to the z-score principle.

[IMAGE OMITTED. SEE PDF]

From Figure 6, we observe a positive correlation both between $${V}_{\mathrm{b}}$$ and $${V}_{\mathrm{o}\mathrm{s}}$$ or $${V}_{\mathrm{b}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$. In order to obtain the specific correlation coefficient between these variables, the MIC analysis is used for statistical calculation. These results are shown in Table 1. It can be clearly found that the correlation coefficient between breakdown voltage and VFTO amplitude or TEV amplitude locates within the general correlation range, not in the strong correlation range as we assumed. Moreover, these two correlation coefficients are close, which means the impact of breakdown voltage on the oscillation amplitude of overshoot voltage in VFTO pulse and the amplitude of micro-oscillation in TEV pulse is almost the same. In addition, we notice a logarithmic normal distribution both in the statistical data of $${V}_{\mathrm{b}}$$, $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$. Indeed, these results conform to the spark discharge regularity between contact gaps during the operation of the disconnector. When the contact gap is short, the breakdown voltage is small, but the number of breakdown times will increase significantly. This characteristic can also be clearly found from the whole waveform of VFTO and TEV.

TABLE 1 The maximal information coefficient (MIC) results between $${V}_{\mathrm{b}}$$, $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$.

Reference variable	Amplitude of VFTO pulse ($${V}_{\mathrm{o}\mathrm{s}}$$)	Amplitude of TEV pulse ($${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$)
Breakdown voltage ($${V}_{\mathrm{b}}$$)	0.663261	0.652368

In this scatter diagram, linear regression equation is considered to further describe the relationship between horizontal and vertical coordinate variables. We have noticed that the coefficient of determination of these two linear fitting lines is all around 0.8, which shows excellent fitting results. Nevertheless, this result seems to contradict the value of MIC, and scatter diagrams also intuitively reflect a large dispersion between statistical data. Hence, it should be noted that the linear regression equation based on the basic assumption of linear correlation can describe the change trend between two variables but cannot reflect the impact of abnormal values between them. It is worth noting that most scatter points can be evenly distributed on both sides of the regression line, so we use the regression line as the reference benchmark for the dispersion trend of scatter points.

Interestingly, the distribution regularity between $${V}_{\mathrm{b}}$$ and $${V}_{\mathrm{o}\mathrm{s}}$$ or $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ is approximately the same, showing a trumpet-shaped distribution characteristic, see in Figure 6. When the breakdown voltage is small, the distribution of scatter points is more concentrated, whereas it gradually becomes scattered as the breakdown voltage gradually increases. In this research, we divide the breakdown voltage with 0.2 p.u. as an interval. The reason behind this choice is to ensure sufficient statistical data in each interval. In order to describe the measures of dispersion of these scatter points, we calculated the standard deviation of $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ in each interval. The results are shown in Table 2 from which it can be observed that the larger the breakdown voltage, the greater the measures of dispersion in $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$.

TABLE 2 The standard deviation of $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ in each interval.

Interval (p.u.)	Standard deviation of $${V}_{\mathrm{o}\mathrm{s}}$$	Standard deviation of $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$
0.3–0.5	0.2297	0.2801
0.5–0.7	0.3958	0.4201
0.7–0.9	0.5260	0.5193
0.9–1.1	0.5325	0.5567
1.1–1.3	0.6356	0.5470
1.3–1.5	0.8209	0.7225
1.5–1.7	1.1152	0.8114
1.7–1.9	1.2836	0.7142

Furthermore, we also observe a tendency that both $${V}_{\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ tend to move in the direction lower than the regression line, while $${V}_{\mathrm{b}}$$ is within the range of 0.3 p.u. to 1.0 p.u. Hence, both $${V}_{\text{os}}$$ and $${V}_{\text{tos}}$$ increase the probability of lower values under the same breakdown voltage. When the breakdown voltage is low, the spark discharge frequency between the contact gaps of disconnectors is high, which enhances the interaction between each spark discharge. Therefore, we believe that it is not accurate to estimate transient pulse amplitude by breakdown voltage under the influence of a repeated breakdown process. It may result in an estimation error of five times at most.

Statistical results of frequency characteristics

The frequency spectrum statistical results of those five main frequencies in the VFTO waveform and TEV waveform are shown in Figure 7a and Figure 7b, respectively. The abscissa values represent 4.5 MHz, 5.5 MHz, 7.7 MHz, 18.7 and 24.5 MHz components from left to right, and the ordinate values represent the amplitude of these component. All statistics are normalised based on its corresponding breakdown voltage $${V}_{\mathrm{b}}$$, which makes it possible to compare the change regularity of them.

[IMAGE OMITTED. SEE PDF]

Indeed, the lower frequencies in the VFTO waveform are the main components, whereas the higher frequencies are the main components in the TEV waveform. The box sizes of different frequency components show large differences in amplitude dispersion. As for the VFTO frequency spectrum, the amplitude dispersion of the 7.7 MHz frequency component, which is the main resonant frequency of the GIS internal circuit, is the largest. It decreases in the order of 4.5 MHz, 5.5 MHz, 18.7 MHz and 24.5 MHz, which means the dispersion and frequency change according to a negative correlation law. However, we notice an increasing trend of the box size with the increase of the main frequency components in the TEV frequency spectrum, as well as the maximum amplitude. This indicates a positive correlation between dispersion and frequency in the GIS external circuit composed of the GIS enclosure and the earth.

Moreover, we find a lognormal distribution in the amplitude of different frequency components in both the VFTO frequency spectrum and TEV frequency spectrum, in the sense that the number of points with smaller amplitude is far greater than the number of points with larger amplitude. This conclusion is unexpected because we normalised the spectrum based on breakdown voltage $${V}_{\mathrm{b}}$$, and it can be considered that the amplitudes of all frequency components are obtained at the unit breakdown voltage. Therefore, the amplitude of different frequencies should not conform to a lognormal distribution law in theory. We infer that this result is related to the normalisation based on breakdown voltage.

Furthermore, the lognormal distribution of frequency component amplitude in the TEV spectrum is more obvious than that in the VFTO spectrum. As shown in Table 3 and Table 4, the standard deviation (SD) and coefficient of variation (CV) of different frequency components in the VFTO frequency spectrum and TEV frequency spectrum are calculated. It can be found that the SD value and CV value have roughly the same change trend. The CV values of 4.5 MHz, 5.5 and 7.7 MHz frequency components are all greater than those of 18.7 and 24.5 MHz frequency components in the VFTO frequency spectrum, which means the lower frequency components usually have greater dispersion. In the statistical results of the TEV frequency spectrum, both the SD value and CV value satisfy the positive correlation with the increasing of frequency, indicating that the dispersion of frequency components also conform to this change regularity. Comparing the CV value of the same frequency component in both the VFTO frequency spectrum and TEV frequency spectrum, it can be noticed that the CV value in TEV frequency spectrum is much greater than that in VFTO frequency spectrum. These results show that in the propagation of the transient wave from the inside to the outside of the GIS circuit, the dispersion of the main frequency components gradually increases, especially for the higher frequency components.

TABLE 3 The SD value of different frequency components in the very fast transient overvoltage (VFTO) frequency spectrum and transient enclosure voltage (TEV) frequency spectrum.

Frequency (MHz)	SD value of VFTO frequency spectrum (p.u.)	SD value of TEV frequency spectrum (V)
4.5	0.0025	11.3614
5.5	0.0017	17.3687
7.7	0.0040	42.2987
18.7	0.0009	44.7335
24.5	0.0006	57.4629

TABLE 4 The CV value of different frequency components in the very fast transient overvoltage (VFTO) frequency spectrum and TEV frequency spectrum.

Frequency (MHz)	CV value of VFTO frequency spectrum (%)	CV value of TEV frequency spectrum (%)
4.5	56.82	117.25
5.5	57.86	131.01
7.7	81.40	136.39
18.7	47.24	143.12
24.5	46.26	134.55

Statistical results of spatial distribution characteristics

Amplitude characteristics of different measuring point

The method, using linear regression to describe the dispersion direction of scatter points and the change trend of the relationship between variables, is still effective while analysing the amplitude characteristics of different measurement points. Hence, the regression lines for correlation between $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{b}}$$ at different measurement points are calculated as shown in Figure 8a–f. Intuitively, most scatter points of $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{b}}$$ are greatly consistent with the linear change regularity in their overall trend. Their determination coefficients are usually greater than 0.75, except the result in point 1. Figure 8a presents a series of scattered points above the fitting line, forming a relatively clear new straight line. We believe the reason behind this result is related to the potential rise caused by the counterattack of the transient current in the grounding wire at this position. Since point 1 is closest to the connection point between the GIS internal circuit and GIS enclosure circuit, most of the transient current leaked from the internal circuit flow into the grounding grid from this position, which is easy to form a strong ground potential rise. Furthermore, the voltage superimposed on the induced enclosure potential causes the amplitude of TEV to increase significantly. Moreover, we observe that $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ all tend to move in the direction lower than regression line in the range of breakdown voltage changing from 0.3 p.u. to 1.0 p.u. at different points. The results are consistent with the conclusion drawn in Section 3.1.

[IMAGE OMITTED. SEE PDF]

Nevertheless, the dispersion of $${V}_{\mathrm{t}\mathrm{o}\mathrm{s}}$$ and $${V}_{\mathrm{b}}$$ obtained at different measuring point are still obvious, and there are some differences between them. A method, using 95% prediction interval of regression line, shows the measures of dispersion for scatter points deviating from the regression line. For instance, the measurement results at point 2 reflect that these scattered points are concentrated near the regression line, as shown in Figure 8b. Contrariwise, these scattered points obtained at point 3 and point 5 are evenly distributed in the whole 95% prediction interval, see in Figure 8c and Figure 8e. The r eason behind this phenomenon is caused by the influence of the structure of GIS external circuit. As mentioned in Section 2, point 3 and point 5 are respectively located at T-shaped bifurcation and L-shaped structure, where the wave impedance changes greatly. Therefore, it is easy to cause obvious amplitude difference in the transient waveforms under multiple progresses of refraction and reflection.

Furthermore, a residual analysis was carried out to describe the dispersion relative to the regression line for scatter points measured at different points, see in Figure 9. Overall, the residual distribution of scatter points measured at different points presents a trumpet shape, which exactly means that the difference between the measured value and the linear fitting result increases with the rise of the breakdown voltage, so does the dispersion. The opening direction of the trumpet is generally lower at the right side, except for the measurement result of point 1. Hence, the number of scattered points below the fitting line is much greater than the number of scattered points above the fitting line. From Figure 9, we observe that the maximum deviation point usually occurs in the range where the residual error is less than zero, and the breakdown voltage is often greater than 1.0 p.u. The residual value at the maximum deviation point usually ranges from two times to five times of the boundary value of 95% fluctuation interval of the residual.

[IMAGE OMITTED. SEE PDF]

In addition, the boxplot of residuals distribution reflects an increasing trend of the measures of dispersion of residuals value with the increasing distance between the measuring point and bushing on the AC side. The SD results of residuals in Table 5 also illustrate this conclusion.

TABLE 5 The SD results of residuals for different measuring points.

Measuring point	Point 1	Point 2	Point 3	Point 4	Point 5
SD value (kV)	0.607966	0.758066	0.754715	0.756093	0.781771

Frequency characteristics of different measuring points

Figure 10 shows the frequency spectrum statistics results of TEV micro-pulse waveform at different measuring points. The black points represent the normalised spectrum statistics of all TEV micro-pulse waveforms measured at different points, and the red curves are the approximate envelope of them. Although the spectral characteristics of each point are obviously different, they generally include 7.7 MHz, 18.7 MHz, 24.5 MHz and 40.6 MHz frequency components, which are similar to the results described in Section 3.3. We calculated the coefficients of variation for these frequencies, and the results are shown in Table 6.

[IMAGE OMITTED. SEE PDF]

TABLE 6 The coefficients of variation of main frequencies in the transient enclosure voltage (TEV) frequency spectrum at different measuring points.

Frequency components (MHz)	CV value of measuring point (%)
Point 1	Point 2	Point 3	Point 4	Point 5
7.7	0.6629	0.6623	0.6990	0.7092	0.6136
18.7	0.4699	0.5149	0.4736	0.5453	0.4563
24.5	0.5106	0.5643	0.5284	0.6158	0.5624
40.6	0.5906	0.5454	0.6297	0.6252	0.5846

Indeed, the CV values of different frequency components at the same measuring point are not quite different. We observed a very interesting conclusion that the frequency component with 7.7 MHz does not have the largest amplitude in the TEV frequency spectrum, but it usually has the largest CV value. Although the resonant frequency of the GIS internal circuit is not the same as that of the GIS external circuit, the main frequency (7.7 MHz) is still easy to cause a large dispersion after being amplified by the GIS external circuit. Except for the main frequency component (7.7 MHz), the CV values of other frequency components roughly meet the regularity that the higher the frequency value, the greater the CV value. Thus, the CV values of the high-frequency component with 40.6 MHz is usually the second largest.

In general, the CV values of the same frequency component at different measuring points are similar. It can be concluded that the structure of the GIS external circuit does not affect the dispersion of different frequency components. Therefore, the fundamental reasons for the dispersion characteristics of different frequency components are still related to the randomness of spark discharge.

CONCLUSION

In this study, thousands switching operations of the disconnector were carried out on the full-scale 1100 kV GIS circuit, and large-scale statistical data of VFTO and TEV was obtained. Interestingly, we notice that for the linear system of the GIS circuit, based on the normalised breakdown voltage, the oscillation amplitude of VFTO waveform and TEV waveform is not completely the linear response of the breakdown voltage, showing obvious dispersion characteristics.

In terms of the amplitude characteristics, the dispersion of VFTO and TEV both tend to increase with the increase of breakdown voltage. Even under the normalised breakdown voltage, the difference between the oscillation amplitudes of micro-pulse in TEV waveform obtained from different discharges can reach five times at most. In terms of the frequency-domain characteristics, the dispersion of the resonant main frequency of VFTO is always the largest, while the dispersions of other main frequency components have a negative correlation with frequency. Contrariwise, the dispersion of the main frequency components obtained from TEV is positively correlated with the frequency. Moreover, the dispersion of different frequency components obtained from TEV is always greater than that obtained from VFTO, especially for the high-frequency components. It is indicated that the high-frequency components in the switching transients are more susceptible to the influence of the dispersion of spark discharge. In terms of spatial distribution characteristics, we observe that the dispersion characteristics of TEV measured at different locations are mainly determined by the dispersion of repeated spark discharges, rather than by the GIS external structure.

These discoveries make up for the lack of theoretical understanding of the correlation among switching transients and indicate that it is necessary to consider the influence of dispersion in the simulation of VFTO and TEV.

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China under Grant No. U20A20305, No. 51977199 and No. U1866201.

CONFLICT OF INTEREST STATEMENT

The authors have no conflict of interest.

DATA AVAILABILITY STATEMENT

Data openly available in a public repository that issues datasets with DOIs.

References

Russell, B.D.: Measurement and Characterization of Substation Electromagnetic Transients (1983)

Okabe, S., et al.: Transient response of a grounding system in an underground GIS substation. Electr. Eng. Jpn. 146(1), 70–77 (2004). [DOI: https://dx.doi.org/10.1002/eej.10214]