study of streamer inception in mineral oil in-point. A plane and semi-uniform geometry has been pre- sented in [l]. In semi-uniform geometry, inception volt-.
Top et al.: Streamer Propagation in Mineral Oil in Semi-Uniform Geometry
76
Streamer Propagation in Mineral Oil in Semi-uniform Geometry T.V. Top, G. Massala and 0. Lesaint LEMD - CNRS, 25 Avenue des Martyrs, BP 166,38042 Grenoble Cedex 9, FRANCE ABSTRACT This paper presents a study of streamer propagation in transformer oil, with point-plane and semi-uniform geometry. The latter is constituted of parallel plane electrodes, with a thin triggering point of calibrated size. By reducing the length of the point, it is possible to move progressively from a point-plane geometry to a quasi uniform geometry. The propagation of streamers is impeded by the presence of a metallic plane behind the triggering point, that reduces the field on propagating streamers. The effect varies widely according to the streamer type considered. The propagation of negative and fast positive streamers is nearly quenched, whereas slower filamentary positive streamers (usually responsible for breakdown in oil) are less affected. This shows that many results obtained in point-plane geometry can not be simply extrapolated to the more realistic case of uniform field.
1
INTRODUCTION
A
study of streamer inception in mineral oil in-point plane and semi-uniform geometry has been presented in [l]. In semi-uniform geometry, inception voltages are shifted to higher values compare to point-plane gaps, due the electrostatic influence of the plane behind the point that reduces the tip field. The purpose of this paper is to study streamer propagation in this geometry, that simulates fairly well a particle-initiated streamer in a uniform field. In'liquids, few studies were devoted to this subject. In [2], it was reported that in a semi-uniform gap the positive streamer velocity in oil is about 20% lower than in point-plane gap at the same distance, and the minimum voltage for propagation is higher. These effects were presumably attributed to the influence of the plane that reduces the field on the point. In [3], it was also observed that the stopping length of positive streamers below the breakdown voltage is reduced in semi-uniform geometry. The purpose of this paper is to present the results of investigations about streamer propagation in oil in semiuniform geometry, in small gaps (some mm), and also in large gaps (some cm) where faster propagation modes initiated with overvoltages can be more conveniently observed [41.
2
EXPERIMENTALTECHNIQUES
The results presented here were obtained with two complementary experimental devices, identical to devices
1 and 2 described in [l],that allowed to carry out experiments from 4 kV up to 4.50 kV. For small gaps, device 1 was used (rectangular impulses, with 20 ns risetime). The test cell was either a point-plane with a gap distance d = 6 mm, or a semi-uniform constituted of two plane electrodes (Figure 11, 4.5 mm in diameter. One plane was covered with a polymer sheet (PTFE or polyethylene, 0.8 mm in thickness) in order to prevent the total breakdown (arc) from occurring. The point-plane distance d (6 mm) and the tip radius of curvature r,, (1 p m ) were fixed. The point length L and the plane-plane distance D could be adjusted in such a way that d remained constant ( d = D-L = 6 mm). In large gaps, device 2 described in [ll was used (0.4/1400 ~s impulses). The semi-uniform test cell had larger planes (lower plane: 20 cm diameter, upper plane: 10 cm diameter). No solid insulating barrier was used, and breakdown occurred at nearly each shot. The point had a constant radius I;, = 100 pm. The commercial transformer oil used throughout these experiments (Voltesso 35) contained 10% carbon in aromatic molecules, 40% in naphthenic, 50% in paraffinic. It was filtered, degassed and dried prior to experiments.
_$
,Len+
Figure 1. Point-plane and semi-uniform gaps used in this study
1070-9878/1/$17.00 0 2002 IEEE
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 9, No. I , February 2002
77
Propagation velocity (km/s)
33 a ( 1 5kV)
b (30kV) 0
5
10
15
20
25
30
35
Applied voltage (kV)
L
I
Figure 4. Propagation velocity of positive streamers versus voltage (d = 6 mm).
c (25kV) Figure 2. Typical shapes of Znd mode positive streamers in pointplane (a, b) and semi-uniform (c) gcometry ( L = 4 mm, d = 6 mm).
3 STREAMER PROPAGATION IN THE SMALL GAP ( d = 6 mm) 3.1 POSITIVE STREAMERS In positive polarity and point-plane, two streamer types (subsonic slow and supersonic filamentary) can be observed in mineral oil below some critical tip radius rc = 2 p m [l].Streamers initiated at the lowest voltage, called "first mode" in [4], get a subsonic velocity (between 0.1 and 1 km/s), nearly identical to that observed in negative polarity in the same conditions. Above some propagation threshold voltage I(, = 8 kV, filamentary streamers appear (previously called "2nd mode"in [4]). Since only 2"d mode filamentary streamers are able to propagate in semi-uniform gaps, only this positive streamer mode will be considered below. Within the investigated voltage range (up to 40 kV), the faster 3'd and 4th modes observed in large gaps [4] were not observed here. Streamer length (mm)
I
25 kV
The recorded shape and velocity in point-plane gap agrees with numerous previous observations carried out in this liquid, for instance in [3-71. Just above the propagation threshold Vp= 8 kV, streamers are composed of few filaments (1.5 kV, Figure 2a). At higher voltage, the streamer is much more branched and composed of a very large number of filaments comprised within a nearly spherical envelope (30 kV, Figure 2b). At nearly the same voltage in semi-uniform gap (2.5 kV, Figure 2c), much less branches emanate from the point, and streamers resemble those observed at about half voltage in point-plane (Figure 2a). The length 1 of streamers vs time t is presented in Figure 3. On this plot, each value reported is the mean of 20 measurements. Streamers propagate with a quasi constant velocity until they stop at some length I, (for instance 1.5 mm at 1.5 kV). As in large gaps 141, the propagation velocity deduced from 1 vs t plots increases very slowly with voltage (Figure 4), and is nearly identical in point-plane and semi-uniform gaps. When the voltage is raised the stopping distance I , of streamers increases rapidly (Figure Stopping length 1$ (mm)
7 J
30
2'
kV
1.51 1f 0.51
0-
o
Semi-uniform
1 0.-5
i
I .5
2
Time (ps)
2.5
3
Figure 3. Positive streamer length versus time in point-plane geometry ( d = 6 mm).
0
IO
20
30
40
Applied voltage (kV) Figure 5. Stopping length I, of positive streamers versus voltage (d = mm).
78
Top et al.: Streamer Propagation in Mineral Oil in Semi-Uniform Geometry
Streamer length (mm)
0.8
0.2
0 0 Figure 6. Typical shapes of negative streamers in point-plane (a, b) and semi-uniform (c) geometry ( L = 3 mm).
5). The scatter of 1, (indicated in Figure 5 for measurements in point-plane) is usually large, and the values reported are the mean of 20 measurements. In this figure it is considered that streamers that touch the polymer sheet would have propagated up to the metallic plane and induced breakdown without this sheet. Thus a stopping length 1,=6 mm is chosen for them. In point-plane, 1, increases rapidly from the threshold propagation voltage V, = 8 kV up to some voltage at which all streamers touch the insulating polymer sheet. At 15 kV very few streamers propagate to the plane (less than 5%), and at 20 kV all reach it. In semi-uniform gaps, the plots 1, vs V are shifted to higher voltages, and the voltage necessary for all streamers to cross the whole gap increases while L is decreased (30 kV at L = 1 mm). In addition, the minimum inception voltage increases rapidly while L is reduced [l].Thus it is not possible to obtain the complete 1, vs V plot such as in point-plane geometry. At L = 0.5 mm nearly all initiated streamers propagated up to the plane.
3.2 NEGATIVE STREAMERS Typical examples of negative streamer shapes are presented in Figure 6. In point-plane at low voltage, streamers get a "bush-like" shape (Figure 6a), and become more and more elongated and rapid when the voltage is increased (Figure 6b). In semi-uniform geometry, a considerable quenching of. the propagation is observed, since streamers always get a "bush-like" shape (Figure 6c), a slow velocity, and a maximum length not exceeding 1/10 of the gap, even at high voltage and with a long point.
A plot of streamer length 1 versus time t obtained in point-plane geometry is presented in Figure 7. As streamers propagate, their velocity decreases until they stop at some length I,. In point-plane, the velocity measured at the beginning of propagation increases with voltage up to 0.9 km/s (Figure 8). In semi-uniform geometry, the propagation velocity is strongly reduced, from 0.9 km/s (point-
2
1
3
4
time (ps)
5
6
Figure 7. Negative streamer length versus time in point-plane geometry (d = 6 mm).
plane at 30 kV), down to less than 100 m/s at the same voltage in semi-uniform ( L = 3 mm). With short points (below L = 2 mm), the propagation phase was hardly observable and the streamer was reduced to a nearly spherical bubble close to the point, some 10 p m in diameter. In negative polarity and point-plane, it is also possible to obtain a plot of I , vs V (Figure 9). Stopping length versus voltage increases much slower than in positive polarity. With the same gap distance (6 mm) l , is only 1.1 mm at 30 kV, while all positive streamers touch the plane at 20 kV. Within the investigated voltage range, no negative streamer reached the plane electrode. In semi-uniform, the difference is even larger. With L = 2 mm, all positive streamers touched the plane at 26 kV, whereas in negative polarity the length did not exceed 50 p m at the same voltage.
3.3 INITIATION AND PROPAGATION-CONTROLLED BREAKDOWN From the preceding results, it appears that breakdown in a semi-uniform gap mainly results from the initiation
Propagation velocity (km/s)
1 ,
point-plane 0.6-
/
0.40.20
r
I
I
I
1'i-m I
I " " I ' " '
5
Figure 8. Negative streamer propagation velocity at the beginning of propagation, in point-plane and semi-uniform gaps ( d = 6 mm).
IEEE Transactions on Dielectrics and Electrical Insulation
1.2,
Stopping length ls (mm)
I
u.4
.2$
IO
20
40
30
Applied voltage (kV)
50
Figure 9. Negative streamer stopping length I,, versus voltage ( d = 6 mm).
and propagation of filamentary positive streamers. Depending on the point length L , breakdown can be controlled either by the initiation or by the propagation. On Figure 10 we have reported the 50% initiation voltage measured as in [l], and the voltage required to observe more than SO% streamers crossing the whole gap. With long points, is lower than the propagation voltage, and breakdown is controlled by streamer propagation as in point-plane gaps (Le. streamers can be initiated without increases causing breakdown). When L is reduced, much more than the propagation voltage. For L less than about 1 mm, I : becomes higher than the propagation voltage, and breakdown becomes controlled by streamer initiation 6.e. every initiated streamer propagates to the plane and induces breakdown). Due to the quite large dispersion of streamer behavior, the transition from one breakdown regime to another occurs over some voltage range. Typically, all streamers initiated at I/> 30 kV cross the gap, corresponding to a mean field E =V/D about 50 kV/cm, higher than in point-plane geometry (about 33
Voltage (kV)
1
40 30
79
kV/cm). This result agrees with the observations of Rzad et al. [2],that found that the minimum voltage for propagation is higher in semi-uniform field than in point-plane. However, this result holds for streamers initiated in a uniform field, but can not be extrapolated to many other field distributions. It was observed in [8] that in a not very divergent field (a sphere-plane gap with a field enhancement factor less than 4), the minimum streamer propagation voltage is identical as in point-plane gap.
3.4 DISCUSSION
0
60
Vol. 9, No. 1, February 2002
voltage required to reach the plane
1
I
20 10
0 0
2
4
6
8
10
Point length L (min)
12
Figure 10. Initiation and propagation voltages versus point length ( d = 6 mm, r,, = 1 pm).
Previous investigations showed that 2”d mode positive filamentary streamers behave as a rather conductive extension of the electrode, and that propagation depends on the field at the tip of filaments. The results of Figures 2 to S show that the presence of a metallic plane behind the streamer makes its propagation more difficult, as compared to a point-plane gap. The study of initiation shows that the field on a metallic point is strongly reduced by the presence of this plane [l].By a similar effect, the field at the tip of streamer filaments is also reduced, and this explains why their propagation becomes more difficult as the point length L is reduced. However, it is difficult to get a quantitative account of this phenomenon, since the shape of the streamer widely varies and cannot be properly compared to a metallic point. It was previously concluded that the branching of streamer filaments in mineral oil constitutes a very efficient self-regulating mechanism, that explains the nearly constancy of velocity over a very wide voltage range [4]. When the voltage is increased, many side branches (that usually stop at low voltage, Figure 2a) propagate, and the whole structure becomes very branched (Figure 2b). As the number of branches increases, they tend to shield each other, which regulates the field on each filament, and thus the propagation velocity. Conversely, when the field on filaments is decreased by the metallic plane in semi-uniform geometry, the streamer accommodates this situation by becoming less branched (Figure 2c). Thus, the field at the tip of filaments remains high enough to allow their propagation, and the streamer behavior is not much affected. This marked “self regulating” behavior of 2”d mode positive streamers in mineral oil explains why their propagation is only slightly modified in semi-uniform gaps (the velocity remains the same, and the voltage required to cross the gap increases only from 20 to 30 kV at L = 1 mm). On the other hand, the propagation of negative streamers is much more affected. With L = 2 mm, 1, is divided by 30 in negative polarity at 30 kV, while the total propagation voltage in positive polarity increased only by 25% (25 kV instead of 20 kV). No self-regulation of propagation exists in negative polarity. In semi-uniform field and at low voltage in point-plane, negative streamers get a nearly spherical shape (Figure 6). If such streamer is sim-
Top et al.: Strcramer Propagation in Mineral Oil in Semi-Uniform Geometry
80
IO'
. Electric field (MV/cm)
1
1
L=42"mm L=
s,\ \
loo; Figure 12. Negative streamers in cyclohexane in sphere-sphere geometry (gap: 0.8 mm, 40 kV).
l
10-3 o
- 10-2
'
l
O
(
Figure 11. Field E, in front of a growing conducting sphere, during its propagation from the point to the plane ( d = 6 mm, V = 30 kV).
In some experiments such as Figure 12, negative streamers propagated for some time, stopped, and breakdown did not occur in spite of the high mean field in the gap.
4 STREAMER PROPAGATION IN LARGE GAPS WITH OVERVOLTAGES ply compared to a conducting sphere of growing diameter
I , the field E , on it during its propagation from the point to the plane can be calculated by charge simulation (Figure 11). Compared to a point-plane gap, the field E, at the beginning of propagation (l/d = is divided by 4 with L = 2 mm, and 40 with L = 0 mm. This large reduction of E, probably explains why propagation of negative streamers is nearly quenched. A similar quenching of negative streamers was observed in large gaps with sphereplane electrodes [B].
3.5 COMPARISON WITH EXPERIMENTS IN UNIFORM FIELD Under uniform field without triggering electrode [9,10,11], a very high field V/D is necessary to initiate streamers (about 0.5 MV/cm). At such high field in mineral oil, both positive and negative streamers are able to cross the gap [ll]. A qualitative correlation can still be observed between velocity and field calculations such as Figure 11. Under uniform field (i.e. L = O), E,7 is minimum and constant up to about 0Sd, and thereafter steeply increases. In experiments reported in [ll],although the mean field is very high, the velocity of streamers at the beginning of propagation compares with values in point plane geometry at much lower voltage (negative streamers: 240 m/s, positive: 3.8 km/s). Afterwards, velocities in both polarities increase up to about 40 km/s, as they would do in point plane gap at such high voltage. Some experiments were carried out in another liquid (cyclohexane) without triggering electrode (sphere-sphere gap, sphere diameter: 12 mm, gap: 0.8 mm). In cyclohexane, negative streamers are initiated at lower voltage than positives, and can be observed alone (Figure 12). Their "bush-like'' shape is identical to that described in [9,101.
In large point-plane gaps, fast streamers with velocity > 100 km/s can be observed in transformer oil when the applied voltage is higher than the breakdown voltage V, (overvoltages) [4,12,13]. Such fast streamers are also observed without overvoltages when the initiation voltage is very high with rounded electrodes [11,12,14]. In positive polarity and point-plane, it was observed that the streamer average velocity (gap distance d divided by time to breakdown t , ) varies as in Figure 13 [4]. At the 50% breakdown voltage V,, a unique streamer mode leads to breakdown (2nd mode, velocity = 2 km/s), similar to that described above. Above V,, a faster mode appears at the beginning of propagation (3'd mode, veloc-
100
80
Average velocity (km/s) 0 X
L=10mm semi-uniform L-15"
60
40
20
0
Figure 13. Average positive streamer velocity versus voltage ( d = 10 cm, 0.4/1400ps impulse).
IEEE Transactions on Dielectrics and Electrical Insulation
mn .
Vol. 9, No. 1, February 2002
82
Es (kV/cm)
-1-
u A
500 -
x 0
L = 0 mm (plane-plane) L=Smm L=10mm point-plane
400 : 300 1 200 ;
0
0.2
0.4
0.6
lld
0.8
1
Figure 14. Electric field E, in front of a "spherical" streamer, versus reduced streamer length l/d. (d = 10 cm, V = 352 kV, upper plane diameter: 10 cm, lower: 20 cm).
ity -- 10 km/s). Above a critical voltage (acceleration voltage Vu>,the average velocity grows quickly. Streamer still start as a 3'd mode streamer, but instead of slowing down to a Znd mode, it switches to a much faster 4th mode (velocity > 100 km/s), constituted of only 1 or 2 bright filaments. This fast 4'h mode always follows a 3'd mode, and the transition from a 2"d mode to a 4th mode was not observed [4,12,131. Figure 14 shows a calculation of E, similar to Figure 11, with parameters representative of streamers between
V, and V,. The hypothesis of a "spherical" conducting streamer at the beginning of propagation was validated by charge measurements and calculations [4]. In point-plane from 0 to 0.2d, E , is very high such as velocity (3rd propagation mode). Then E, passes through a minimum, and is nearly constant from 0.3d to 0.8d. This is correlated to a lower propagation velocity (2nd mode).
In semi-uniform geometry, the streamer field at the beginning of propagation is reduced (Figure 14). This is correlated to the suppression of the 3rd streamer mode observed in experiments. Figure 15 shows examples of streak images obtained at the beginning of streamer propagation with the same distance and voltage, in semi-uniform (a) and point-plane (b) geometry. In point-plane geometry (b), a luminous fast 3rd mode streamer first propagates for about 2 ps, and later transforms into a slower 2"d mode. In semi-uniform geometry (b), the first 3'd mode is suppressed and the streamer propagates as a 2"d mode. It becomes identical to streamers observed in point-plane geometry at about half voltage [4]. This is in qualitative agreement with calculations that predict a large reduction of the field E,. A consequence of the suppression of the initial 3'd mode is that acceleration of streamers at V = V, is not any more observed in semi-uniform geometry. In point-plane, acceleration is correlated to the appearance of fast 41h mode streamers (Figure 13). In semi-uniform geometry, the sup-
Figure 15. Streak images of positive streamers ( d = 10 cm, V = 352 kV). a: semi-uniform geometry ( L = 10 mm), b: point-plane.
pression of the initial 3'd mode makes that the 4'h mode also disappear, since the transition from a 2"d to a 4'h mode is never observed. This effect is seen on Figure 13. In semi-uniform geometry at d = 10 cm, the acceleration of streamers was not any more observed with the available maximum voltage. The average velocity recorded at high voltage (2 to 3 km/s) is typical for 2"d mode streamers. Figure 16 shows photographs of streamers obtained at I/ > V,. In point-plane (a) streamers already accelerated (fast filamentary 4'h mode), whereas in semi-uniform (b) slower and very branched 2"d mode is observed. At shorter gap distances (Figure 171, an acceleration was observed, but at higher voltage than in point-plane. The acceleration voltage increases when the point length L is decreased (Figure 18). Measurements of the streamer maximum charge Q, were also taken (Figure 19). The charge Q, is the streamer charge measured just before breakdown [4]. The sudden drop of Q, at V = V, correlated to the appearance of monofilamentary 4'h mode [4] is observed on all plots.
Figure 16. Typical images of streamers obtained with a large overvoltage in point-plane (a) and semi-uniform (b) geometry ( d = 10 cm).
Top et al.: Streamer Propagation in Mineral Oil in Semi-uniform Geometry
82
Average velocity ( k d s )
35
Charge (nC)
2000
II
I-
30 Point-plane L=5mm L= 10” L=lSmm
0
25
A
X
20
0
15
‘“1
500
5
50
d=5cm*
150 200 250 300 350 400 450 Applied voltage (kV)
100
Figure 17. Average streamer velocity versus voltage in point-plane and semi-uniform geometry ( d = 5 cm).
5 CONCLUSIONS
T
H E experimental results presented in this paper show the influence of the electrode geometry on streamer propagation in small and large gaps,.It is observed that streamers initiated in the vicinity of aplane electrode behave in a quite different way as compared to those propagating from a point electrode. The plane electrode acts as an electrostatic shield that reduces the streamer field, and hence impedes its propagation. Field calculations performed by modeling a streamer by a growing conducting sphere are in qualitative agreement with experiments. They show the very important influence of the streamerplane distance L , also observed in experiments. The streamer is mainly affected at t h e b e g i n n i n g of propaga-
tion. As concerns practical consequences, it is concluded that many phenomena observed in point-plane geometry cannot simply be extrapolated to the more realistic case of uniform fields. Negative streamers initiated in the vicinity of a plane electrode are quenched, and do not propagate any more. Initiation of fast positive streamers (3rd and 4Ih modes) with overvoltages is shifted to higher voltages. Jf
Acceleration voltage (kV)
500
II
4
0
100
L=15&
L=lOmm
200 300 Voltage (kV)
400
.
500
Figure 19. Streamer maximum charge Q,, versus voltage (d = 5 cm).
we extrapolate results of Figure 18 to the realistic case of a streamer initiated at the surface of a plane electrode (or at the extremity of a small particle L
