238
NON-UNIFORM FIELD BREAKDOWN OF GASES
J.-F. Drapeau, G. Olivier, Y. Gervais
Department of Electrical Engineering
Ecole Polytechnique de Montreal
P.O. Box 6079, Station A , Montreal, Canada, H3C 3A7
INTRODUCTION
In
1977, a new law was proposed to describe the
uniform field breakdown of gases: a simple empirical
relation enabled the prediction of breakdown voltage of
pure gases. Later, this approach was successfully applied
to gas mixtures.
This paper presents an attempt to
extend this method for evaluation of breakdown voltage
under non-uniform field conditions.
THE EMPIRICAL BREAKDOWN L A W
Past
works have clearly shown that, under uniform
field condition, breakdown voltage of gases can be satisfactorily described by a simple empirical law:
U
- fiG*
do* t
where: U is the dc or peak ac breakdown voltage in kV, d
is the gap length in millimeters, 6 is the molecular
density in mole per liter, and G, 0 , t constitute a set
of experimentally determined coefficients which characterizes each gas.
In the case of binary gaz mixtures, the knowledge of
the coefficients of individual gases is sufficient to
predict the behavior of the mixture [3]:
where U1 and U 1 are the breakdown voltages of the
individual gases which may be calculated from equation 1,
and n2 is the concentration of gas 2 in p.u.
Up to now, as long as the field uniformity is maintained, these equations appear to apply over an extremely
239
wide range of experimental conditions and for all the
gases tested in laboratory or for which data was available in literature. Furthermore, it was recently shown
that equation 1 is consistent with Townsend's theory [ 4 ] .
EXTENSION TO NON-UNIFORM FIELD CONDITIONS
Based on the knowledge of uniform field breakdown,
two assumptions were postulated for non-uniform field
behavior. First, it was suggested that the configuration
of the electric field, if not too distorted, does not
affect the molecular density term (coefficient G) of
equation 1. This hypothesis was based on the fact that
the breakdown mechanism does not change as long as the
maximum stress to the mean stress ratio does not exceed
five [5]. Secondly, it was proposed that all gases should
have a similar behavior under identical non-uniform field
configuration. Unlike the first hypothesis, the second
one was not sustained by experimental evidence.
Two different electrode configurations where chosen
for the experimental work: small, 1.25 inch in diameter
sphere electrodes and sphere-to-plane electrodes consisting of a 4 inch diameter disk and a 1.25 inch sphere.
The cell used, described in [l], enables tests to be
carried out with pressure ranging from 5 to 700 kPa and
gaps up to 60 mm. The high voltage generator is limited
to 150 kV rms. Seven gases were tested: nitrogen, carbon
dioxide, helium, argon, freons 116, 115 and 12.
Figures 1 to 4 and table 2 present a partial but
representative sample of the data recorded.
EFFECT OF PRESSURE
To infer the hypothesis that the electric field configuration does not modify the exponential relation
existing in uniform field between breakdown voltage and
molecular density (pressure), the basic aspect of the
disruptive voltage plots must be preserved. Therefore,
the breakdown voltages, for a given gap length, must
remain straight lines when plotted on logarithmic scales,
and the slope of these lines must conserve the same value
than in uniform field conditions. It has to be remembered
that this slope corresponds to the G coefficient. Experimental results confirmed this hypothesis. Figures 1 and
3
clearly
show that the first condition is well
240
respected. In these figures, there is no visible differences between data obtained in uniform field (curves 1
and 2) and data obtained with gradually distorted fields.
Table 1 summaries the value of the G coefficient obtained
in uniform field conditions [ 1 , 2 ] and in non-uniform
field with sphere-to-sphere and sphere-to-plane electrodes for various gases. This table clearly indicates
that G is constant and, therefore, is not affected by the
field configuration. Except for freon 12, experimental
dispersion easily explains the minute differences found
in this table. In the case of freon 12, severe decomposition occurred after only several breakdowns.
TABLE 1: Values of coefficient G in uniform and nonuniform field configurations
EFFECT OF GAP LENGTH
The second hypothesis suggested that, for a given
field configuration, the reduction of breakdown voltage,
expressed as a ratio of the actual breakdown voltage to
the uniform field value, should be independent of the
nature of the gas. Figure 5 clearly shows that this
assumption was no supported by experimental evidence.
The different gases behave very differently. The first
group of gases (nitrogen, carbon dioxide, helium and
argon) shows a similar pattern of breakdown voltage
reduction with gap length and almost supports our
hypothesis. However, further tests with several freons
shown a completely different pattern.
These results
indicate that other factors than molecular density and
gap spacing affect dielectric withstand in non-uniform
field .
24 1
Nevertheless, data obtained in non-uniform field,
can still be described by equation 1:
where G has the same value than in uniform field, and 0'
and t' have different values that are valid only for only
one electrode configuration. Table 2 gives values of 0'
and t' for the two electrode configurations studied.
These coefficients are valid only for the straight lines
appearing on right half-planes of figures 2 and 4, where
the field configuration is non-uniform.
In the fuzzy area between uniform and distorted
fields, both equations 1 and 3 do not apply; the breakdown voltage evolves smoothly from one mode to the other.
In that area of quasi-uniform fields, equation 1 and 3
overestimate the disruptive voltage for the various gases
with a maximum error varying from 4 to 12 percent.
CONCLUSION
In non-uniform field conditions, the exponential
relation existing between breakdown voltage and molecular
density (pressure) is not affected. However, it was found
that the different gases d o not have the same behavior
under non-uniform field configuration. The breakdown voltage is affected by the nature of the gas. Particularly,
the disruptive voltage of freons is greatly reduced by
the non-uniformity of the field.
REFERENCES
[l] OLIVIER G., GERVAIS Y., MUKHEDKAR D., "A New Approach
to Compute Uniform Field Breakdown of Gases", IEEE Trans.
on Pow. App. Syst., Vol. PAS-97, No.3, pp. 969-976.
[2] OLIVIER G., DAIGNEAULT G., GERVAIS Y., "Uniform Field
Breakdown of Fluocarbons and Other Gases", IEEE 1984
CEIDP Annual Report, pp. 358-363, 84CH1994-3.
[3] DAIGNEAULT G., OLIVIER G., GERVAIS Y., GALARNEAU A . ,
"Uniform Field Breakdown of Gas Mixtures", IEEE 1985
CEIDP Annual Report, pp. 130-136, {I 85CH2165-9.
[ 4 ] DAIGNEAULT G., OLIVIER G., GERVAIS Y., "Uniform Field
Breakdown of Gases, Revisited", IEEE 1986 CEIDP Annual
Report, pp. 316-320, {/ 86CH2315-0.
[ 51 ALSTON
L.L. , "High Voltage Technology", Oxford
University Press, London, 1968, pp. 17-54.
242
I
I
hV
917054
NITROGEN
J
z
1
zw
CI
0
6
v
0)
m
100
m
-0
c
C
z
50
1: 10 mm
2 15 mm
3: 20 mm
4: 25 mm
5: 30 mm
6: 35 mm
7: 40 mm
0
U
Y
m
9)
L
m
8: 45 mm
9: 60 mm
10
/
01
I
L
0.1
1
Molecular density (rnole/liter)
Fig. 1 : Constant electrode spacing curves for nitrogen
LV
P
200
I
7
5
0
CI
0
6
W
9)
w
100
m
-0
c
C
%
50
0
U
Y
m
f
m
NITROGEN
/
"
Q
10
6:
7:
8:
A
D: 1.25'
9
0.020
0.041
0.061
0.082
0.102
0.123
0.143
0.163
0.184
m/l
m/l
m/\
m/l
m/l
m/l
m/l
m/l
m/l
L
0
50
Gap length (rnrn)
Fig. 2 : Constant density curves for nitrogen
10
243
kV
FREON 116
7
9 1
6
5
PW
4
a
2
1
50
5rnrn
7.5 rnrn
1:
2
3: 10 rnrn
4: 15rnrn
20 rnm
5
6 30 rnrn
7 40 rnrn
8: 50 rnrn
9 60 rnrn
10
I
0.1
0.05
aoi
Molecular density (mole/liter)
Fig. 3 : Constant electrode spacing curves for freon 116
LV
. . . .
. ..,
.
6
200
.
5
4
loo
50
10
10
Gap length (mm)
Fig. 4 : Constant density curves for freon 116
100
244
TABLE 2 : Coefficients G.0.T
in uniform and non-uniform
fields
1.0
I
0.8
I
10
I
50
Gap length (mm)
Fig. 5 : Non-uniformity breakdown voltage ratio
100