ABSTRACT. This paper presents a study of streamer inception in mineral transformer oil, in point-plane and rod-plane geometry under impulse voltage, The ...
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Lesaint and Top: Streamer Initiation in Mineral Oil Part I: Electrode Surface Effect Under Impulse Voltage
Streamer Initiation in Mineral Oil Part I: Electrode Surface Effect Under Impulse Voltage 0. Lesaint and T.V. Top LEMD - CNRS, 25 Avenue des Martyrs BP 166,38042 Grenoble Cedex 9 FRANCE
ABSTRACT This paper presents a study of streamer inception in mineral transformer oil, in point-plane and rod-plane geometry under impulse voltage, The measurements performed with points and rods over a wide range of tip radii show a marked decrease of initiation fields when the electrode radius is increased. The initiation field is divided by 30 over the investigated range (from 1 p m points up to 2 cm rods). This effect compares fairly well with the “surface effect”known for breakdown voltages under uniform field with large electrodes. Plotting these results together shows the decrease of streamer initiation fields over a very wide electrode surface range (12 decades), proportional to S -’.” ( S: electrode surface area, cm’). These results suggest the influence of electrode surface defects on streamer initiation under impulse voltage.
1
INTRODUCTION
T has been known for a long time that breakdown fields of liquids decrease when the surface of electrodes and/or the stressed liquid volume are increased [1,2,3]. These effects are very important for applications, and are usually attributed to the increase of number of defects able to trigger breakdown when the size of the electrode system increases. Electrode surface defects (such as asperities) produce a “surface effect,” and defects in the liquid volume (such as solid particles) produce a “volume effect.” Usually these two effects are both at work, and depending on conditions, one of them may dominate [l]. With a uniform field under lightning impulse, the breakdown field E, is less dependent on the presence of particles than under ac [l]. In fact, the impulse duration is too short to allow particle motion from the liquid volume up to one electrode in order to trigger breakdown. Thus breakdown can be triggered mainly by surface defects or by some particles adhering to the surface. In oil, E , drops from about 1 MV/cm at S = 0.1 cm2 ( S : electrode surface) down to 0.1 MV/cm with very large electrodes (S = lo5 cm2 ) [l]. With long voltage waves (ac or dc) particles can move and trigger breakdown, and their influence on E, is much larger [l].A “volume effect”can thus be invoked. Breakdown measurements under dc or ac are much more scattered than under impulse voltage.
I
As concerns streamers in liquids, similar effects can be deduced from measurements of initiation voltage, although they were usually obtained with much smaller electrodes and divergent fields (point-plane gaps). Streamer initiation
fields Eiwith sharp points (tip radius of curvature r,, about 1 p m ) are usually comprised in the 5 to 10 MV/cm range. A decrease of E, when the point tip radius rp is increased up to 100 p m was reported in hexane and cyclohexane [4-71. From breakdown experiments under impulse voltage with rounded rod electrodes, Rzad et al. [SI evidenced a
decrease of negative streamer initiation field in Marcol 70 (1.S to 0.5 MV/cm), when the rod radius was increased (0.05 to 2.5 cm). Under uniform field with 2.5 cm diameter electrodes, streamers were observed in various liquids at fields in the 0.3 to 0.5 MV/cm range [91. In this paper, we present a systematic study of such electrode size effects on streamer inception, carried out in both polarities in mineral transformer oil. First, we report the influence of the electrode radius of curvature rp from sharp points (r,, = 1 pm) up to large rounded rods (r,, = 2 cm). These experiments are carried out with impulse voltage in order to obtain results not influenced by the particle content of the oil and space charge effects. These results are then compared to breakdown fields obtained under uniform field with much larger electrodes. In a second paper (part 111, we will present a study of streamer inception carried out in a plane parallel electrode system, with a small calibrated triggering point. This will help us to understand the conditions required to initiate a streamer in mineral oil by a protrusion of p m size.
2
EXPERIMENTALTECHNIQUES
The results presented here were obtained with two complementary experimental devices, that allowed to carry
1070-9878/1/$17.00 0 2002 IEEE
IEEE Transactions on Dielectrics and Electrical Insulation out experiments over a wide voltage range, from 4 kV up to 450 kV.
2.1
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Inception voltage V, (kV)
DEVICE 1, SMALL GAP EXPERIMENTS
A description of the experimental set-up used for small gaps and sharp tips was given in [4,10]. A rectangular high voltage pulse (maximum voltage: 80 kV) was used. Its fast rise time (about 20 ns) allows to minimize the influence of injected space charges during the voltage rise, in order to take correct measurements of initiation voltages [4]. This is important especially for very sharp point radii rp below 10 p m . With larger tip radii the influence of charge injection becomes less important, and proper measurements can also be taken with a slower risetime (down to 1 ps). The test cell used was a point-plane gap with a fixed gap distance d ( d = 6 mm). The plane electrode, 45 mm in diameter, was covered with a polymer sheet (PTFE or polyethylene, 0.8 mm in thickness) in order to prevent the breakdown arc from occurring. Point electrodes of various radii rp (1 p m to 200 p m ) were built with electrochemically etched tungsten wires. The initiation of streamers was detected by high speed visualization with a high magnification device. The optical resolution was about 1 pm. This is necessary since smallest streamers at the initiation voltage can be as short as a few p m in size 141. The commercial transformer oil used throughout these experiments (Voltesso 35) contained 30% carbon atoms in aromatic molecules, 40% in naphthenic, 50% in paraffinic. It was filtered, degassed and dried prior to experiments.
2.2 DEVICE 2, HIGH VOLTAGE EXPERlMENTS Experiments in larger gaps with voltage up to 450 kV were carried out using the system described in [ll]. The high voltage impulse had a 0.4/1400 p s shape and was delivered by a Marx generator. Photographs of the light emitted by streamers were obtained with a gated image intensifier (integral images) or with a streak camera. Light emission from streamers was recorded with a photomultiplier, and transient currents with a fiber optically coupled probe. The test cell had a grounded plane electrode 20 cm in diameter, gap distance d up to 5 cm. No insulating solid was placed on the plane, and breakdown occurred at nearly every shot. High voltage electrodes were steel rounded rods, 0.5 mm to 20 mm in-radius. They were made by machining, and polished to a mirror finish. A 320 ohm resistor was placed in series with the high voltage connection. This resistor, together with the small energy available from the Marx generator (less than 400 Joules), contributed to limit the breakdown energy, and thus the
L
Tip radiusr (pm)
P Figure 1. Inception voltage of positive streamers versus tip radius. Gap distance d = 6 mm.
degradation of the oil and electrodes by repeated breakdown.
3 STREAMER INCEPTION WITH SHARP POINTS (1 p m < rp < 200 p m ) Streamer inception was first investigated in point-plane gaps with a fixed distance ( d = 6 mm) with device 1, using the statistical method described in [41. The inception probability was determined by counting the number of streamers produced during series of 25 shots at a fixed voltage level, and the inception voltage (corresponding to a 50% probability) was obtained. Slightly different results are obtained with either increasing or decreasing voltage increments during measurements. Both methods were used for each experiment, and the reported values of constitute the average of measurements obtained with these up and down procedures.
3.1
POSITIVE POLARITY
Figure 1 shows the variation of inception voltage versus r p . Below some critical tip radius r, (2 p m in this oil), two streamer types (slow subsonic and supersonic filamentary) can be observed, as previously reported in cyclohexane, pentane and other liquids [4,5,71. Streamers initiated at the lowest voltage have a subsonic velocity (between 0.1 and 1 km/s). This mode (called “first mode” in [ll]) resembles that observed in negative polarity in the same conditions. When the applied voltage exceeds some threshold voltage V,, filamentary streamers appear, with a velocity close to 2 km/s (previously called “2nd mode” in [111). Above r,, the minimum voltage required to initiate streamers is higher than the threshold Vp,and hence only filamentary streamers are observed. In the oil studied, the critical point radius (2 p m ) is smaller than in pentane and cyclohexane (resp. 3 pm and 6 p m [41). The minimum propagation voltage V, of filamentary streamers CV, = 8
Lesaint and Top: Streamer Initiation in Mineral Oil Part I: Electrode Surface Effect Under Impulse Voltage
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100
Streamer inception probability (%)I
e
m
-
l
a)
b)
Figure 3. Images of filamentary positive streamers (a: rI, = 2 pm, V = 15kV; b: r,, = 190 p m ; V = 62 kV; d = 6 mm).
Figure 2. Inception probability of positive streamers below the critical tip radius (rD= 1.7 pm, d = 6 mm).
kV) is close to that previously reported in a different mineral oil (7.6 kV at d = 1.6 mm El). Figure 2 shows a typical example of inception probability versus voltage recorded below rc. The variation of inception probability over some voltage range illustrates the statistical character of streamer inception, observed throughout the experiments reported here. On Figure 1, errors bars correspond to 10% inception probability (lower limit) and 90% (upper limit). The recorded shape and velocity of streamers agrees with previous observations carried out in this liquid, for instance in [11,12,13,14], and is described in more details in [151. With sharp points, just above the propagation threshold V, = 8 kV, filamentary streamers are composed of few filaments (Figure 3a). When larger rp are used, the inception voltage increases and the streamer becomes more and more ramified. Eventually, it is composed at high voltage of a very large number of filaments comprised within a nearly spherical envelope (figure 3b). When the voltage is raised the velocity of streamers remains nearly constant, but their stopping distance increases quickly: at 15 kV only few streamers propagated up to the insulating plane, but at 20 kV all reached it. At high voltage (V > 50 kV), total breakdown due to perforation of the polymer sheet occurred frequently.
3.2 NEGATIVE POLARITY In negative polarity (figure 4), increases from about 5 kV ( r p = 1 pm, up to 60 kV ( r p= 200 pm). As previously observed in this liquid [13,14], negative streamers get a roughly spherical shape at low voltage (figure 5a). When the voltage is increased, streamers become more and more elongated (figure 5b), and their velocity increases from 0.1 km/s to 1 km/s. The propagation of negative streamers is less easy than for positives: at V = 30 kV the average stopping distance is about 1 mm, whereas all positive streamers touch the plane at this voltage. The shape and velocity of negative streamers gradually change with voltage and
no steep transition between slow and fast streamers is observed such as in positive polarity at I/= Vp.Also, the basic form of transient currents remains unchanged (it is composed of series of fast impulses [14]). Thus, it is considered that a single streamer type is in fact observed within this voltage range.
3.3 INCEPTION DELAY AND LOCATION In these experiments, the single shot visualization used did not allow us to determine the precise instant of streamer inception. With large points, initiation may occur at other locations than the point apex, for instance at the side of the point as can be seen on figures 3b and 5b. This shows that the electrode surface is not homogeneous. -
^ ^
Inception voltage Vi (kV)
Tip radius r (pn)'b
I00
Figure 4. Inception voltage of negative streamers versus tip radius. Gap distance d = 6 mm.
a) Figure 5. Images of negative streamers (a: r,, b: r,, = 65 pm; V = 35 kV; d = 6 mm).
w
= 1.2
p m , V = 10 kV;
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Initiation sites are probably constituted of surface defects
of sub-micrometer size, not visible with the visualization performed. Streamers were initiated at the same site for some shots, and then changed location.
4
STREAMER INCEPTION WITH ROD ELECTRODES (0.5 mm < rp < 2 cm)
With the large test cell used for measurements with device 2, it was not possible to obtain shadowgraphic images with enough resolution to detect accurately streamer inception. The detection of streamer inception was done via the measurement of the streamer transient current and the associated light emission. Experiments were carried out at two distances d = 2 cm and d = 5 cm. In positive polarity the voltage required for streamer propagation up to the plane was 75 kV and 10.5 kV for these distances [ll].Since inception voltages with r, > 0.5 mm were higher than these values, breakdown occurred at nearly each shot.
As described above, stainless steel rounded rods were obtained by machining, and polished to a mirror finish. Then, they were conditioned by doing series of breakdown experiments (some tens), until a nearly stable breakdown voltage was obtained. This procedure led to a visible degradation of rod electrode surface. Re-polishing the rods produced no positive effect since lower breakdown voltages frequently resulted from this operation, and electrodes had to be conditioned again by sparking. Such effect is consistent with previous observations that sophisticated surface processing does not always lead to an increased breakdown field in quasi uniform gaps [16,17].
4.1
INCEPTION VOLTAGE
v.
Inceution voltage (kV)
1
.
sults obtained at d = 6 mm. The continuity between measurements is good. This is not surprising since the variation of the tip field with distance is small, especially with sharp radii r,. This is illustrated by results obtained in measured at d = 50 positive polarity with rp = 0.1 mm: mm and d = 6 mm are very close. When r, is increased up to 5 mm, t h e difference between m e a s u r e m e n t s at d = 20 mm and d = 50 mm increases. Inception voltages in both polarities are close to each other is about 5% lower in negative polarity).
(v
4.2
Figure 6 shows measurements of inception voltages obtained with these conditions, plotted together with re-
100
Figure 7. Typical recording of voltage, emitted light and transient current corresponding to the inception, propagation and breakdown of a positive filamentary streamer (V = 84 kV, rp = 0.5 mm, d = 20 mm).
d=50mm
0
INCEPTION DELAY
With large steel rods, streamers did not always appear as soon as the voltage reached its maximum value. Figure 7 shows a typical recording obtained with r, = 0.5 mm. The transient current associated to the propagation of the positive filamentary streamer is mainly constituted of a continuous current, some tens of mA in amplitude, characteristic for such streamer mode [MI. The current and light recordings show that propagation starts after some delay ti. During the initiation time ti no current or luminous signals were detected. The total delay to breakdown t , is the sum of inception time ti plus propagation time t,. Some measurements of ti versus voltage I/ were taken in positive polarity with r, = 0.5 mm and r, = 2.5 mm (figure 8). The inception time ti , measured from the onset of voltage rise, decreases over some voltage range down to ti = t , = 0.4 ps (t,: voltage rise time), and even less when the voltage was further increased (i.e. streamers were initiated during the voltage rise).
v,
0.001 0.01 0.1 1 10 Figure 6. 50% inception voltage of positive streamers (open symbols) and negative streamers (black symbols), versus tip radius r,,.
With r, = 0.5 mm at the 50% initiation voltage t, was close to t,, i.e. streamers appeared at the top of the high voltage pulse. Long initiation times were observed only at lower voltage, corresponding to a low inception probability. Thus it was necessary to perform a large num-
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Lesaint and Top: Streamer Initiation in Mineral Oil Part I: Electrode Sugace Effect Under Impulse Voltage
Inception field (MV/cm)
Inception timet, (ps)
Figure 8. Inception delay time t, of positive streamers versus voltage ( d = 20 mm).
ber of experiments to obtain recordings with large ti up to 4 ps. With rp = 2.5 mm the situation was rather different since ti was about 8 ps at V = y , and it was necessary to apply overvoltages to obtain ti = t,.
5 . DISCUSSION: INCEPTION WITH
POINT AND ROD ELECTRODES INCEPTION FIELD VERSUS ELECTRODE SIZE presented on figure 6, From the inception voltages inception fields Eion points and rods (figure 9) were calculated with formula (1) for rp < 0.5 mm [191, and by 5.1
Figure 10. Comparison of inception fields measured in this work (black line, positive streamers) with previous measurements (open symbols: positive streamers, black symbols: negative streamers).
In positive polarity below the critical radius r, = 2 pm, the minimum streamer inception voltage only was considered here, i.e. the inception voltage of slow positive streamers. Inceptions fields obtained at different distances group together to form a single plot. The inception fields E, are close in both polarities, and decrease when rp is increased. Over the investigated range, E, is divided by about 30 and can be fitted by: positive polarity:
Ei= 0.93 rp0,35
(2)
negative polarity:
Ei= 0.78 r;0.35
(3)
E, is expressed in MV/cm and r,, in mm. These variations compare fairly well with those previously reported under impulse voltage in various liquids [4,6,7,8] (figure 10). Despite the different liquids, experimental conditions, and measurements used to obtain these results, the general tendency is identical in these measurements. Under dc in ultra pure cyclohexane, a slight decrease was also recorded, although less marked than under impulse voltage [21].
charge simulation (CSM [20]) for larger radii.
inception field E, (MV/cm)
5.2 COMPARISON WITH BREAKDOWN MEASUREMENTS UNDER UNIFORM FIELD
Radius of curvature r (mm) 0.1
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These measurements can also be compared with the "surface effect" observed in uniform fields under impulse voltage. On figure 11, we have plotted Eiversus the electrode surface area S submitted to the high field. In non uniform field, the area S can be determined by fixing an arbitrary lower bound for the field (for instance 80% of the maximum field), and calculating the electrode area with a field higher than this value. The area obtained is strongly dependent on the arbitrary lower bound chosen. With large points or rods, visualization shows that streamer initiation sites are randomly distributed over an area roughly corresponding to the hemispherical part of the electrode (see figures 3b, 5b). Thus, instead of fixing
IEEE Transactions on Dielectrics and Electrical Insulation Electric ficld (MV/cm) Trinh et al.[l I
10 10 10 10 l o - Electrode area (cm’) Figure 11. Comparison of measured positive streamer inception fields E, with impulse breakdown fields Eb in large uniform gaps [l], versus S. 10-
10.’
an arbitrary lower field value, we have estimated the electrode surface by S = 2rr; in figure 11. On this figure, we have also reported impulse breakdown fields in oil quoted in [I] (obtained with plane parallel electrodes). The agreement is satisfactory, regarding differences in the nature and experimental conditions of these measurements. It is striking to observe the overall variation of E versus S ( E proportional to S-O ”) over a very wide surface range (12 decades). The error bars quoted for breakdown under uniform field [I] correspond to data obtained with either a heavily polluted oil (lowest values), and a very clean oil (highest value). These extreme values differ by a factor of about 2 (under ac, a factor up to 5 can be observed). On the other hand, particles have almost no influence on streamer inception under impulse in point plane gaps. However, a similar average variation of E, and E, versus S is observed (figure 11). This strongly suggests that impulse breakdown with large electrodes results from two superposed mechanisms: i. a basic decrease of E, versus S due to the properties of the electrode surface only. This decrease is observed with small points or rods, but also with larger electrodes and very clean liquids; ii. with large electrodes and polluted oil, particles present on the electrode surface may induce a further decrease of E,.
5.3 TIME DELAY TO INCEPTION A more accurate description of inception could probably be obtained by also considering the inception time ti. In fact, figure 8 shows that the 50% inception voltage measured with rp = 0.5 and 2.5 mm indeed correspond to different electrode area, but also to different inception times ti. Unfortunately, inception times were not systematically measured here and it is not possible to fully describe the variations of E, vs. S and ti. In this work, ti was measured only with large rods (rp > 0.5 mm). In similar conditions, delay times were previously deduced from measurements of time to breakdown
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[SI, and can be directly seen on streak photographs of streamers (rp = 5 mm) [22]. Under uniform field at short distances, Lewis and Ward [23], followed by others [24,25,261, demonstrated the existence of a statistical inception time ti. They reported that ti strongly depends on the electric field, but also on several other parameters such as electrode area S (ti rapidly decreases when S is increased), dissolved gases, metal nature, electrode conditioning. Typical values with S = 21 mm2 can be ti = 1- 10 ps for Ei= 0.4 - 0.6 MV/cm, and decrease very quickly to ti < 10 ns for Ei> 1 MV/cm [24]. Our measurements (figures 7,8) roughly agree with these values. With sharp tips at high field, inception times ti were also reported 16,271. The largest ti reported (up to 1 ps) correspond to low inception probability, and ti decreases very quickly when the voltage is increased. In negative polarity, sensitive charge measurements [27] show that no current is detected before the first streamer current pulse (due to an electronic avalanche) at t =ti. Thus ti represents a statistical “waiting time”. In positive polarity, the same experiments suggest that ti could represent a “formative time”necessary to boil the liquid (see next section).
5.4 MECHANISMS No simple explanation for the decrease of E, versus rp (or S ) can be found. Electrode size effects are also reported in solids, gases and vacuum, and various phenomena can contribute to the observed variations. In gases, Peek’s empirical law of corona onset [28] and theoretical models based on self-sustaining discharge criteria in divergent fields can explain the decrease of E, over a large range of tip radii [29]. In vacuum, the initiation of breakdown is determined by discrete sites of micrometer size, randomly distributed on electrode surfaces, and leading to an apparent area effect more pronounced than in liquids (breakdown fields proportional to S-O 23 are reported [30]). In vacuum, initiation sites able to trigger breakdown are metallic protrusions [31] and insulating inclusions [32]. In liquids, no breakdown criterion such as Townsend’s criterion in gases still exists. However, experiments carried out with sharp tips (some p m ) have permitted to evidence some facts. With a negative point, the existence of electronic avalanches occurring in the liquid phase has been demonstrated under dc in some hydrocarbons [21,33]. The ionization path and the charge of avalanches increase with tip radius (0.5 p m < rp < 10 pm). Avalanches in the liquid phase are independent of hydrostatic pressure (up to 10 MPa), and were also evidenced under impulse voltage [27]. It was estimated that electronic multiplication in cyclohexane becomes negligible below a threshold field close to 2.5 MV/cm. With a positive point, the situation is rather different and less clear [4,27,331. No fast initiating event such as an avalanche is observed, and initiation is affected by hydrostatic pressure [271. Injection currents detected prior to
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Lesaint and Top: Streamer Initiation in Mineral Oil Part I: Electrode S u ~ a c Effect e Under Impulse Voltage
streamer inception during the delay time ti could be responsible for initiation, by producing a local boiling of the liquid. However, even with sharp tips (some pm), energetic considerations show that this mechanism is possible only if current is injected by local small sites, less than 1 p m in size [27]. In both polarities, these mechanisms require electric fields of some MV/cm. Looking at figures 9 and 10 shows that they may happen only with sharp tips, with rp less than say 10 pm. At higher radii, calculated fields below 1 MV/cm are unable to allow such processes, and it is necessary to consider the existence of surface defects producing some local field enhancement to explain streamer initiation. Thus, it is clear that calculated fields in figures 9 and 11 represent “macroscopic” field values necessary to initiate streamers, and that local fields on initiation sites are higher. Local field enhancement factors p up to about 10 are necessary to explain streamer initiation with the largest rods used here, and up to about 100 with very large plane electrodes (figure 11). Photographs of streamers at large tip radii (figures 3 and 5 ) show the initiation of streamers on specific sites different from the point apex. As noted above, in vacuum such sites have been identified [31,32]. They produce a local enhancement of electron emission from cathodes. In liquids, their existence can be also suspected, but unfortunately the techniques used in vacuum to locate, visualize and study such sites cannot be applied. The conditions required to initiate a streamer by a metallic protrusion on a flat surface are studied in part I1 of this study, with the view to understand the contribution of surface defects and particles on the triggering of breakdown.
6 CONCLUSIONS
U
SING point and rod electrodes, it is shown in this paper that initiation fields of positive and negative streamers in mineral transformer oil are nearly identical, and decrease when the size of the points or rods is increased. This effect compares well with the “surface effect” usually observed in breakdown experiments under uniform fields. Putting these results together shows a regular decrease of initiation fields versus electrode surface over a very wide surface range (12 decades). Electrode surface defects and particles (in the case of polluted oil) are probably responsible for these effects.
ACKNOWLEDGMENTS The authors wish to acknowledge Mr. M. Hilaire and F. Montanvert for their contributions to the building of experiments, G. Laulier for his help with field calculations, R. TobazCon for fruitful discussions throughout this work. This paper constitutes an extended version of paper B6 presented at the ICDL conference in Nara (Japan, July 20-25, 1999). Some results also previously appeared in the IEEE Int. Symp. on Elec. Insul. (Arlington, USA, 1998).
REFERENCES [1] N. G. Trinh, C. Vincent, and J. RCgis, “Statistical Degradation of Large-Volume Oil Insulation,”IEEE Trans. on PAS., Vol.101, pp. 3712-3721, 1982. [2] W.R. Wilson, “A Fundamental Factor Controlling the Unit Dielectric Strength of Oi1,”AIEE Trans., pp. 68-74, 1953. [31 K.H. Weber and H. S. Endicott, “Extrema1 Area Effect for Large Area Electrode for the Electric Breakdown of Transformer Oil,” AIEE Trans., pp. 1091-1098, 1957. [4] P. Gournay and 0. Lesaint, “A Study of the Inception of Positive Streamers in Cyclohexane and Pentane,” J. Phys. D: Appl. Phys., 26, pp. 1966-1974, 1993. [SI 0. Lesaint and P. Gournay, “Initiation and Propagation Thresholds of Positive Prebreakdown Phenomena in Hydrocarbon Liquids,”IEEE Trans. on Diel. and Elec. Insul., Vol.1, pp.702-708, 1994. 161 A. Btroual and R. TobazCon, “Propagation et GCnCration des Streamers dans les Ditlectriques Liquides,” Revue Phys. Appl., 22, pp. 1117-1123, 1987. 171 H. Yamashita, K. Yamazawa and Y. S. Wang, “The Effect of Tip Curvature on the Prebreakdown Streamer Structure in Cyclohexane,” IEEE Trans. on Dielectrics and Electrical Insulation, Vol. 5, pp. 396-401, 1998. [8] S. J. Rzad, J. C. Devins and R. J. Schwabe, “Transient Behaviour in Transformer Oils: Prebreakdown and Breakdown Phenomena,” IEEE Trans. EI, Vol. 14, pp. 289-296, 1979. [9] E. 0. Forster and P. P. Wong, “High Speed Laser Schlieren Studies of Electrical Breakdown in Liquid Hydrocarbons,” IEEE Trans. EI, Vol. 12, pp. 435-442, 1977. [lo] 0. Lesaint and P. Gournay, “On the Gaseous Nature of Positive Filamentary Streamers in Hydrocarbon Liquids. I: Influence of the Hydrostatic Pressure on the Propagation,” J. Phys. D: Appl. Phys., 27, pp. 2111-2116, 1994. [11] 0. Lesaint and G. Massala, “Positive Streamer Propagation in Large Oil Gaps, Parts 1 and 2,”lEEE Trans. on Dielectrics and Electrical Insulation, Vol. 5, pp. 360-381, 1998. [12] W. G. Chadband, “On Variations in the Propagation of Positive Discharges Between Transformer Oil and Silicone Fluids,” J. Phys. D: Appl. Phys., 13, pp. 1299-1307, 1980. [13] H. Yamashita and H. Amano, “Pre-Breakdown Current and Light Emission in Transformer Oi1,”IEEE Trans. on Elec. Insul., El 20, pp. 247-255, 1985. [I41 0. Lesaint and R. TobazCon, “Streamer Generation and Propagation in Transformer Oil Under AC Divergent Field Conditions,” IEEE Trans. on Elec. Insul., E1 23, pp.941-954, 1988. [15] T. V. Top, 0. Lesaint and G. Massala, “Streamer Propagation in Mineral Oil in Semi-uniform Geometry,” submitted for publication in IEEE Trans. on DEI (this issue). [16] T. J. Lewis, Progress in Dielectrics, Vol. 1, J. B. Birks and J.H. Schulman eds., Heywood, London, 1959. I171 D. F. Binns, “Breakdown Between Bare Electrodes in Trans-’ former Oil,” Proc. of the 6th. Int. Conf. on Cond. and Break. in Diel. Liq. (ICDL), eds. Frontitres, Dreux, pp. 111-116, Mont Saint Aignan, France, July 24-28, 1978. [I81 P. Rain and 0. Lesaint, “Prebreakdown Phenomena in Mineral Oil Under Step and AC Voltages in Large Gap Divergent Fields,” IEEE Trans. on Diel. and Elec. Insul., Vol.1, pp.692-701, 1994. [19] R. Coelho and J. Debeau, “Properties of the Tip-Plane Configuration,” J. Phys. D: Appl. Phys., Vo1.4, pp. 1266-1280, 1971. [20] P.L. Levin, A.J. Hansen, D. Beatovic, H. Gan and J. H. Petrangelo, “A Unified Boundary-Element Finite-Element Package,”IEEE Trans. Electr. Insul., Vol. 28, pp. 161-167, 1993. [21] M. Haidara and A. Denat, “Electron Multiplication in Liquid Cyclohexane and Propane,” IEEE Trans. on Elec. Insul., E1 26, pp.592-597, 1991. [22] L. Lundgaard, D. Linhjell, G. Berg and S. Sigmond, “Propagation of Positive and Negative Streamers in Oil With and Without Pressboard Interfaces,” IEEE Trans. on Dielectrics and Electrical Insulation, Vol. 5, pp. 388-395, 1998. [23] T.J. Lewis and B. W. Ward, “ A Statistical Interpretation of the Electrical Breakdown of Liquid Dielectrics,” Proc. Roy. SOC., Vol.A269, pp. 233-248, 1962.
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This paper is based partly on a presentation givrn at the XIII‘“ International Conference on Conduction and Breakdown in Dielectric Liquids, Nara (Japan), July 20-25, 1999. Manuscript receiued 16 October; 1999, in final form 6 October: 2001.
