2007 International Conference on Solid Dielectrics, Winchester, UK, July 8-13, 2007

Modeling of Electrical Tree Propagation in the Presence of Voids in Epoxy Resin

A Mahajan, K E Seralathan and Nandini Gupta*Department of Electrical Engineering, Indian Institute of Technology Kanpur,

Kanpur - 208016, India* E-mail: nguptagiitk.ac.in

Abstract: Electrical treeing is one of the principalroutes to dielectric failure in solid insulating materials.Researchers around the world are still struggling toformulate acceptable theories that explain the processesinvolved. Tree initiation and growth require localizedfield-enhancement that results in material erosion anddegradation, and consequent partial discharges withinthe tree tubules. Polymeric dielectrics include voids inthe base matrix due to limitations in the manufacturingprocess. These can enhance the tree initiation andgrowth of tree structures. In this work, an attempt hasbeen made to understand qualitatively how the presenceof voids affects tree growth. Experiments wereperformed with voids of different sizes and at differentlocations. Computer simulations were carried out tounderstand the experimental results in terms of spacecharge fields produced in the vicinity of a void as wellas in the bulk dielectric from hv needle electrode

INTRODUCTIONResearchers around the world are still struggling toformulate acceptable theories that explain the processesinvolved in tree initiation and progression, and todetermine the parameters that decide the nature of treegrowth. Some trees grow to bridge the electrode gap andcause puncture, some trees exhibit arrested growth aftera certain time and cause no perceptible damage to theinsulation over long periods of time. Field enhancementcould be due to many factors: protrusions in the highvoltage electrode, material in-homogeneities due tomanufacturing defects, presence of conducting particles,or voids. Research has shown that voids in the soliddielectrics becomes the sites of ionization andeventually causes tree growth when exposed to electricfield. Kageyama et al has reported that the XLPEinsulation produced through steam curing processcontains approximately one million voids per cubicmeter [1]. The size and density of voids causesformation of bow tie trees. However they do not affectshort term insulation life.

Trees initiate in a high-field region, and progressthrough the dielectric by forming fine filamentary treechannels where pd occurs. During pd activity, charge istransferred and deposited on the walls of the tree tubule.At the end of the pd activity a space charge distributionresults along the walls and at the tip of the tree tubule aswell as in the bulk dielectric. Additionally, voids in thepolymeric dielectrics also grow when subjected toelectric field, thermal aging radiation exposure evenunder harsh environmental effects [2]. These can help in

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initiation and growth oftree structures [3, 4].

In this paper, an attempt has been made to understandhow the presence of voids in polymeric insulatingmaterials that are commonly used in power apparatusaffects nature of tree growth in the needle planeelectrode configuration. There exists a significantamount of published literature aimed at understandinginternal discharges in voids under the influence ofapplied field [5-8].

In this work, spherical air-filled voids were injected intothe dielectric solid at selected locations. Experimentswere performed with voids of different sizes and atdifferent locations with respect to the needle electrodeconfiguration. Simulations were carried out tounderstand the experimental results in terms of spacecharge fields produced in the vicinity of a void as wellas in the bulk dielectric injected from hv needleelectrode.

EXPERIMENTSMaterial chosen was Epoxy (CY230) and Hardener(HY95 1). A non-uniform field was established byadopting needle-plate geometry with a gap-distance of2-3 mm; the stainless steel needle had typically a tip-radius of about 7 pm shown in Fig 2. The voidsproduced ranged in sizes from 0.25 to 1.2mm. Thegrowth of the electrical tree was monitored on-line witha high-resolution high-speed camera. Simultaneously,the partial discharge activity within the tree channelswas monitored using a partial discharge detector.Camera images and pd detector output were transferredonline to a PC using a data acquisition module, foronline monitoring and further data-processing.

HVTransfrmer\

Figure 1: Experimental Setup

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HV

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Needle

Figure 2: Sample Geometry

RESULTS AND DISCUSSIONSome typical case-studies are described below in orderto bring out the salient features of tree propagation inthe presence of voids. In Fig.3, a void of diameter 0.8mm is horizontally displaced by 0.3 mm and verticallyby 0.45 mm from the needle tip. A voltage of 12.5 kVwas applied for 50 minutes. The tree initially grows likea bush-branch tree, in a manner similar to whensignificant voids are absent. As the tree progresses, one

of the branches reaches the top of the void, and a smallbranch deviates from the main tree branch growingtowards the bottom electrode to reach the bottom ofvoid. Figure 4 shows a void with diameter of 0.25 mmwas placed at 1.1 mm from the needle tip, in a samplewith a needle-plate gap distance of 2 mm. Onapplication of 12kV, tree was seen to start from theneedle tip and grow into a bush-branch tree. As can beseen from Fig.4, the presence of the void does not seem

to affect the shape of the tree significantly; in fact thetree branches skirt around the void passing close to itwithout touching it. A large number of experimentswere performed of which only two typical cases havebeen reported above. Essentially, it was seen that theeffect of the presence of the void on tree progressiondepended on the location of the void. When the voidwas situated in a highly stressed region, e.g. directlybelow the needle, the tree showed a tendency to grow

towards the void.

This is observed in Fig.3. Here, the void is placed a littledisplaced from the needle-electrode axis along whichfield would be highest. However, it is still located in a

high field region, and high pd values were registered.The tree branches were seen to be perceptibly attractedtowards the void, both from the top as well as thebottom.

Voids located in a low-field region are seen to registermuch lower values of pd magnitude. The tree in Fig. 4appears to grow around the void, toward the oppositeelectrode, without being attracted to it. This was alsoobserved in samples where the void was placed away

from the inter-electrode gap close to the side of theneedle, as shown in Fig. 5.

SIMULATION STUDIES

The experimental findings reported above can beexplained to a certain extent by considering the fact thatthe applied field is accentuated or diminished locally bya superimposed space charge field. It has beenpostulated by Tanaka [3] that tree initiation is mostlikely to occur during the positive half-cycle when thespace charge injected into the dielectric from the needletip enhances the field ahead of the tip. It is a reasonablehypothesis that tree progression takes place by a similarprocess of space charge injection from the tree-tips intothe neighboring dielectric.

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Epoxy -*sample

Planeelectrode

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A negative space charge region is produced around atree-tip due to charge injection into the dielectric, whilepositive charges are trapped on the tree walls. In aseparate study, the authors were able to simulate treeprogression in epoxy as a consequence of the spacecharge modified field [9].

The simulations were based on a stochastic model fortree growth. The tree is assumed to progress in a step-wise manner; the site and direction of propagation ofthetree at any point of time is assumed to be probabilisticin nature, probability being proportional to the localfield. The space charge enhanced field at any point oftime during tree progression was calculated accuratelywith the Finite Element Method using moving boundaryconditions.

It was assumed that when very high voltages applied tothe needle electrode, considerable charge was injectedinto the dielectric medium from the needle electrode.Additionally, high discharge activity within the treechannels resulted in high positive charge density to betrapped within the walls of the channels, with most ofthe charge residing on the tree-tips. Under thesesimulation conditions, the tree progression was seen tomatch experimentally grown trees in high-voltageconditions (15 kV), as shown in Fig. 6. Figure 7a showsa tree grown at considerably lower voltage (7 kV) in thesame time. Assumption of lower charges in medium,walls and tree tips produced a simulated tree (shown inFig. 7b) that matches the experimental.

(a) (b)Figure 6: (a) Experimentally generated tree at 15 kV (b) Computer

simulated tree with charge in medium -ixlO-9 C/m2, charge onsegment I x I 0-1 1 C/m2 and on tip I xl 0-9 C/m2

Ja) (b)

Figure 7: (a) Experimentally generated tree at 7 kV (b) Computersimulated tree with charge in medium -3xlO-11 C/m2,on segment

lx 10-11 C/m2 and on tip 5xlO-10 C/m2

Figure 8: Highly stressed void

Figure 9: Void in Low Field region

The same argument may be extended to the case ofvoids. As mentioned above, voids embedded within thedielectric are seats of high discharge activity, and maybe assumed to inject a high negative space chargeregion around the voids. The amount of space chargewould depend on the size and location of the void,applied voltage, and the ensuing discharge activity.

To simulate the presence of a void in a high field regionas shown in Fig.3, a high charge in assumed around thevoid. High charge is assumed in bulk medium and wallsof the tubule, similar to Fig. 6b, in order to simulatehigh applied field conditions. The simulated tree inFig.8 shows is a bush-branch similar to one grownunder high voltage conditions. Additionally, branchesare seen to be attracted towards the void, reaching itfrom top as well as bottom, as seen in Fig. 3.

Simulations were also performed where the void wasassumed to be in a low field region, and was assumed toinject very low charge densities. The simulation in Fig.9shows a tree grown under moderate charge densityconditions, with very low charge density around thevoid. It can be seen that the tree grows around the voidand does not seem to be affected by the presence of thevoid. In Fig. 10, it is seen that a void placed away fromthe high-stress region does not affect the tree growth.

Thus, it becomes evident that the effect of void on treeprogression is related to pd activity within the void,which in turn depends upon the stress conditions in thevoid. More importantly, it was observed that once a treebranch reaches the void, pd magnitudes increasemanifold. This is seen in Figs. 11 (a) and (b) whichshow the phase-resolved pd patterns before and after avoid is breached by the tree. Discharges are seen toincrease inside the branching channel, resulting ingradual widening. Such a channel is shown in Fig. 12. Itis expected that with further stressing, puncture wouldproceed along the widened tree tubule.

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Jeon et al [10] have undertaken measurements of spacecharge injection from discharging voids. However thenature of these trapping sites such as trap depth and trapdensity is not clear. More studies need to be done inorder to establish the correlation between space chargeaccumulation and partial discharges. It is also seen thatwhen tree tubules reach the void, pd magnitude isincreased considerably. Damage due to pd is related tothe material properties and the energy of discharge.Research is underway to correlate the discharge energyto the damage energy.

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(b)Figure 11. Phase resolved pd patterns (a) at start, (b) on reaching void

CONCLUSIONIt becomes evident from the above discussion that themanner in which the presence of voids affects treeprogression is closely linked to the pd activity withinthe voids. The pd activity has a two-fold effect: damagedue to pd and modification of local field due toaccumulation of space charge. In this work, it has beenshown that the space charge field plays a major role inattracting the tree tubules towards the void. Work incurrently underway to establish the exact parametersthat affect the space charge distribution. In the absenceof measurable space charge data during treeprogression, simulation studies have been undertaken.

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Crosslinked Polyethylene Insulated Cables, IEEETrans. PAS, Vol.PAS-94 (4), pp. 1258-1263, 1975.

[2] Laurent, Mayoux and S.Noel, "DielectricBreakdown of polyethylene in divergent field:Roleof dissolved gases and electroluminescence",Vol.54, No.3, pp.1532-1539, 1983.

[3] T.Tanaka, "Space charge injected via interfaces andtree initiation in polymers", 2001 Annual Report,CEIDP, pp 1- 15.

[4] L.A.Dissado, "Understanding electrical trees insolids: From experiment to theory", IEEE TransDEI, Vol.9, No.4, Aug 2002, pp 483-497.

[5]. P. H. F. Morshuis, "Partial Discharge Mechanismin Cavities Related to Dielectric Degradation", IEEProc. Sci., Measurement and Technology, Vol. 142,pp. 62_68, 1995.

[6]. P. H. F. Morshuis and F. H. Kreuger, "Transitionfrom Streamer to Townsend Mechanisms inDielectric Voids", J. Phys. D: Appl. Phys. 23,pp.1562 1568, 1990.

[7] K. Nakao, T. Kondo, Y. Suzuoki and T. Mizutani,"Phi-q-n Patterns and Current Shapes of PartialDischarges in Void", Intl. Sympos. Electr.Insulating Materials, pp. 665-668,1998.

[8].K. Wu, Y. Suzuoki and L. A. Dissado, "TheContribution of Discharge Area Variation toPartial-discharge Patterns in Disc voids", J. Phys.D: Appl. Phys., Vol. 37, pp. 1815 1823, 2004.

[9] Elan Seralathan K and Nandini Gupta, "StochasticModeling of Electric Tree progression due to partialdischarge activity", ICPADM, Bali, 2006.

[10].S.I.Jeon, S.H.Nam, D.S.Shin,I.H.Park, andM.K.Han, "The correlation between partialdischarge characteristics and space chargeaccumulation under AC voltage", IEEE CEIDPpp.653-656,2000.

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