6
I"~X'7"STJ~ ~ ELSEVIER Journal of Electrostatics 40&41 (1997) 389-394 Journal of ELECTROSTATICS Breakdown of liquids: area effect, volume effect or... particle effect ? R. Tobazron Laboratoire d'Electrostatique et de Mat6riaux Dirlectriques - Centre National de la Recherche Scientifique (CNRS) et Universit6 Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France It has been known for a long time that the electric strength of insulating materials decreased when the size of the material was increased. This size influence has been interpreted either as an "area effect" or as a "volume effect". The controversy between the two effects still persists. From the physical standpoint, a clarification is desirable. This article states that conducting particles (omnipresent in liquids) are able to produce high local field enhancements and act as triggers which reduce the breakdown field of uniform and non- uniform gaps. Numerical computations of field distribution modified by the presence of a single particle (of different shape) are presented. From an analysis of typical data on particle counting and distribution size in transformer oils, associated with the present knowledge of streamer generation and propagation in oils, the author shows how particles present in the bulk of the liquid or at the electrode surface could trigger a breakdown. 1. INTRODUCTION The ac, dc and even impulse breakdown strengths of any dielectric material (gas, liquid, solid) is reduced when the size (gap distance or electrode area or material volume) of the stressed material is increased. The service stress in most large scale insulations hardly reaches a few kV/mm while the "intrinsic" electric strength of the insulating material is higher by approximately two orders of magnitude. Several hypotheses may be put forward to explain the reduced reliability of a large power apparatus such as high voltage transformers (mainly insulated with oil-impregnated cellulosic materials). Some of these hypothesis are: presence of solid contaminants, degradation of material quality under stress, large electrode area, large stressed volume. Many features are common to the breakdown of insulating materials, for instance: (i) breakdown is localized, the spark or arc being preceded by a luminous tree-like pattem; (ii) the breakdown voltage is a statistically distributed quantity; (iii) the electric strength decreases when the time duration at constant voltage application is increased. Concerning liquids, breakdown is under the dependency of many interrelated factors (electronic, hydrodynamic, thermal...) and also of several "flaws". These are randomly distributed either at the macroscopic scale both in the volume (foreign particles, bubbles) and on the electrode surface (protrusions, gas trapped in crevices) or at the microscopic scale (spots of particular properties on the electrodes possibly enhancing charge injection). The alms of this work are the following: (i) to briefly review the litterature on area effect and volume effect; (ii) to summarize some salient effects of large conducting particles in liquids; (iii) to scrutinize the data on particle counting and size distribution in transformer oils; (iv) to present some new computed results on field-enhancement due to single particles in divergent geometry; (v) to propose an interpretation of the breakdown lowering of large scale oils gaps based on the behaviour of conducting particles. 0304-3886/97/$17.00 © Elsevier Science B.V. All rights reserved. 1'1I S0304-3886(97)00076-4

Breakdown of liquids: area effect, volume effect or … particle effect?

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Page 1: Breakdown of liquids: area effect, volume effect or … particle effect?

I"~X'7"STJ~ ~

ELSEVIER Journal of Electrostatics 40&41 (1997) 389-394

Journal of

ELECTROSTATICS

B r e a k d o w n o f l iquids : a rea effect , v o l u m e effect or... par t ic le effect ?

R. Tobazron

Laboratoire d'Electrostatique et de Mat6riaux Dirlectriques - Centre National de la Recherche Scientifique (CNRS) et Universit6 Joseph Fourier, BP 166, 38042 Grenoble Cedex 9, France

It has been known for a long time that the electric strength of insulating materials decreased when the size of the material was increased. This size influence has been interpreted either as an "area effect" or as a "volume effect". The controversy between the two effects still persists. From the physical standpoint, a clarification is desirable. This article states that conducting particles (omnipresent in liquids) are able to produce high local field enhancements and act as triggers which reduce the breakdown field of uniform and non- uniform gaps. Numerical computations of field distribution modified by the presence of a single particle (of different shape) are presented. From an analysis of typical data on particle counting and distribution size in transformer oils, associated with the present knowledge of streamer generation and propagation in oils, the author shows how particles present in the bulk of the liquid or at the electrode surface could trigger a breakdown.

1. INTRODUCTION

The ac, dc and even impulse breakdown strengths of any dielectric material (gas, liquid, solid) is reduced when the size (gap distance or electrode area or material volume) of the stressed material is increased. The service stress in most large scale insulations hardly reaches a few kV/mm while the "intrinsic" electric strength of the insulating material is higher by approximately two orders of magnitude.

Several hypotheses may be put forward to explain the reduced reliability of a large power apparatus such as high voltage transformers (mainly insulated with oil-impregnated cellulosic materials). Some of these hypothesis are: presence of solid contaminants, degradation of material quality under stress, large electrode area, large stressed volume. Many features are common to the breakdown of insulating materials, for instance: (i) breakdown is localized, the spark or arc being preceded by a luminous tree-like pattem; (ii) the breakdown voltage is a statistically distributed quantity; (iii) the electric strength decreases when the time duration at constant voltage application is increased.

Concerning liquids, breakdown is under the dependency of many interrelated factors (electronic, hydrodynamic, thermal...) and also of several "flaws". These are randomly distributed either at the macroscopic scale both in the volume (foreign particles, bubbles) and on the electrode surface (protrusions, gas trapped in crevices) or at the microscopic scale (spots of particular properties on the electrodes possibly enhancing charge injection).

The alms of this work are the following: (i) to briefly review the litterature on area effect and volume effect; (ii) to summarize some salient effects of large conducting particles in liquids; (iii) to scrutinize the data on particle counting and size distribution in transformer oils; (iv) to present some new computed results on field-enhancement due to single particles in divergent geometry; (v) to propose an interpretation of the breakdown lowering of large scale oils gaps based on the behaviour of conducting particles.

0304-3886/97/$17.00 © Elsevier Science B.V. All rights reserved. 1'1I S0304-3886(97)00076-4

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390 R. Tobaz~on/Journal of Electrostatics 40&41 (1997) 389-394

2. A R E A E F F E C T VERSUS V O L U M E E F F E C T

2.1. Influence of electrode area The decrease of breakdown strength with the increase in area of the electrodes was already

observed more than half a century ago by several authors either on solid materials (varnished cloth, papers) and on insulating liquids (mainly transformer oils). It was suggested that the larger the electrode area the greater the probability of obtaining high local fields at asperities on the electrodes. More extensive studies of the area effect on the breakdown of transformer oil were initiated at the end of the fifties by Weber and Endicott [1]. They carried out a statistical analysis showing that the ac breakdown of transformer oil in a uniform field followed the extreme value theory rather than normal probability. This theory yields a linear dependence of electric strength on logarithm of area. This relation was acceptably verified in a 400 to 1 increase in area (gap spacing: 1.9 mm; maximum area -- 50 cm 2) both with the ac 60 Hz voltage raised uniformly and with impulse voltages.

2.2. Influence of volume of oil under stress Wilson [2] proposed that the stressed volume was the predominant size-effect criterion:

breakdown in a given gap is initiated at the "weakest spot"; if a greater volume is stressed to the same level, a still weaker spot is likely to be present, triggering a breakdown at a lower voltage. So, dielectric strength will decrease as volume increases. Wilson established a relationship between strength and volume by applying the weak-link theory in the gap subdivided into n elementary volumes each having a finite probability to breakdown (the normal law was used). The Wilson's calculations lead to a reduction of the electric strength by a factor of five from volumes v varying from 10 .3 cm 3 to 103 cm 3. Incidentally, a replot of these data yields a power law of the form: v °'14.

Moreover, Wilson proposed an ingenious attempt to predict the strength for any configuration of electrodes. For curved electrodes, this consists of using an equivalent volume of liquid in which the stress is low enough for its probability of failure to be negligible. This is done by finding the volume which has, in a uniform field, the same strength as the maximum stress at the surface of the curved electrode. Wilson showed that this volume was approximately limited to the 90 % equigradient surface i.e. the volume in which the medium was stressed between the maximum value and 90 % of that maximum (often called the "90 % stressed volume"). This method checked many experimental data on changes in oil electric strength with the radii and separations of spheres and cylinders.

2.3. Further developments In the published discussion of reference [1], Wilson rightly put forward that "if the oil

contains appreciable contamination (lint, gas bubbles, etc.), its strength will be moderate and the statistical relationship is likely to be primarily with volume and secondarily with area; if the oil has higher strength, the relationship is likely to be more with area;.., another oil may exhibit combined volume and area effect". Notwithstanding, the further studies of more than two decades tended to accentuate the controversy area effect versus volume effect until Trinh et al. [3] investigated under what conditions either one of these effects would be most pronounced. They used plane electrodes allowing them to test a broad range of electrode areas (from 102 to 4.1 x 104 cm 2) and stressed oil-volumes (5 to 6.2 x 105 cm3). They demonstrated that the volume effect was more pronounced with oil contaminated with particles, whereas evidence of an electrode area effect could be found with clean oil. However, no interpretation was proposed as concerns the way by which particles influenced breakdown initiation.

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R. TobazJon/Journal of Electrostatics 40&41 (1997) 389-394 391

3. PARTICLE C H A R A C T E R I Z A T I O N IN LIQUIDS. FIELD ENHANCEMENT DUE TO CONDUCTING PARTICLES

3.1. Particle characterization in liquids Any liquid contains particles of various size, shape and nature (organic, mineral, insulating,

conducting). Direct microscopic observation reveals that widely different shapes can be present: thick-set particles (with more or less irregular contour) or elongated particles. The largest particles (possibly found in large vessels) reach several tens of microns or more, whereas submicronic particles, obviously omnipresent, are very difficult and even impossible to identify and count in situ.

Particle counting using the following optical method is presently widely in use and considered to be satisfactory. The liquid sample flows in a test cell through which a light beam passes. The variations of light intensity due to the passing particles depend on their cross sectional area. This area is converted to an equivalent circle or ellipse; the particle size may be expressed as the diameter 5 of the circle or as the major axis of the ellipse. Counting is generally done in the cumulative mode for 100 cm 3 of liquid. Figure 1 shows particle-count distributions: curve 1 represents the particle counting in a 200 1 tank used in [3]; curve 2 was constructed to approximate the average slope of the distribution curves in many transformer oils [4].

Let us underline the following features: (i) in large liquid volumes the presence of largc particles is likely; (ii) extremely numerous small particles are present in small volumes.

I0

0

- R , r [4 ]

l I l J l l l l 0

R r[3]

I I I~111

Figure 1. N: number of particles per 1 cm 3 of oil having a diameter > ~i.

(i)

+[~..65 _ ~

5 ~ 3

(ii) (iii)

Figure 2. Field enhancement factors 13 in a uniform field E produced by charged and uncharged sphere and cylinders (l/r = 20). (i) in contact with an electrode; (ii) in bulk; (iii) in the vicinity of an electrode 13 = EA/E increases sharply when d is lower than R or r. Q is the charge acquired by the particle in contact with an electrode.

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392 R. Tobazdon/Journal of Electrostatics 40&41 (1997.) 389-394

It is interesting to have a crude idea of the spatial distribution of particles. From figure 1, we can roughly infer that a 1 cm ridge cube contains 1 single 50 gm panicle, surrounded by 50 particles of 10 p.m, and possibly by 1,000 particles of 1 I.tm. We can deduce that, whatever their size, the particles are "geometrically" far from each other (for instance, the number of 1 p.m particles if placed in a line is: ~1,000= 10 at a 1,000 gm distance). Indeed, their distribution being at random, many panicles come near to others and coalesce. Particles can also come in contact with the walls of the vessel and can remain stuck on them regardless of the nature of the particles or of the walls (conducting, insulating).

3.2. Field-enhancement produced by particles From simple electrostatic considerations we know that acute conducting objects are the

most capable of producing large field intensification in stressed insulating media. Free conducting particles of millimetric size have been shown to reduce thoroughly the electric strength of gas-insulated equipment [5] and also of transformer oil [6]. The predominant role of the particles is to provide field-enhancement which precipitates the breakdown of the full gap.

In a fluid, particles can be free (able to move) or attached to the electrodes. They can acquire a charge either by contact with an electrode or in the bulk of the fluid. The field- enhancement factor [3 depends widely on the shape, the charge and the location of the particle. Figure 2 gives a glimpse of the calculated values of [3 in a uniform field E for a sphere and a hemispherically terminated rod in 3 different situations: (i) in contact with the electrode; (ii) in the bulk of the material; (iii) in the vicinity of one electrode. These data are taken out of references [7] to [9]; other data can be found in [I0].

Notice that the field enhancement at the extremities of the particle is strongly dependent on its shape. As an example, for an elongated rod in contact with an electrode [8]: [3 = l/r + 2, whereas for an elongated prolate semi-ellipsoid [7]: 13 = (1/02 [In (21/r) - 1] l . If I/r = 20, the first expression gives: 13 = 22 while ~ -- 200 with the second.

4. P A R T I C L E S AS T R I G G E R S OF L I Q U I D B R E A K D O W N

4.1. Generalities about liquid breakdown In order for liquid breakdown to occur, a "streamer" must be initiated and propagated

across the gap. Streamers is the term used for the luminous and tree-like figures which issue from a highly stressed electrode. The use of sharp points of calibrated radii has allowed us to reach very high fields, as well as to clarify the mechanisms of charge carriers generation, multiplication by avalanches, and transition to the streamer. On the other hand, from the results in the divergent field, we know that very low mean fields (= 10 kV/cm) are sufficient to propagate negative or positive streamers (for more details, see [ l 1] and references therein).

Whereas with sharp points, characteristic streamer initiation fields could be calculated. An increase in the radius of points or rod radii can lead to a decrease of the calculated initiation field. The purpose of the next paragraph is to show how the presence of conducting particles could explain such a decrease.

4.2. The role of conducting particles in rod.plane geometry The field-enhancement produced by particles has been computed with the Charge

Simulation Program (CSP) of Levin et al. [12]. We used a model presenting an axial

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R. Tobaz~onlJournal of Electrostatics 40&41 (1997) 389-394 393

symmetry: rods hemispherically terminated (radii Rr = 50 ~tm to 10 mm) facing a plane 30 cm in diameter at a distance L = 10 cm. The influence of rather large elongated particles in contact with the rod was investigated: cylinders hemispherically terminated at both ends with l/r = 20 (1 = 1 mm and 0.4 mm); spheres of radii R = 5, 20, 50 rtm were also considered.

/3 20

10

1

lo-Z

xCyl. [= |mm;r--SO~m 22.

%Sphere : 2 0 p r o / ~ / " oS phere: 50#Ln~/ /

- I " . . . . . . 4 . 2

I0 "'~ I R~mm) 10

Figure 3. Field-enhancement factor 13 calculated by CSP for cylinders (l/r=20) and spheres (R=20 ktrn, 50 I.tm) in a rod- plane gap. Rr: rod radius. Gap distance: 10 cm.

V oR:20~m

~ - kE ~ {=400~Ltm; r.=20/~ m ""

~0' I Rr(mrp)

Io "z IO ~ I to

Figure 4. Ec: "apparent" field at the tip of the rod free from particle to which corresponds a field of 1 MV/cm at the tip of spherical or cylindrical particles. R~.: rod radius.

Figure 3 shows the variations of 13 versus Rr. If we suppose arbitrarily that a field of 1 MV/cm is needed to initiate a streamer, this is reached at the tip of the particle for a certain voltage to which would correspond an "apparent" field Ec at the tip of the rod free from particle. The variations of Ec versus Rr are shown in figure 4. Similar shaped curves are obtained with different l/r ratios and with particles of different shapes. The shapes of these curves are reminiscent of those reported in the literature and generally interpreted as a volume effect. From figure 4, we can propose an alternative explanation: for small rod radii, the influence of particles is weak whereas it becomes dominant as Rr is increased. As pointed out previously, spontaneous coalescence of particles exists. It is likely that coalescence will be enhanced under the action of the electric field: the largest particles may attract smaller ones and construct more numerous elongated assemblies as the time of voltage application increases. This could possibly explain why the rigidity is much higher (by a factor of 3 typically) under a lighting voltage than under an ac ramp voltage.

5. C O N C L U S I O N

In large scale tests on rigidity of liquids, both large volumes and large areas are involved. The probability to find large elongated particles increases as the scale increases; the probability to find such particles in the vicinity of the electrodes also increases and thus the probability to facilitate streamer initiation. Since streamer propagation is easy, breakdown is controlled by initiation which is under the dependence of particles. This is a possible explanation to the so-called volume or area effects.

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394 R. Tobaz~on/Journal of Electrostatics 40&41 (1997) 389-394

ACKNOWLEDGMENTS

The author is very grateful to Mr. G. Laulier for performing many calculations with the Charge Simulation Program.

REFERENCES

1. K.H. Weber and H.S. Endicott, Trans. AIEE, 75 (1956) 371 and 76 (1957) 1091. 2. W.R. Wilson, Trans. AIEE, 72 (1953) 68. 3. N. Giao Trinh, C. Vincent and J. R~gis, IEEE Trans. PAS-101 (1982) 3712. 4. T.V. Oomen and E.M. Petrie, IEEE Trans. PAS-102 (1983) 1459. 5. A.K. Cookson, P.C. Bolin, H.C. Doepken, R.E. Wootton, C.M. Cooke and J.G. Trump,

CIGRE, WG 15-09 (1976) 1. 6. F. Carraz, P. Rain and R. Tobaz6on, IEEE Trans. Diel. Electr. Insul., 2 (1995) 1052. 7. N.J. F61ici, Rev. G6n. Electr., 75 (1966), 1145. 8. P.A. Chatterton, Vacuum Breakdown, in Electrical Breakdown of Gases (J.M. Meek and

J.D. Craggs, eds), Wiley, 1978. 9. H. Anis and K.D. Srivastava, IEEE Trans. Elec. Insul., 16 (1981) 327. 10. R. Tobaz6on, J. Phys. D: Appl. Phys., 1996 (inpress). 11. R. Tobaz6on, IEEE Trans. Diel. Electr. Insul., 1 (1994) 1132. 12. P.L. Levin, A.J. Hansen, D. Beatovic, H. Gan and J.H. Petrangelo, IEEE Trans. Elec.

Insul., 28 (1993) 161.