Electrical Trees and Their Growth in Silicone Rubber at Various Voltage Frequencies

energies

Article Electrical Trees and Their Growth in Silicone Rubber at Various Voltage Frequencies

Yunxiao Zhang 1, Yuanxiang Zhou 1,*, Ling Zhang 1,2, Zhongliu Zhou 1 and Qiong Nie 3

1 State Key Lab of Electrical Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China; [email protected] (Y.Z.); [email protected] (L.Z.); [email protected] (Z.Z.) 2 State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China 3 AC Project Construction Branch, State Grid Corporation of China, Beijing 100052, China; [email protected] * Correspondence: [email protected]; Tel.: +86-10-6279-2303

Received: 28 December 2017; Accepted: 26 January 2018; Published: 2 February 2018

Abstract: The insulation property at high voltage frequencies has become a tough challenge with the rapid development of high-voltage and high-frequency power electronics. In this paper, the electrical treeing behavior of silicone rubber (SIR) is examined and determined at various voltage frequencies, ranging from 50 Hz to 130 kHz. The results show that the initiation voltage of electrical trees decreased by 27.9% monotonically, and they became denser when the voltage frequency increased. A bubble-shaped deterioration phenomenon was observed when the voltage frequency exceeded 100 kHz. We analyze the typical treeing growth pattern at 50 Hz (including pine-like treeing growth and bush-like treeing growth) and the bubble-growing pattern at 130 kHz. Bubbles grew exponentially within several seconds. Moreover, bubble cavities were detected in electrical tree channels at 50 Hz. Combined with the bubble-growing characteristics at 130 kHz, a potential growing model for electrical trees and bubbles in SIR is proposed to explain the growing patterns at various voltage frequencies.

Keywords: silicone rubber; electrical tree; bubble; high frequency; initiation voltage; growing model

1. Introduction Electrical trees are pre-breakdown phenomena that accelerate the occurrence of insulation failure [1–7]. Owing to the harsh working conditions of power electrical equipment, there have been many investigations to determine the inﬂuence of temperature, voltage type, voltage frequency, thermal aging, and moisture on electrical treeing characteristics [8–15]. Partial discharge characteristics, treeing imaging technology, and channel characteristics have also been studied in order to better understanding the initiation and growth mechanisms of electrical treeing [2,7,16–18]. High-power, medium-voltage (several kV), and high-frequency (up to ~20 kHz) electronic equipment, i.e., insulated-gate bipolar transistors (IGBTs) and integrated gate-commutated thyristors (IGCTs), are critical to modern electrical power systems. With the widespread use of power electronics, insulation properties, i.e., the dielectric breakdown strength, surface charging, and electrical treeing characteristics, of polymeric materials have become critical issues, and have attracted increasing attention [12,19,20]. As mentioned above, electrical trees are among the main reasons of insulation failure. Trees will initiate and grow from dielectric defects. Once formed, they will develop within a short time and will lead to breakdown in dielectric materials in advance, especially under high-frequency voltages. Studies have shown that the electrical-treeing initiation voltage decreases with an increase in the voltage frequency. Meanwhile, electrical trees tend to be denser with increasing voltage frequency [12,13]. However, most experiments were carried out below 10 kHz, and there

Energies 2018, 11, 327; doi:10.3390/en11020327 www.mdpi.com/journal/energies Energies 2018, 11, x FOR PEER REVIEW 2 of 12

Energiesvoltage2018 frequency, 11, 327 [12,13]. However, most experiments were carried out below 10 kHz, and 2there of 12 remain uncertainties to determine the mechanisms responsible for electrical treeing development under high voltage frequencies. remain uncertainties to determine the mechanisms responsible for electrical treeing development Silicone rubber (SIR) is an advanced insulating material that is widely used in high-voltage electrical under high voltage frequencies. equipment insulation, owing to its excellent electrical, thermal, and mechanical performance [14,21,22]. Silicone rubber (SIR) is an advanced insulating material that is widely used in high-voltage Because SIR is an elastic material, the mechanism responsible for electrical trees in SIR is different electrical equipment insulation, owing to its excellent electrical, thermal, and mechanical from that in polyethylene [2,7]. There are fewer studies that are aimed to determine electrical treeing performance [14,21,22]. Because SIR is an elastic material, the mechanism responsible for electrical behaviors in SIR compared to those that focus on polyethylene. trees in SIR is different from that in polyethylene [2,7]. There are fewer studies that are aimed to In this work, needle-plate samples are used to study the electrical treeing behavior in SIR determine electrical treeing behaviors in SIR compared to those that focus on polyethylene. materials. The processes of the initiation and development of electrical trees were automatically In this work, needle-plate samples are used to study the electrical treeing behavior in SIR recorded via a digital microscopic imaging system at various voltage frequencies that range from 50 Hz materials. The processes of the initiation and development of electrical trees were automatically to 130 kHz. Electrical treeing initiation and growing patterns of SIR samples were systematically recorded via a digital microscopic imaging system at various voltage frequencies that range from analyzed. Bubble-shaped deterioration, which is a special breakdown phenomenon that has never 50 Hz to 130 kHz. Electrical treeing initiation and growing patterns of SIR samples were systematically been observed at lower voltage frequencies, occurred at 130 kHz. Then, the bubble-growing analyzed. Bubble-shaped deterioration, which is a special breakdown phenomenon that has never been characteristics were evaluated. Moreover, a potential growing model for electrical trees in SIR was observed at lower voltage frequencies, occurred at 130 kHz. Then, the bubble-growing characteristics proposed to provide a reasonable explanation for the different tree-growing patterns at different were evaluated. Moreover, a potential growing model for electrical trees in SIR was proposed to provide voltage frequencies. a reasonable explanation for the different tree-growing patterns at different voltage frequencies.

2. Experimental Details

2.1. SIR Samples In this this study, study, we wechose chose the needle-plate the needle-plate electrode electrode model to modelstudy the to electrical study the tree electricalcharacteristics tree characteristics[14]. The two-component [14]. The two-component high-temperature high-temperature vulcanization vulcanization (HTV) liquid (HTV) SIR (produced liquid SIR by (produced Chinese byBlue-star Chinese Chemical Blue-star Company, Chemical Chengdu, Company, China) Chengdu, was China) selected. was Figure selected. 1 shows Figure the1 shows sample’s the schematic sample’s schematicwith needle-plate with needle-plate electrode system. electrode The system.details of The the detailsneedle electrode of the needle are as electrode follows: The are ascone follows: angle Thewas cone30°, the angle diameter was 30was◦, thearound diameter 250 μm, was and around the curvature 250 µm, radius and the was curvature 3 μm. The radius needle was electrode 3 µm. Thewas needleconnected electrode to one was semiconductor connected to in one a steel semiconductor mold, and the ina vertical steel mold, distance and thebetween vertical the distance tip and betweenthe other thesemiconductor tip and the was other adjusted semiconductor to (3 ± 0.1) was mm adjusted (shown in to Figure (3 ± 0.1) 1). The mm well-mixed (shown in liquid Figure SIR1). Thewas well-mixedpoured into liquid the mold. SIR was This poured process into has the been mold. proven This process to avoid has mechanical been proven destruction to avoid mechanical near the destructionneedle tip as near much the as needle possible. tip Then, as much another as possible. flat steel Then, was placed another to ﬂatcover steel it. wasFinally, placed the steel to cover mode it. Finally,with the the poured steel modeliquid with SIR and the pouredneedle liquidtip was SIR put and under needle a hot-press tip was put machine under at a hot-press165 °C and machine 6 MPa atfor 165 10 ◦minC and to form 6 MPa the for test 10 SIR min samples. to form the test SIR samples.

Figure 1. Silicone rubber (SIR) samples with needle tip.

2.2. Electrical Treeing InitiationInitiation andand GrowingGrowing TestsTests We employedemployed conventionalconventional methodsmethods ofof testingtesting thethe breakdownbreakdown characteristicscharacteristics for solidsolid materialsmaterials to measure the the treeing treeing initiation initiation voltage. voltage. The The volt voltageage was was continuously continuously increased increased to develop to develop trees trees for forsamples. samples. We Weused used sine-wave sine-wave power power supplies supplies with with adjustable adjustable frequency frequency (50 Hz–130 (50 Hz–130 kHz) kHz) to meet to meet the thevoltage-frequency voltage-frequency requirements. requirements. The voltage The voltage was gradua waslly gradually increased increased with a rate with of 500 a rate V/s. ofThe 500 treeing V/s. Theinitiation treeing voltage initiation was recorded voltage waswhen recorded the tree length when theexceeded tree length 10 μm. exceeded Then, the 10ACµ m.voltage Then, amplitude the AC voltage amplitude was ﬁxed and applied for a further 1 min at that value. Next, the image of the

Energies 2018, 11, 327 3 of 12 Energies 2018, 11, x FOR PEER REVIEW 3 of 12 treewas fixed was recordedand applied as thefor a initiated further 1 tree min shape.at that valu Eache. testNext, was the repeatedimage of the more tree than was 20recorded times underas the identicalinitiated tree conditions. shape. Each test was repeated more than 20 times under identical conditions. To analyze the the electrical electrical treeing treeing development development and and growth growth pattern, pattern, a constant a constant voltage voltage was used. was used.We recorded We recorded videos videos of the of growth the growth process process of ofelectrical electrical trees trees and and measured measured the the tree tree length simultaneously. The The experimental experimental system system is shown is shown in Figure in Figure 2. R2z .is aR protectionz is a protection resistance resistance of 20 MΩ of. 20The M microscope,Ω. The microscope, CCD camera CCD camera and a and computer a computer were were used used to observe to observe tree tree characteristics characteristics clearly. clearly. A high-voltage (HV) probe (P6015A, produced by Tektronix, Inc.,Inc., Beaverton,Beaverton, OR, USA) was used to measure the voltage acrossacross thethe samplessamples (the(the dividerdivider ratioratio isis 1000:1).1000:1).

Figure 2. Electrical treeing observation system.

2.3. Tree InitiationInitiation ProbabilityProbability The two-parameter Weibull distribution could be used to detect the breakdown strength of insulating materials.materials. Moreover, Moreover, electrical electrical treeing treeing initiation initiation can be can seen be as seen the result as the of aresult local breakdownof a local inbreakdown the solid. in The the function solid. The could function be expressed could be as expressed follows [14 as]: follows [14]: αβ U β FU（,,exp{(）=1–)–}U β (1) F(U, α, β) = 1 − exp{−(α ) } (1) α where F(U) is the Weibull probability, U is the voltage applied to the sample, and α and β are the scale whereparameterF(U )and is the the Weibull shape probability,parameter, Urespectively.is the voltage α represents applied to the sample,voltage andwhenα andthe initiationβ are the scaleprobability parameter reached and to the 63.2%, shape and parameter, β can characterize respectively. the αdata’srepresents dispersion. the voltage when the initiation probability reached to 63.2%, and β can characterize the data’s dispersion. 3. Experimental Results 3. Experimental Results 3.1. Electrical Tree Initiation Behaviors 3.1. Electrical Tree Initiation Behaviors Figure 3 shows the electrical tree initiation voltages at different voltage frequencies. It can be Figure3 shows the electrical tree initiation voltages at different voltage frequencies. It can be seen that they agree with the Weibull’s distributions well. The distribution of α and β are shown in seen that they agree with the Weibull’s distributions well. The distribution of α and β are shown in Table 1. As mentioned above, α is the voltage with initiation probability of 63.2%, β is the parameter Table1. As mentioned above, α is the voltage with initiation probability of 63.2%, β is the parameter representing the data’s dispersion. As the voltage frequency increased from 50 Hz to 130 kHz, α representing the data’s dispersion. As the voltage frequency increased from 50 Hz to 130 kHz, decreased by 27.9% from 8.5 kV to 6.13 kV, while β had increasing trend as the voltage frequency α decreased by 27.9% from 8.5 kV to 6.13 kV, while β had increasing trend as the voltage frequency increased. The bigger β means the smaller data deviation, thus, the deviation of electrical tree increased. The bigger β means the smaller data deviation, thus, the deviation of electrical tree initiation initiation voltage decreases with increasing voltage frequency. Moreover, as the voltage frequency voltage decreases with increasing voltage frequency. Moreover, as the voltage frequency increased increased from 50 Hz to 1 kHz, α decreased by 22.4% from 8.5 kV to 6.59 kV. However, there was no from 50 Hz to 1 kHz, α decreased by 22.4% from 8.5 kV to 6.59 kV. However, there was no obvious obvious reduction of α above 1 kHz. reduction of α above 1 kHz. Tree shapes differ from each other after they are initiated. In addition, they can be divided into Tree shapes differ from each other after they are initiated. In addition, they can be divided into four typical types in SIR, as shown in Figure 4. Figure 4a shows the branch-like trees. The tree four typical types in SIR, as shown in Figure4. Figure4a shows the branch-like trees. The tree channels channels were sparse and small. The pine-like trees are shown in Figure 4b, and they contained some were sparse and small. The pine-like trees are shown in Figure4b, and they contained some thicker thicker main channels. Some serried leaves were generated near the main channels, which looked like pine trees. For bush-like trees, as shown in Figure 4c, a large number of small channels gathered

Energies 2018, 11, 327 4 of 12 main channels. Some serried leaves were generated near the main channels, which looked like pine trees. ForEnergies bush-like 2018, 11, trees,x FOR PEER as shown REVIEW in Figure4c, a large number of small channels gathered4 around of 12 the needle tip, and the trees were dense and looked like bush trees. Besides, when the applied frequency around the needle tip, and the trees were dense and looked like bush trees. Besides, when the applied exceededEnergiesfrequency 100 2018 kHz, , exceeded11,a x specialFOR PEER 100 type REVIEWkHz, ofa special bubble-shaped type of bubble-shaped deterioration deterioration can be detected can be detected (shown (shown in4 of Figure 12 4d). A bubblein grewFigurewithin 4d). A bubble the tree grew channels within the after tree the channels tree was afterinitiated the tree was for initiated a fewseconds. for a few seconds. around the needle tip, and the trees were dense and looked like bush trees. Besides, when the applied frequency exceeded 100 kHz, a special type of bubble-shaped deterioration can be detected (shown in Figure 4d). A bubble grew within the tree channels after the tree was initiated for a few seconds.

Figure 3. Weibull distribution of electrical tree initiation voltage at different voltage frequencies. Figure 3. Weibull distribution of electrical tree initiation voltage at different voltage frequencies.

Table 1. Distribution of α and β corresponding to Figure 3. Figure 3. WeibullTable distribution 1. Distribution of electrical of αtreeand initiaβ correspondingtion voltage at different to Figure voltage3. frequencies. Frequency (Hz) α (kV) β Table 1. Distribution50 of α and β corresponding 8.50 5.47 to Figure 3. Frequency (Hz) α (kV) β 500 7.84 5.50 Frequency (Hz) α (kV) β 501 k 8.506.59 7.47 5.47 50 8.50 5.47 50010 k 7.846.27 6.66 5.50 500 7.84 5.50 180 k k 6.596.61 8.68 7.47 1 k 6.59 7.47 10130 k k 6.276.12 7.99 6.66 8010 k k 6.276.61 6.66 8.68 13080 kk 6.616.12 8.68 7.99 130 k 6.12 7.99

Figure 4. Four typical electrical tree shapes in SIR: (a–c) are branch-like trees, pine-like trees, and bush-like trees, respectively; (d) is bubble-shaped deterioration (applied by 7.8 kV with 130 kHz). Figure 4. Four typical electrical tree shapes in SIR: (a–c) are branch-like trees, pine-like trees, and Figure 4.The Fourprobabilities typical of electrical different initiated tree shapes tree shapes in SIR: at (differenta–c) are voltage branch-like frequencies trees, (within pine-like 1 min) trees, bush-like trees, respectively; (d) is bubble-shaped deterioration (applied by 7.8 kV with 130 kHz). andare bush-like displayed trees, in respectively;Figure 5. As ( dthe) is bubble-shapedvoltage frequency deterioration increased, (appliedthe tree bybecame 7.8 kV denser. with 130 This kHz). phenomenon could be divided into three stages. In the first stage, for voltage-frequency values The probabilities of different initiated tree shapes at different voltage frequencies (within 1 min) ranging from 50 Hz to 500 Hz, branch-like and pine-like trees were generated, there being a greater are displayed in Figure 5. As the voltage frequency increased, the tree became denser. This Theprobability probabilities of the of differentlatter. In the initiated second tree stage, shapes after ata break different point voltage of 1 kH frequenciesz, bush-like (withintrees were 1 min) are phenomenon could be divided into three stages. In the first stage, for voltage-frequency values displayedgenerated, in Figure and5. Aswithin the voltage voltage frequencies frequency from increased, 1 kHz theto 10 tree kHz, became their probabilities denser. This remained phenomenon ranging from 50 Hz to 500 Hz, branch-like and pine-like trees were generated, there being a greater could be divided into three stages. In the ﬁrst stage, for voltage-frequency values ranging from 50 Hz probability of the latter. In the second stage, after a break point of 1 kHz, bush-like trees were to 500 Hzgenerated,, branch-like and within and pine-likevoltage frequencies trees were from generated, 1 kHz to 10 there kHz, being their aprobabilities greater probability remained of the latter. In the second stage, after a break point of 1 kHz, bush-like trees were generated, and within voltage frequencies from 1 kHz to 10 kHz, their probabilities remained constant. It should be noted Energies 2018, 11, 327 5 of 12 Energies 2018, 11, x FOR PEER REVIEW 5 of 12 Energies 2018, 11, x FOR PEER REVIEW 5 of 12 thatconstant. this break It should point (1be kHz) noted is consistentthat this break with point the initiation (1 kHz) voltageis consistent behaviors with discussedthe initiation above. voltage In the constant. It should be noted that this break point (1 kHz) is consistent with the initiation voltage behaviors discussed above. In the third stage, when the voltage frequency is higher than 10 kHz, all of third stage,behaviors when discussed the voltage above. frequency In the third is stage, higher when than the 10 voltage kHz, allfrequency of the initiatedis higher than trees 10 became kHz, all of bush-like trees.the initiated Inthe particular, initiated trees trees became when became bush-lik the bush-lik voltagee trees.e trees. frequency In In particular, particular, exceeded whenwhen the the 100 voltage voltage kHz, frequency frequency bubble-shaped exceeded exceeded 100 deterioration kHz, 100 kHz, wasbubble-shaped observed.bubble-shaped deterioration deterioration was was observed. observed.

1.01.0 Branch-likeBranch-like tree tree Pine-likePine-like tree tree Bush-like tree 0.8 Bush-like tree 0.8 Bubble-shapedBubble-shaped deterioration deterioration 0.6 0.6

0.4 0.4 0.2 0.2Tree shape probability Tree shape probability 0.0 50 500 1000 10k 80k 130k 0.0 50 500Frequency 1000 10k(Hz) 80k 130k Figure 5. Probabilities of initiated tree-shapeFrequency types at various (Hz) voltage frequencies (within 1 min). Figure 5. Probabilities of initiated tree-shape types at various voltage frequencies (within 1 min). 3.2.Figure Electrical 5. Probabilities Treeing Pattern of initiated tree-shape types at various voltage frequencies (within 1 min). 3.2. ElectricalElectrical Treeing trees Pattern grow larger over time, eventually causing breakdown. As mentioned above, below 3.2. Electrical Treeing Pattern Electrical100 kHz, treesthere are grow three larger main types over of time,tree shapes. eventually In long-term causing aging breakdown.tests, the tree shape As changes mentioned with above, time under different conditions [23]. We roughly divided the treeing pattern below 100 kHz into the below 100Electrical kHz, trees there grow are larger three mainover time, types eventua of treelly shapes. causing Inbreakdown. long-term As aging mentioned tests, above, the tree below shape following two modes: bush-like treeing and pine-like treeing. When the voltage frequency exceeded changes100 kHz, with there time are three under main different types of conditions tree shapes. [23 In]. long-term We roughly aging divided tests, the the tree treeing shape changes pattern with below time under100 kHz, different different conditions breakdown [23]. phenomena We roughly were divided observed the accompanied treeing patter by nbubble below growth, 100 kHz which into the 100 kHzwas into similar the followingto that in liquid two [24]. modes: For the bush-like analysis, we treeing chose the and typical pine-like growth treeing. pattern at When 50 Hzthe and voltage following two modes: bush-like treeing and pine-like treeing. When the voltage frequency exceeded frequencythe exceededbubble growth 100 pattern kHz, different at 130 kHz breakdown (as discussed phenomena in Section 3.3). were observed accompanied by bubble 100 kHz, different breakdown phenomena were observed accompanied by bubble growth, which growth, whichFigure was 6a similar shows a to typical that inbush-like liquid [treeing24]. For pa thettern analysis, at 50 Hz weand chose the corresponding the typical growthgrowing pattern was similar to that in liquid [24]. For the analysis, we chose the typical growth pattern at 50 Hz and at 50 Hzlength. and the When bubble a tree growthwas initiated pattern after atthe 130 application kHz (as of discussed a voltage for in 3Section min, bush-like 3.3). electrical trees the bubblewere formed. growth When pattern the at total 130 time kHz was (as 0.1discussed h, trees stoppedin Section growing 3.3). and the tree lengths remained Figure6a shows a typical bush-like treeing pattern at 50 Hz and the corresponding growing Figurestable between 6a shows 0.1 ah typicalto 0.9 h. bush-likeAfter that, largetreeing new pa channelsttern at formed50 Hz inand front the of corresponding bush-like trees, andgrowing length.length.trees When When grew a a tree rapidlytree was was until initiated initiated they broke after after down. thethe applicationapplication The total time of of a a fromvoltage voltage tree for initiation for 3 3min, min, to bush-like bush-likeits breakdown electrical electrical was trees trees werewere formed. aboutformed. 3 Whenh. When Figure the the 6b total illustratestotal timetime a waswas typical 0.10.1 pine-lik h,h, treese treeingstopped pattern growing growing at 50 and andHz theand the treethe tree correspondinglengths lengths remained remained stablestable betweengrowing between 0.1length. 0.1 h toh Pine-like 0.9to 0.9 h. Afterh. treesAfter that, were that, large generated large new new channelsun channelsder a higher formed formed excited in frontin voltage,front of bush-likeof and bush-like the speed trees, trees, of and and trees grewtrees rapidly growthgrew rapidly untilwas faster. they until The broke they pine-like down.broke trees down. The developed total The timetota ralpidly fromtime until treefrom they initiation tree were initiation punctured, to its to breakdown its and breakdown the whole was was about process took less than 1 min. 3 h.about Figure 3 h.6b Figure illustrates 6b illustrates a typical a pine-like typical pine-lik treeinge patterntreeing atpattern 50 Hz at and 50 Hz the and corresponding the corresponding growing length.growing Pine-like length. trees Pine-like were trees generated were undergenerated a higher under excited a higher voltage, excited and voltage, the speed and the of growth speed of was 3.0 (b) faster.growth The was pine-like faster. treesThe pine-like developed trees rapidly developed until ra theypidly were until punctured, they were andpunctured, the whole and processthe whole took 2.5 lessprocess than 1 took min. less than 1 min. 2.0

1.5 43 s 65 s 3.0 (b) 1.0 2.5

Tree Length (mm) 0.5 65.04 s 65.08 s 2.0 1 mm 0.0 43 s 65 s 1.540 50 60 70 80 90 100 Time (s) 1.0

Figure 6. Typical treeing pattern and the correspondingTree Length (mm) 0.5 tree length: (a) bush-like65.04 streeing pattern65.08 s (after applying 7.5 kV at 50 Hz); (b) pine-like treeing pattern (after applying1 mm 11 kV at 50 Hz). 0.0

40 50 60 70 80 90 100 Time (s) Figure 6. Typical treeing pattern and the corresponding tree length: (a) bush-like treeing pattern Figure 6. Typical treeing pattern and the corresponding tree length: (a) bush-like treeing pattern (after applying 7.5 kV at 50 Hz); (b) pine-like treeing pattern (after applying 11 kV at 50 Hz). (after applying 7.5 kV at 50 Hz); (b) pine-like treeing pattern (after applying 11 kV at 50 Hz).

Energies 2018, 11, 327 6 of 12

Table2 shows the probability of occurrence of different types of trees, as well as the corresponding average durations that were calculated when 10 kV AC voltage of 50 Hz was applied to the samples. Energies 2018, 11, x FOR PEER REVIEW 6 of 12 Under this condition, the probability of pine-like treeing was higher than that of bush-like treeing. Pine-likeTable trees 2 developedshows the probability rapidly, of and occurrence the average of differe breakdownnt types of trees, duration as well was as the 4.98 corresponding min. However, the durationaverage durations from the that development were calculated of bush-like when 10 kV trees AC voltage to breakdown of 50 Hz waswas applied 90 min, to which the samples. was much longerUnder than this that condition, of pine-like the probability treeing breakdown. of pine-like treeing was higher than that of bush-like treeing. Pine-like trees developed rapidly, and the average breakdown duration was 4.98 min. However, Tablethe duration 2. Probabilities from the of development different breakdown of bush-like types trees and theto breakdown average breakdown was 90 min, duration which under was a much 10 kV voltagelonger than at 50 that Hz. of pine-like treeing breakdown.

Table 2. Probabilities of different breakdown types and the average breakdown duration under a 10 kV Type Probability Average Breakdown Duration (min) voltage at 50 Hz. Bush-like treeing 37.5% 90.0 Pine-likeType treeing Probability 62.5% Average Breakdown 4.98 Duration (min) Bush-like treeing 37.5% 90.0 Pine-like treeing 62.5% 4.98 3.3. Bubble Growth at 130 kHz 3.3.Figure Bubble7 describes Growth at the130 kHz entire bubble-breakdown phenomenon at 130 kHz, which involved the followingFigure three 7 stages:describes tree-growth the entire bubble-breakdown stage, bubble-expansion phenomenon stage, at 130 and kHz, breakdown which involved stage. the In the tree-growthfollowing stage, three stages: after thetree-growth tree was stage, initiated, bubble-ex therepansion was stage, a violent and breakdown discharge stage. inside In the the tree- channel, whichgrowth caused stage, serious after erosionthe tree was in the initiated, SIR material, there was and a violent led to discharge the expansion inside andthe channel, growth which of the tree channelcaused in SIR serious elastomers erosion (Figurein the SIR7a). material, During and the led bubble-expansion to the expansion stage,and growth a bubble of the was tree created channel inside the treein SIR channel elastomers (Figure (Figure7b), and7a). overDuring time, the thebubble-expansion bubble began stage, to swell a bubble rapidly was with created the inside highlevels the of visibletree partial channel discharge, (Figure 7b), remaining and over roughly time, the spherical bubble began as it gotto swell larger rapidly (Figure with7c,d). the Whenhigh levels the bubbleof visible partial discharge, remaining roughly spherical as it got larger (Figure 7c,d). When the bubble developed on the opposite grounding electrode, there was a strong primary discharge inside the developed on the opposite grounding electrode, there was a strong primary discharge inside the bubble, and it eventually punctured the sample (Figure7e). When the sample broke down, a large bubble, and it eventually punctured the sample (Figure 7e). When the sample broke down, a large holehole appeared appeared in the in the breakdown breakdown part, part, and and it it waswas completely carbonized carbonized (Figure (Figure 7f).7 f).

FigureFigure 7. Bubble-treeing 7. Bubble-treeing breakdown breakdown phenomenon phenomenon under under a a7.8 7.8 kV kV voltage voltage at 130 at 130kHz: kHz: (a) Bush-like (a) Bush-like tree generatedtree generated after after tree tree initiated; initiated; (b (b)) Bubble Bubble generatedgenerated within within the the tree; tree; (c,d (c) ,Bubbled) Bubble expanded expanded rapidly; rapidly; (e) The increasing bubbles reached the grounding electrode with a strong discharge arc; and (f) The (e) The increasing bubbles reached the grounding electrode with a strong discharge arc; and (f) The sample broke down. sample broke down. Figure 8 shows the increases in the radii of the bubbles (R) upon the application of AC voltages withFigure different8 shows magnitudes. the increases As time in the increased, radii of R the increased bubbles exponentially. ( R) upon the As application the voltage ofincreased, AC voltages withthe different growthmagnitudes. rate also increased. As time The increased,time from tree R increasedinitiation to exponentially. breakdown is within As the several voltage seconds: increased, the growth rate also increased. The time from tree initiation to breakdown is within several seconds:

Energies 2018, 11, 327 7 of 12 Energies 2018, 11, x FOR PEER REVIEW 7 of 12 aboutabout 3.843.84 ss at 10.5 kV, 9.329.32 ss at 9.1 kV, andand 19.119.1 ss at 7.8 kV (for all cases, the applied voltage frequency waswas 130130 kHz).kHz).

3 R

Po 2 Pi Ft Fe

1 10.5 kV Growth Length (mm) Length Growth 9.1 kV 7.8 kV 0 0 5 10 15 20 Time (s)

Figure 8. Increasing radius of bubbles forfor voltagesvoltages havinghaving differentdifferent magnitudesmagnitudes (at(at 130130 kHz).kHz).

Because the bubble expanded spherically after the trees were initiated, we could roughly establish Because the bubble expanded spherically after the trees were initiated, we could roughly establish the bubble-growth dynamics by analyzing the force. Assuming that the bubble remains spherical the bubble-growth dynamics by analyzing the force. Assuming that the bubble remains spherical during the growth process, R can be determined by the following equation: during the growth process, R can be determined by the following equation: θθ=+Δ RtR(,)0 (,) t (2) R(θ, t) = R0 + ∆(θ, t) (2) where R0 is the initial bubble radius, Δ is the function of the incremental radius, t is the growth time, whereand θ isR 0theis thepolar initial angle. bubble According radius, to∆ Newton’sis the function Second of Law, the incremental the bubble’s radius, equationt is of the motion growth is given time, andas followsθ is the (shown polar angle. in Figure According 8): [24] to Newton’s Second Law, the bubble’s equation of motion is given as follows (shown in Figure8): [24] ∂2R mFFPP=++− (3) ∂ 2 teio ∂2R t = + + − m 2 Ft Fe Pi Po (3) where m is the surface mass density, Ft ∂ist the surface tension [24], Fe is the electrical stress [25], Pi is the internal pressure of a bubble, and Po is the external pressure of a bubble [26]. where m is the surface mass density, Ft is the surface tension [24], Fe is the electrical stress [25], Pi is the According to the calculation methods cited in [24], the growing R along the direction from the internal pressure of a bubble, and Po is the external pressure of a bubble [26]. needleAccording tip to the to plate the calculationfollows the methodsfollowing cited equation: in [24 ], the growing R along the direction from the needle tip to the plate follows the followingθ equation:=+⋅λt RtRKe(,)00 (4) λt where K is a constant that corresponds Rto( θθ00,.t [24]) = RIf0 λ+ isK positive,·e R will increase exponentially with(4) time. We developed the exponential fitting for the growing length of bubbles in Figure 8 and found wherethat theyK is were a constant well fitted. that corresponds The results todemonstrateθ0.[24] If λ thatis positive, λ wouldR bewill positive increase when exponentially a 130-kHz with AC time.voltage We is developedapplied in our the experimental exponential ﬁtting conditions, for the and growing the bubbles length grew of bubbles exponentially in Figure in8 our and samples. found that they were well ﬁtted. The results demonstrate that λ would be positive when a 130-kHz AC voltage4. Discussion is applied in our experimental conditions, and the bubbles grew exponentially in our samples.

4.4.1. Discussion Effects of Voltage Frequency on Electrical Tree Initiation 4.1. EffectsIt is believed of Voltage that Frequency electrons on Electricalplay a vital Tree role Initiation in the electrical treeing initiation mechanism for polymersIt is believed under AC that voltages electrons [4,11,23]. play a vitalWhen role in inth thee negative electrical half treeing cycle, initiation electrons mechanism drift into the for polymersinsulating undermaterials. AC When voltages the [voltage4,11,23]. is Whenin the posi in thetive negative half cycle, half most cycle, of electrons electrons are drift extracted into the to insulatingthe positive materials. electrode, When however, the voltage some of is inthem the positivehave not half been cycle, captured most of[27]. electrons Those areelectrons extracted are toaccelerated the positive under electrode, the high however, electric field, some and of accu themmulate have notenough been energy captured to penetrate [27]. Those the electronsSIR material, are causing the molecular chain to break. At the same time, under an AC voltage excitation, electrons and holes are injected from the electrodes in the opposite half cycles. The injected carriers fall into the trap immediately or recombine with the opposite charges, and energy released by the composite is

Energies 2018, 11, 327 8 of 12 accelerated under the high electric ﬁeld, and accumulate enough energy to penetrate the SIR material, causing the molecular chain to break. At the same time, under an AC voltage excitation, electrons Energiesand holes 2018, are11, x injected FOR PEER from REVIEW the electrodes in the opposite half cycles. The injected carriers fall into8 of the12 trap immediately or recombine with the opposite charges, and energy released by the composite is partiallypartially converted converted into into the the energy energy for for fracturing fracturing polymer polymer chains. chains. Polymer Polymer mo molecularlecular chains chains are are cut cut off,off, forming forming free free radicals radicals and and leading leading to to a a chain chain reaction reaction (following (following the the reaction reaction function function shown shown in in FigureFigure 9).9). Then, low molecular chains and micro voidsvoids are produced, initiating the electricalelectrical trees.trees.

FigureFigure 9. 9. ChainChain reaction reaction function function unde underr high high electric electric field ﬁeld in in SIR SIR

To consider the treeing initiation characteristics, Tanaka and Greenwood proposed a mathematical To consider the treeing initiation characteristics, Tanaka and Greenwood proposed a mathematical model to relate the initiation time (tI) and the applied voltage (V) [28]. Considering the effect of the model to relate the initiation time (t ) and the applied voltage (V)[28]. Considering the effect of the voltage frequency (f), the equation canI be written as follows [29]: voltage frequency (f ), the equation can be written as follows [29]: ()−= ftIn G G tht C (5) f tI(Gn − Gth) = Ct (5) where Gn is the energy available from the displacement of the electrons under electric field, Gth is the thresholdwhere Gn valueis the to energy damage available the insulation from the dielectric, displacement and Ct is of the the energy electrons that under expects electric to be the ﬁeld, intrinsicGth is propertythe threshold of a material value to and damage is related the to insulation the tensile dielectric, strength [29]. and GCnt andis the Gth energy can be thatexpressed expects as tofollows: be the intrinsic property of a material and is related to the tensile strength [29]. Gn and Gth can be expressed =−Φ()3/2− 1 as follows: GVn Aexp B 3/2 −1 (6) G = Aexp (−B Φ 3/2V − 1 ) GVn =−ΦAexp () B th o (6) 3/2 −1 where A and B are constants and Φ is Gtheth effective= Aexp (work−B Φ function.Vo ) The critical value stated above is V0. Based on the initiation method employed in our experiments, because the voltage on a tree- where A and B are constants and Φ is the effective work function. The critical value stated above is V0. initiatingBased ramp on is the proportional initiation to method the time, employed V and tI satisfy in our the experiments, following equation: because the voltage on a tree-initiating ramp is proportional to the time, V=and tI satisfy the following equation: VrtI (7) where r is the voltage-ramping rate (500 V/s in ourV =experiments).rtI Combined with Equations (6) and (7),(7) the relationship between V and f satisfies the following equation: where r is the voltage-ramping rate (500 V/s in our experiments). Combined with Equations (6) and (7), the relationship between V and f satisﬁes the following3/2− 1 equation:rCt VVG[Aexp () −Φ B − ] = (8) th f rC V[Aexp (−B Φ3/2V−1) − G ] = t (8) Because the value of the left side in Equation (8) decreasesth monotonicallyf as V decreases, and the value of the right side decreases with increasing f, it can be expected that the treeing initiation voltageBecause would the decrease value of with the leftincreasing side in Equationvoltage frequency, (8) decreases as monotonicallyobserved for the as VSIRdecreases, samples andin our the experiments.value of the With right respect side decreases to the tree with shape increasing after it wasf, it initiated, can be expectedwith increasing that the voltage treeing frequency, initiation thevoltage electrical-mechanical would decrease withstresses increasing applied voltagearound frequency,the tip becomes as observed more frequent for the SIR [12,13]. samples During in our a unitexperiments. time, the Withnumber respect of loading to the tree flows shape injected after itinto was the initiated, SIR increases with increasing gradually; voltage the number frequency, of discharged branches also increased [12]. Both of them cause the initiation of denser electrical trees with increasing voltage frequency. The mechanisms responsible for bubble-shaped deterioration are discussed in the next section.

Energies 2018, 11, 327 9 of 12 the electrical-mechanical stresses applied around the tip becomes more frequent [12,13]. During a unit time, the number of loading ﬂows injected into the SIR increases gradually; the number of discharged branches also increased [12]. Both of them cause the initiation of denser electrical trees with increasing voltage frequency. The mechanisms responsible for bubble-shaped deterioration are discussed in the next section.

4.2. PotentialEnergies 2018 Growth, 11, x FOR Model PEER forREVIEW Electrical Tree in SIR 9 of 12

In4.2. order Potential to Growth determine Model thefor Electrical growth Tree mechanisms in SIR of electrical treeing in SIR, tree channels at 50 Hz were pictured under transmission light with high-resolution and high-magnification observing In order to determine the growth mechanisms of electrical treeing in SIR, tree channels at 50 Hz conditions (shown in Figure 10). We found that electrical tree channels in SIR were spherical and were pictured under transmission light with high-resolution and high-magnification observing punctate. Combined with the spherical bubble growing at high frequencies, it is reasonable to deduce conditions (shown in Figure 10). We found that electrical tree channels in SIR were spherical and that thepunctate. growth Combined of electrical with the trees spherical in SIR bubble is closely growing related at high to frequencies, the expansion it is reasonable of bubble to deduce cavities in the treethat channel.the growth Thisof electrical is consistent trees in SIR with is closely our previous related to study the expansion [7], where of bubble we brieflycavities discussedin the tree the growthchannel. patterns This ofis consistent trees at 50with Hz. our Moreover, previous study the [7], bubble where cavities we briefly were discussed observed the growth in silicone patterns gels as well [of30 trees–32]. at It50 is Hz. found Moreover, that thethe formbubble of cavities electrical were treeobserved is strongly in silicone related gels as to well the [30–32]. mechanical It is found strength of thethat silicone the form gels of [electrical30]. The tree bubble is strongly cavities related would to the be mechanical less visible strength as the of mechanical the silicone strengthgels [30]. gets larger.The As bubble for the cavities SIR we would used be in less our visible tests, as the the elastic mechanical shear strength modulus gets is larger. around As 1~3for the MPa SIR which we is largerused than in that our intests, silicone the elastic gels (Theshear maximummodulus is isaround 1.5 × 101~35 PaMPa [30 which]). Although is larger nothan bubble that in cavities silicone were gels (The maximum is 1.5 × 105 Pa [30]). Although no bubble cavities were detected under the tree detected under the tree observing system in our tests (shown in Figure2) when applied by 50-Hz AC observing system in our tests (shown in Figure 2) when applied by 50-Hz AC voltage, the small voltage, the small punctate cavities could still be observed when the tree channels were exposed under punctate cavities could still be observed when the tree channels were exposed under higherhigher-magnificationmagnification conditions conditions (shown (shown in Figure in Figure 10). 10).

Figure 10. Enlarged pictures of electrical tree channels: (a) Transmission light image of electrical trees Figure 10. Enlarged pictures of electrical tree channels: (a) Transmission light image of electrical trees (upon application of 10-kV voltage at 50 Hz for 5 min); (b) Partial enlarged image of Figure 9a. (upon application of 10-kV voltage at 50 Hz for 5 min); (b) Partial enlarged image of Figure9a. In this section, thus, we propose a possible growth model in SIR for electrical trees considering Indifferent this section, frequencies. thus, Figure we propose 11 shows a possiblethe growth growth process model of schematic in SIR trees for electricalin SIR. Partial trees discharge considering different(PD)frequencies. is a major contributing Figure 11 shows factor, the which growth results process in electrical of schematic tree growth trees inafter SIR. inception Partial discharge[33]. (PD) isPD a majorinside contributingthe channels generates factor, which high-energy results incharges electrical that treehit the growth SIR network. after inception According [33]. to PD the inside calculation and analysis of energies needed to form free radicals in SIR materials [34], gases such as the channels generates high-energy charges that hit the SIR network. According to the calculation and hydrogen and methane could be produced more easily in SIR materials using energetic particles analysis of energies needed to form free radicals in SIR materials [34], gases such as hydrogen and (shown in Figure 12). methane couldThe tree be producedgrowth mechanisms more easily at ina frequency SIR materials of 50 using Hz have energetic been particlesdiscussed (shownin our previous in Figure 12). Thestudies tree [7], growth and the mechanismsspecific growth at pattern a frequency is summarized of 50 as Hz follows: have beenpressure discussed increases in as ourthe gases previous studiesaccumulate [7], and thein the speciﬁc tree channels, growth causing pattern the is summarizedspherical hollow as follows:cavity to expand pressure in increasesSIR. In the ascase the of gases accumulatesamples into which the tree an AC channels, voltage is causing applied with the sphericallower frequencies, hollow Ft cavity, Fe, Pi, and to expandPo (given in Equation SIR. In the(3)) case of sampleswill be toin whichequilibrium an AC when voltage the cavity is applied expands with to a lowercertain frequencies,size. The bubbleFt, cavityFe, Pi ,stops and growingPo (given in Equationuntil (3))another will small be in branch equilibrium incepts when from its the weak cavity plac expandse under the to aaction certain of a size. space The charge bubble and cavityelectric stops growingfield until (shown another in Figure small 11a) branch [35]. Then, incepts the frompreviously its weak mentioned place underprocedures theaction will beof repeated, a space and charge the and bubble cavity will be generated one-by-one, eventually forming the electrical trees (shown in Figure 11b). electric ﬁeld (shown in Figure 11a) [35]. Then, the previously mentioned procedures will be repeated, and the bubble cavity will be generated one-by-one, eventually forming the electrical trees (shown in Figure 11b).

Energies 2018, 11, 327 10 of 12

EnergiesEnergies 2018 2018, 11, 11, x, xFOR FOR PEER PEER REVIEW REVIEW 1010 of of 12 12

Figure 11. Growth model for electrical tree in SIR at different frequencies: (a) Electrical treeing FigureFigure 11. GrowthGrowth modelmodel for for electrical electrical tree tree in SIR in atSIR different at different frequencies: frequencies: (a) Electrical (a) Electrical treeing initiation; treeing initiation; (b) Trees growing under lower frequencies [7]; (c) Bubble growing under frequencies initiation;(b) Trees growing(b) Trees under growing lower under frequencies lower frequencies [7]; (c) Bubble [7]; growing(c) Bubble under growing frequencies under greaterfrequencies than greater than 100 kHz. greater100 kHz. than 100 kHz.

FigureFigureFigure 12. 12.12. Reaction Reaction function function of of producing producingproducing gases gasesgases (hyd (hydrogen(hydrogenrogen and andand methane) methane)methane) in inin SIR SIRSIR materials materialsmaterials using usingusing energeticenergeticenergetic particles. particles.particles.

Under the action of a high-frequency voltage, electron injection and extraction are more frequent, UnderUnder the the action action of of a a high-frequency high-frequency voltage, voltage, elec electrontron injection injection and and extraction extraction are are more more frequent, frequent, and the PD energy generated also increases. According to the bubble-shaped deterioration that occurred andand the the PD PD energy energy generated generated also also increases. increases. Accordin Accordingg to the bubble-shaped to the bubble-shaped deterioration deterioration that occurred that at 130 kHz, a possible mechanism responsible for bubble growth can be explained as follows: when atoccurred 130 kHz, at a 130 possible kHz, a mechanism possible mechanism responsible responsible for bubble for growth bubble can growth be explained can be explained as follows: as follows: when samples are applied at a specific high voltage frequency (e.g., 130 kHz), after trees are initiated, the sampleswhen samples are applied are applied at a specific at a specific high voltage high voltage frequency frequency (e.g., 130 (e.g., kHz), 130 kHz), after aftertrees treesare initiated, are initiated, the PD energy in the channel is so high that a large number of gases will be generated. The sum of the PDthe energy PD energy in the in channel the channel is so ishigh so that high a that large a largenumber number of gases of gaseswill be will generated. be generated. The sum The of sumthe electric-field force and gas-pressure force is much larger than the elasticity force, causing the punctate electric-fieldof the electric-field force and force gas-pressure and gas-pressure force is much force islarger much than larger the elasticity than the elasticityforce, causing force, the causing punctate the cavity to expand continuously and form the bubble that we observed under a microscope. The bubble cavitypunctate to expand cavity tocontinuously expand continuously and form the and bubbl forme that the bubblewe observed that we under observed a microscope. under a microscope.The bubble grows exponentially, finally leading to breakdown within a few seconds. The whole process is growsThe bubble exponentially, grows exponentially, finally leading finally to breakdown leading to breakdownwithin a few within seconds. a few The seconds. whole Theprocess whole is displayed in Figure 11c. It can be deduced that under a high-frequency voltage in SIR, once displayedprocess is in displayed Figure 11c. in Figure It can 11 bec. Itdeduced can be deducedthat under that a underhigh-frequency a high-frequency voltage voltagein SIR, inonce SIR, discharges are generated and bubbles are produced, test samples are soon punctured. dischargesonce discharges are generated are generated and bubbles and bubbles are pr areoduced, produced, test samples test samples are soon are punctured. soon punctured.

5.5.5. Conclusions ConclusionsConclusions InInIn this thisthis study, study,study, we wewe investigated investigatedinvestigated the thethe electrical electricalelectrical treeing treeingtreeing initiation initiationinitiation and andand breakdown breakdownbreakdown characteristics characteristicscharacteristics in inin SIRSIRSIR at atat various variousvarious frequencies. frequencies.frequencies. The TheThe electrical electricalelectrical treeing treeingtreeing initiation initiationinitiation voltage voltagevoltage of ofof SIR SIRSIR decreased decreaseddecreased with withwith increasing increasingincreasing frequency.frequency.frequency. α α decreased decreaseddecreased to to 6.13 6.136.13 kV kVkV at at 130 130130 kHz, kHz,kHz, which which is is 27.9% 27.9% lower lower than than that that at at 50 50 Hz Hz (8.50 (8.50 kV). kV). TheTheThe density densitydensity of ofof the thethe initiated initiatedinitiated electrical electricalelectrical trees treestrees was waswas gr greatergreatereater with withwith higher higherhigher frequencies. frequencies.frequencies. When WhenWhen the thethe frequency frequencyfrequency exceededexceededexceeded 10 1010 kHz, kHz,kHz, all allall of ofof the thethe trees treestrees turned turnedturned into intointo bush-like bush-likebush-like ones. ones.ones. More MoreMore specifically, speciﬁcally,specifically, when whenwhen the thethe frequency frequencyfrequency exceededexceededexceeded 100 100100 kHz, kHz,kHz, there therethere was waswas bubble-shaped bubble-shapedbubble-shaped deterioration. deterioration.deterioration. BothBothBoth bush-like bush-likebush-like treeing treeingtreeing and andand pine-like pine-likepine-like treeing treeingtreeing patterns patternspatterns exist existexist simultaneously simultaneouslysimultaneously at at lower lower frequencies. frequencies. Pine-likePine-likePine-like trees treestrees grew grewgrew rapidly rapidlyrapidly to toto breakdown, breakdown,breakdown, whil whilewhilee bush-like bush-likebush-like treeing treeingtreeing breakdown breakdownbreakdown may maymay have havehave a aa longer longerlonger latency.latency.latency. Moreover, Moreover,Moreover, bubble-growing bubble-growingbubble-growing characteristics characteristicscharacteristics at atat 130 130130 kHz kHzkHz were werewere analyzed. analyzed.analyzed. The TheThe bubbles bubblesbubbles grew grewgrew exponentially,exponentially, eventually eventually leading leading to to breakdown breakdown within within a a few few seconds. seconds. It It should should be be noted noted that that electrical electrical treetree channels channels comprised comprised spherical spherical and and hollow hollow cavities. cavities. Combined Combined with with the the bubble bubble characteristics characteristics at at

Energies 2018, 11, 327 11 of 12 exponentially, eventually leading to breakdown within a few seconds. It should be noted that electrical tree channels comprised spherical and hollow cavities. Combined with the bubble characteristics at high frequencies, a possible growth model was proposed for electrical trees in SIR considering different frequencies. This model may provide a reasonable explanation to the different growth phenomena at various frequencies.

Acknowledgments: The authors are grateful to the Special Fund of the National Priority Basic Research of China under Grant 2014CB239501, the National Natural Science Foundation of China (NSFC 51377089), and the fund given by State Key Laboratory of Electrical Insulation and Power Equipment (EIPE16208). Author Contributions: Yunxiao Zhang and Yuanxiang Zhou conceived and designed the experiments; Qiong Nie performed the experiments; Ling Zhang and Zhongliu Zhou analyzed the data; Yunxiao Zhang wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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