Study on Surface Rainwater and Arc Characteristics of High-Voltage Bushing With Booster Sheds Under Heavy Rainfall

The flashover performance of insulators can be improved by BS (booster sheds) in the rain, which is mainly attributed to the reasons that BS break up long cascades of water and block connections of arcs. However, surface rainwater characteristics and arc characteristics of bushing have not been quantitatively studied under heavy rainfall. In this article, the artificial rain tests were conducted on a 500 kV transformer high-voltage bushing equipped with and without BS under the rainfall intensity of 10 mm/min. <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> (the total length of water column) and <inline-formula> <tex-math notation="LaTeX">$L_{\mathrm {arc}}$ </tex-math></inline-formula> (the critical length of arc) on the bushing surface were taken as the feature parameters of surface rainwater characteristics and arc characteristics, respectively. The effects of BS on <inline-formula> <tex-math notation="LaTeX">$E_{\mathrm {h}}$ </tex-math></inline-formula> (the rain flashover voltage gradient along the insulation height), <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$L_{\mathrm {arc}}$ </tex-math></inline-formula> were investigated, respectively. Furtherly, the relationships were studied among <inline-formula> <tex-math notation="LaTeX">$E_{\mathrm {h}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$L_{\mathrm {arc}}$ </tex-math></inline-formula>. Results indicate that <inline-formula> <tex-math notation="LaTeX">$E_{\mathrm {h}}$ </tex-math></inline-formula> has a sharp rise as the number of BS (<inline-formula> <tex-math notation="LaTeX">$N_{\mathrm {BS}}$ </tex-math></inline-formula>) is from one to two, however the rise of <inline-formula> <tex-math notation="LaTeX">$E_{\mathrm {h}}$ </tex-math></inline-formula> gradually decreases when <inline-formula> <tex-math notation="LaTeX">$N_{\mathrm {BS}}$ </tex-math></inline-formula> exceeds two. <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> decreases while <inline-formula> <tex-math notation="LaTeX">$L_{\mathrm {arc}}$ </tex-math></inline-formula> increases with the rise of <inline-formula> <tex-math notation="LaTeX">$N_{\mathrm {BS}}$ </tex-math></inline-formula>, however both the change ranges of them continually fall. Furthermore, <inline-formula> <tex-math notation="LaTeX">$L_{\mathrm {arc}}$ </tex-math></inline-formula> presents remarkable negative correlation to <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> because of the effect of the electric field. <inline-formula> <tex-math notation="LaTeX">$E_{\mathrm {h}}$ </tex-math></inline-formula> rises nonlinearly with the decrease of <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>, which is due to the change of the wetting uniformity on the bushing surface and the potential redistribution along air gaps in the presence of the local arc.


I. INTRODUCTION
The rain flashovers of insulators often occurred in the power system, which threatened power system security severely [1]- [3]. According to the statistics of flashover accidents in the Nelson River converter station from 1975 to 2013, the rain flashovers accounted for about half of the total and the most of them happened on the bushings [4]. As for the external insulation flashovers in ± 500 kV DC converter stations in China, the rain flashovers accounted for about 60% [5]. Besides, the rain flashovers have also been reported in the external insulation flashover accidents The associate editor coordinating the review of this manuscript and approving it for publication was Mehdi Bagheri .
in 500 kV AC substations and become one of the main factors that affect the operation safety of EHV equipment in the power system.
There were a host of experimental researches on the prevention approaches for the rain flashovers on the external insulation of power equipment. Results showed that the flashover voltages of insulators could be raised by installing booster sheds (BS). Orsino et al. found that the flashover voltage of 800 kV post insulator with 3-6 BS (spacing distance of 700 mm) was 18%-24% higher than that without BS under rain of 5 mm/min [6]. Yu et al. performed the tests on the 500 kV porcelain bushing with 4 and 8 BS (spacing distance of 1165 and 580 mm) and found the maximum withstand voltage increased by 72.7% and 127.3%, VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ respectively, compared with that without BS under rain of 10 mm/min [7]. A recent study by Liu et al. indicated that the flashover voltage of 110 kV porcelain post insulator with 3 BS (spacing distance of 400 mm) was 26.5% higher than that without BS under rain of 2 mm/min [8]. Furthermore, many qualitative studies have been carried out on the reasons why the rain flashover voltage of insulator was improved by BS. According to the study by Ely et al., there were three possible reasons for the insulation performances of post insulator and bushing improved by booster sheds under rain of 0.3-4.3 mm/min as follows: prevention of the bypassing of leakage path by cascading water, inhibition of discharge development and suppression of discharges running between booster sheds and skirts [9]. However, Lambeth et al. thought that the most important effect of booster sheds might be to hinder the development of the surface arc of the wall bushing, rather than shield the rainwater under non-uniform rain of 6.5 mm/min [10]. A study by Xu et al. indicated that under the rain of 3 mm/min, the effects of booster sheds were to separate the rainwater flowing and to avoid excessive rainwater bridging the air gap between the skirts [11]. Yu et al. found booster sheds can greatly improve the withstand voltage of bushing under rain of 10 mm/min because of breaking the formation of the rain streams and blocking the connection of the arcs [7].
As for the studies mentioned above, it was found that the effects of booster sheds were not exactly the same under different conditions, and the rainfall intensities were no more than 10 mm/min in the most of experiments. These studies qualitatively indicated that the booster sheds could break up long cascades of water and block the arc propagation. However, there are no quantitative analyses on the rain or arc characteristics of the high-voltage bushing. Besides, the relationships have not been explored among the rain flashover voltage, surface rainwater characteristics and arc characteristics.
In this article, the artificial rain tests are carried out on a 500 kV transformer high-voltage bushing equipped with and without booster sheds under the rainfall intensity of 10 mm/min. In order to quantitatively investigate the effects of booster sheds on the rain flashover voltage, surface rainwater characteristics and arc characteristics of the bushing, the total length of water column and the critical length of arc are taken as the feature parameters of surface rainwater characteristics and arc characteristics, respectively. Furthermore, the relationships among the rain flashover voltage, surface rainwater characteristics and arc characteristics are revealed, which contributes to explain the mechanism of the rain flashover voltage raised by installing booster sheds.

A. EXPERIMENTAL SET-UP
The schematic diagram of the experimental set-up is shown in Fig. 1. AC high voltage through the wall bushing was led to the test sample vertically locating in the climate chamber. In Fig. 1, the AC power supply system was composed of 10 kV, 3000 kVA post voltage regulator, 450 kV, 2700 kVA high-voltage test transformer and 450 kV AC capacitor voltage divider. The relevant indicators met the requirements of standard IEC 60507 [12].
The climate chamber was 16 m × 12 m × 16 m in size. The rain shelf, consisting of 5 × 20 nozzle arrays, was 12m high, and each nozzle can be independently controlled to adjust rainfall.
In order to study surface rainwater characteristics, a Canon 5D camera was adopted to take photos of the rain condition on bushing in the artificial rain. No less than eight consecutive photos with the interval time of 125 ms were taken to reduce the data dispersion. With the purpose of investigating arc characteristics, a Vision Research Phantom 12.1 high-speed camera at the shooting speed of 1000 frames/s was used to record the process of arc propagation on the bushing surface in the tests.

B. TEST SAMPLE AND CONDITION
In this article, the bottom half of a 500 kV transformer porcelain bushing was selected as the test sample with a single large and small shed configuration, and the sample parameters were shown in Table 1. In the tests, both the horizontal and vertical components of rain were 10 mm/min to simulate the natural heavy rain. The rainfall angle was 45 • to simulate a windy environment, and rainwater conductivity was 300 µS/cm. The sample surface was coated by pollution layer with the salt deposit density (SDD) of 0.06 mg/cm 2 and the non-soluble deposit density (NSDD) of 0.36 mg/cm 2 .
The rain flashover tests on the sample equipped without BS and with 1-4 BS were carried out. According to China electric power industry standard DL/T 1469 [13], the first booster shed was installed on the third large shed under the high-voltage wire. When the number of booster sheds (N BS ) was more than one, BS were positioned uniformly along the sample, as shown in Fig. 2. In Fig. 2, BS mn was the label of booster shed installed on the sample. For instance, BS 32 was the second booster shed from top to bottom of the sample when N BS was 3. h was the insulation height of the sample and l 1 was the height from BS 11 to the grounding end. l 2 , l 3 , and l 4 were the spacing distances of 2, 3, and 4 BS, respectively.

C. TEST PROCEDURES 1) PROCEDURES OF FLASHOVER TEST
The constant voltage up-and-down method [14] was adopted for the tests, and the test procedures were as follows: a) The sample was washed clean and dried at room temperature, and then the solid layer method [12] was applied to contaminate the sample surface. b) 75% of the predetermined voltage U i was applied for a while, and then rose to U i at the range of about 2% of U i per second. The voltage was kept at U i constantly after that.
c) The rain device started up after the test voltage U i maintained for 5 min. If flashover did not occur within 15 min, the test was stopped. d) Returned to step a) for the next test. If flashover occurred in the last test, U i in b) should be reduced by 5%, otherwise raised by 5%.
The sample needed to be contaminated again after cleaned no matter flashover occurring or not in the last test, and ten useful tests were required at least. The rain flashover voltage (U 50% ) and its relative standard deviation error (σ ) can be calculated as follows [15], [16]: where U i is an applied voltage level and n i is the number of groups of tests carried out at the same applied voltage level; N is the number of useful tests; N = 10. Furthermore, the rain flashover voltage gradient along the insulation height (E h ) can be gained by the following formula [17], [18]:

2) PROCEDURES OF SURFACE RAINWATER CHARACTERISTICS TEST a: SELECTION OF FEATURE PARAMETER OF SURFACE RAINWATER CHARACTERISTICS
The rainwater accumulated on the edge of the bushing shed will form a water column under the effects of gravity and surface tension. Generally, the water column does not bridge the next shed and there is a ''water column-air gap'' between two adjacent sheds [19]. The streamer discharge [20] and the streamerlike discharge [21], across the tip of the droplets and water runnels hanging on insulator shed, develop in the air gap between the sheds. Therefore, this article photographed the discharge paths between bushing sheds as shown in Fig. 3.  shows that the discharge on the bushing surface started from the breakdown of the air gap at the end of the water column, which is in agreement with the studies on arc propagation in [22], [23]. The experimental phenomenon demonstrates that the length of the water column hanging on the shed edge plays a very important role in the whole process of the discharge.
Consequently, in order to quantitatively explore the relationship between surface rainwater characteristics and arc characteristics, the length of water column between two large sheds is used to characterize surface rainwater characteristics. In this article, the water column refers to the water drop which is elongating and about to break up according to [22]. Finally, the total length of water column, which can reflect the overall rain situation on the bushing surface, is taken as the feature parameter of surface rainwater characteristics.

b: MEASUREMENT OF THE TOTAL LENGTH OF WATER COLUMN
The shape of water column hanging at the edge of shed is so random that it may be vertical or sloping. Therefore, VOLUME 8, 2020 the vertical distance from the edge of the large shed to the end of water column is taken as the length of water column, which is denoted as x, as shown in Fig. 4. The sample has 32 large shed units named S 1 -S 32 from top to bottom. S 1 represents the shed unit where the high-voltage wire is located, and S 32 is the shed unit closest to the grounding end. The length of water column (x i ) can be calculated by the following formula: where j is the order number of the tests and k is the order number of the photos in one test; x ijk is the average length of all water columns of the shed unit S i in the k-th photo of the j-th test; x ij is the average length of water column for M consecutive photos of the j-th test; N is the number of repeated experiments; M = 8 and N = 3. Therefore, the total length of water column (X ) on the sample surface can be gained as follows: where N sh is the number of shed units of the sample, N sh = 32. The relative standard deviation error (σ i ) is employed to represent the dispersion of x i . Based on the Bessel formula [24], σ i can be derived as follows: Similarly, the relative standard deviation error of X (σ X ) can be calculated by the following equation: 3

) PROCEDURES OF ARC CHARACTERISTICS TEST a: SELECTION AND DETERMINATION OF FEATURE PARAMETER OF ARC CHARACTERISTICS
References [7] and [9] pointed out that the booster sheds can hinder the arc propagation and increase the difficulty in the connection of the partial arcs. However, there was no discussion about which feature parameter was involved in the arc propagation. Based on the Obenaus pollution flashover model, reference [25] derived the relationship between the arc length and the minimum voltage required to maintain the arc. The voltage required to maintain the arc dramatically dropped once the arc length exceeded the critical length of arc, which led to an inevitable flashover. Therefore, this article selects the critical length of arc [26], [27] as the feature parameter of arc characteristics to explore the effects of booster sheds on the arc propagation. According to reference [25], the flashover occurred immediately after the arc suddenly developed downward rapidly. So, the arc propagation velocity (v) was measured through recording the arc propagation process by a high-speed camera. Therefore, the length of the arc corresponding to the moment when v started to change from low to high was defined as the critical length of arc (L arc ).
During the arc propagation process as shown in Fig. 5, s is the vertical distance of the downward propagation path in the period of t 1 to t 2 . Taking the arc propagation direction from the HV end to the grounding end as the positive, v within t ( t = t 1 -t 2 ) can be calculated by the equation:

b: MEASUREMENT OF THE CRITICAL LENGTH OF ARC
Complex thermal forces [28]- [30] and some random environmental forces can cause the arc forming an irregular shape, which makes it difficult to measure the arc length accurately [31]. The test phenomenon in this article shows that most of partial arcs develop along the axial direction, and there is almost no arc on the surface of BS before flashover. In order to measure the arc length conveniently, the length in the vertical direction is taken as the local arc length in this article. Therefore, L arc is the sum of the lengths of local under BS at the critical moment.

A. RESULTS AND ANALYSES OF FLASHOVER TEST
The results of flashover test are presented in Table 2. The increase range of E h is the percentage of the ratio between E hm -E hn and E hn , and it can effectively reflect the change of E h with the increase of N BS . Based on the test results in Table 2, the relationships between N BS and E h and the increase range of E h are obtained as shown in Fig. 6.   Fig. 6 show that: 1) Compared with that without BS, E h of the sample with 1-4 BS increases by 39%, 150%, 176% and 194%, respectively, which indicates that BS can effectively improve the flashover performance of the sample under heavy rainfall.
2) When N BS exceeds two, the increase range of E h gradually decreases and is no more than 10%. That is to say, E h of the sample appears to grow with saturation as N BS continuously increase.

B. RESULTS AND ANALYSES OF SURFACE RAINWATER CHARACTERISTICS TEST
The measured results of x i , X and σ X are listed in Table 3, and the distributions of x i and σ i along the bushing shed unit S i are shown in Fig. 7.
The results in Table 3 and Fig. 7 indicate: a) σ i concentrates upon 4%-10% and σ X is no more than 8%, which means that the precision of the measured results with low dispersion is satisfactory. b) There is almost no water column between large sheds of the first three shed units under each booster shed, which is visible in the photos of the partial rain situation of the sample as shown in Fig. 8. Moreover, x i under BS is generally rising. c) Generally, x i under BS decreases compared with that without BS, and the closer to BS S i is, the greater is decrease in x i .
According to the test results in Table 3, the relationship between X and N BS is shown in Fig. 9. Fig. 9 shows that X decreases with the increase of N BS while the decrease range of X gradually falls. It is because booster sheds play an important role in sheltering rainwater and breaking up long cascades. However, as N BS increases, the accumulation of rainwater on the sample sheds surface decreases gradually, leading to the falling of the decrease range of X . Fig. 10 shows the results of arc propagation velocity (v) in 100 ms before flashover without BS and with 1-4 BS installed, and the critical arcs are shown in Fig. 11. VOLUME 8, 2020   In the enlarged part of Fig. 10, the points are marked as A-E where the significant rise of v emerges as 0-4 BS are installed, respectively. The length of the corresponding arc at that point is measured and defined as the critical length of arc (L arc ).

C. RESULTS AND ANALYSES OF ARC CHARACTERISTICS TEST
According to the determination of the critical length of arc, the measured results are listed in Table 4.
Based on the test results in Table 4, the relationship between L arc and N BS is obtained, as shown in Fig. 12.
In Figure 12, L arc appears to grow with saturation as N BS rises. It can be explained as follows:  From earlier study [32], the maximum electric field strength on the bushing surface appears on the booster shed edge. As a result, the arcs hang on the booster shed edges and almost develop synchronously as shown in Fig. 13, leading to the rising of L arc . However, the spacing distance of booster sheds decreases with the increase of N BS and the arcs are easy to bridge the adjacent booster sheds, which corresponds to the result that f arcm continuously increases in Table 4. Consequently, the increase range of L arc is falling with N BS rising.

A. EFFECT OF WATER COLUMN ON ELECTRIC FIELD
In order to study the effect of water column on the electric field, the electric field simulation was carried out for the sample without BS and with 1-4 BS. According to the test results in Table 3, the length of water column at the edge of shed in the simulation was determined.
The distribution of the electric field is shown in Fig. 14. Taking Fig. 14 (a), (b) and (c) as examples, the distribution   of the electric field strength (E) along the air gaps between the sheds from the top to the bottom of the sample is shown in Fig. 15. It can be seen from Fig. 14 and Fig. 15 that: 1) When there is no hanging water column on the surface of bushing without BS, the overall electric field strength is remarkably lower than that with water column. When the sample is equipped without BS and with 1-4 BS in the presence of water column, respectively, the distribution of the electric field has no significant change on the whole.
2) Fig. 14 (g) shows that the electric field within the air gap between two adjacent sheds is obviously distorted by the water column, which is illustrated by the abrupt peaks in Fig. 15.
3) The maximum electric field strength occurs at the airwater interface at the end of water column. The electric field strength on the shed surface is far less than that within the air gap at the end of water column.

B. RELATIONSHIP BETWEEN X AND L arc
Based on the test results in Table 2 and Table 3, the relationship between E h and X can be obtained as shown in Fig. 16, which shows that E h decreases as X increases, while there is not a linear relationship between them.
Form the test results in Tables 2 and 4, the relationship between E h and L arc is gained, as also shown in Fig. 16, where E h rises with the increase of L arc , yet not linearly.
It is worth mentioning that the two trends of E h with the decrease of X and with the increase of L arc are synchronous in Fig. 16, demonstrating a significant correlation between X and L arc . According to Tables 3 and 4, the relationship between X and L arc obtained by fitting is shown in Fig. 17 and  equation 9, where the correlation coefficient R 2 is 0.9985. Fig. 17 and equation (9) show that there is a remarkable negative correlation between X and L arc . In order to explore whether there is such a relationship between surface rainwater characteristics and arc characteristics at the local position of the sample, the test results in Tables 3 and 4 are further analyzed.
The relationship between X m and L arcm can be obtained as shown in Fig. 18, where X m is the total length of water column between two adjacent booster sheds and L arcm is the length of local arc between two adjacent booster sheds when N BS is m. R 2 in Fig. 18 called correlation coefficient greater than 0.96 means there is an approximate negative correlation between the length of water column and the length of local arc at the local position of the sample, which is attributed to the effect of the electric field.
According to the simulation results, it can be inferred thatthe electric field strength along the shed surface is too low to promote the streamer development, whereas the electric field strength within the air gap at the end of water column is far greater due to the presence of water column, leading to the streamer discharge along the air gap. Besides, the water drop in the strong electric field will deform and then spray the charged particles at its tip, thus promoting the breakdown of air gap [22]. Therefore, when the applied voltage increases gradually, a local arc with higher energy will form in the air gap at the end of water column, which starts at the end of water column and develops to the upper surface edge of the shed below,  as shown in Fig. 3. The water column and the arc bridge two adjacent bushing sheds, and the longer the water column is, the smaller the arc length is. As a result, L arcm presents remarkable negative correlation to X m , as well as L arc to X . Fig. 16 indicates that E h increases with the decrease of X , the reason of which is discussed as the following.

C. EFFECT OF X ON E h
Under the rain condition, the insulation task between the insulator sheds is mainly performed by the air gap, which bears most of the applied voltage [23]. As the water column between two adjacent sheds becomes shorter, the air gap at the end of the water column is longer and less likely to be broken down, which explains why E h rises with the decrease of X .
Furthermore, the increase range of E h rises in the beginning and then falls as X decreases in Fig. 16. When N BS is one, E h is higher than that without BS, but the rise of E h is not  remarkable. E h has a sharp rise as N BS is from one to two, whereas the rise of E h gradually falls as N BS exceeds two. Based on the results in Table 3 and Fig. 7, the trend of curve E h (X ) can be well explained as follows: 1) Compared with that without BS, X of the sample with only one booster shed (BS 11 ) is reduced. However, the length of water column (x i ) of the first several bushing sheds under BS 11 is significantly smaller than that farther from BS 11 , leading to relatively uneven wetting of the sample. As a result, E h is higher than that without BS while the increase range of E h is unremarkable.
2) X continuously decreases when two booster sheds (BS 21 and BS 22 ) are installed. Moreover, x 9 -x 19 under BS 21 are not much different from x 22 -x 32 under BS 22 , and the variations of x i under BS 21 and BS 22 are approximately identical. The sample is equivalently divided into two units with similar surface rainwater characteristics, causing a more uniform wetting and an improved insulation performance of the sample on the whole. Moreover, according to [33] and [34], the local arc under BS 21 causes an increase of voltage drop along the air gap between BS 22 and the grounding end, and the air gap playing the role of a potential barrier prevents the re-equilibrium of the potential distribution, leading to a higher flashover voltage. E h therefore increases significantly as N BS is from one to two.
3) Simulation studies indicate that the higher N BS is, the higher is resistance of the air gaps against voltage redistribution in the presence of the local arc, and the higher the final flashover voltage is [33], [34]. Although the sample is divided into three units with similar surface rainwater characteristics, the wetting uniformity of the sample is worse due to the increase of the dry bushing sheds without water column. Consequently, as N BS is from two to three, E h rises while its increase range falls, compared with that of two BS. In the same vein, there is the similar variation of E h as N BS is from three to four.

V. CONCLUSION
The following conclusions can be drawn: 1) The rain flashover voltages of the sample equipped with 1-4 BS are 39%, 150%, 176%, and 194% higher than that without BS, respectively, which indicates that BS can effectively improve the flashover performance of the sample under heavy rainfall.
2) As the number of booster sheds rises, the total length of water column decreases while the critical length of arc increases nonlinearly, however the both change ranges of them continually fall.
3)There is not only a remarkable negative correlation between the total length of water column and the critical length of arc on the whole sample but also on the local, which is attributed to the effect of the electric field.
4) The rain flashover voltage gradient along the insulation height is improved nonlinearly, and its increase range first rises and then falls with the total length of water column decreasing. It is not only because booster sheds divide the bushing into several units and lead to the changes of the wetting uniformity, but also the potential redistribution along air gaps varies in the presence of the local arc.