4354
IEEE Transactions on Electrical Insulation Vol.. EI-17 No.5, October 1982
ON
CALCULATION OF BREAKDOWN VOLTAGES OF MIXTURES
OF ELECTRON ATTACHING GASES
R. S. Nema, S. V. Kulkarni, and E. Husain
Department of High Voltage Engineering
Indian Institute of Science
Bangalore, India
ABSTRACT
In this paper
breakdown tests
the analysis
of CC12F2,
we
report
on
mixtures
of
dc
SF6,
C-C4F8, 2-C4F8, N2, C02, CF4, CHF3, and
1,1,1-CH3CF3 gases on the basis of the NKH
formula Vmix=k(pd)aNbUC developed by us
earlier for the binary mixtures of SF6 with
air, N2, N20, and CO2.
It
is shown that while
a and c have the values 0.915 and 0.850
tively as earlier, k and b depend on the com-
respec-
ponent gases.
There is a good agreement between the calculated values on the basis of
the formula and measured values reported in
the literature.
TABLE 1
INTRODUCTION
Heavy gases such as fluorine, chlorine, etc., belonging to the seventh group of the Periodic Table,
are known to have considerably higher breakdown
strengths compared to air, N2, and CO2 under similar
experimental conditions beacuse of the electronattaching property of these gases. Due to the high
cost of SF6, there is a considerable amount of experimental work in progress [1] to find alternative gases
and gas mixtures which may have comparable breakdown
strengths at reduced cost. It has also been shown [2]
that CHF3, CF4, and 1,1,1-CH3CF3 have electronmoderating qualities resulting in improved properties
when mixed with SF6 or any other electron-attaching
gases. Quite a few studies [2,3] are available reporting the static breakdown voltages of these gases
and gas mixtures in uniform and non-uniform filed conditions for different mixture ratios tested at different pressures. As before, we have analyzed the data
of [1-3,6] and shown that the NKH formula developed by
us earlier [4] can be applied to these gases and their
mixtures to predict the breakdown voltages and thus
putting the measured data in a handy form so that it
is useful to practicing engineers.
ANALYSIS AND RESULTS
The breakdown voltage of the gases under consideration relative to SF6 are shown in Table 1. The measurements [1-3,6] indicate that the breakdown voltage of a
mixture containing an electronegative gas is related to
its breakdown voltage. The available data also show
that any correlation between the mixture proportion and
breakdown voltage obtained from measurements at a
Breakdown Characteristics of Gases
Gas
RBDV
S?6
CC1 2F2
1
c-4 8
1*22
2-C04F8
1.54
1.05
,l,l-CH3CF3
CHF3
Gas
RBDV
CF4
0-39
0.36
C02
N2
N20
0*4
Air
0*39
0'41
0*27
0°39
RBDV = Relative Breakdown Voltage
particular pd (pressure times electrode gap) is also
true for other pd values. Earlier [4] it has been
shown by us that a simple mathematical expression fits
such data for computing the breakdown voltages. The
expression is given as
VMI&x
. = k
(pd)a Nb Uc
(1)
which gives Vmix in V, when pd is in kPa-cm. N is the
percentage of the electronegative gas in the mixture
and U is the field utilization factor. The values of
constants a and c are 0.915 and 0.850 respectively,
whereas k and b depend on the component gases. The
0018-9367/62/ 1000-0434$00. 75 (D 1982 IEEE
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Nema, Kulkarni, and Husain: Calculation of breakdown voltages of mixtures of gases
above formula can be used to a minimum pd value of
1.0 kPa*cm and a minimum N of 5%. Eq. (1) is valid
in uniform fields when U=1 and in non-uniform fields
when the non-uniformity is obtained by calculating
a field utilization factor U in case of hemispherical
point-plane or coaxial cylindrical geometries [4,7].
In the present case the measurements are available in
coaxial cylinders only; U is therefore calculated
from
U=
R.
-IL
R -R.
0
Ro
c-
where R. and
1
R
ln R.
R
(2)
400,
*
-300
__
-
1341 (pd)
0%
$,I'
=200
l13
-
-
/
L.
0.9F 1 5
Measurements [1] show that the breakdown voltage of
a mixture containing CC12F2 is a certain fixed percentage of the breakdown voltage of CC12F2 itself. It can
also be seen that any correlation between the mixture
proportion and the breakdown voltage obtained from
measurements at a particular pd is also true for other
pd values. On the basis of this information, the
breakdown voltage of mixtures of CC12F2 with N2 can
be put into a formula (Appendix 1) such as:
(N)02'
200
-
o'
-~~~~~~~
'9
_
4
100
_
_
_
_
_.
Eqs. (3) and (4) can be combined into a simple expression to give the breakdown voltage of the mixture
V .
mI-x as
=
510(pd)0915
I
I
0
20
I
40
_
_
_
_
_
_
_
_
_
_10
_
~~~I60
_
_
_
I
Percentage of CCL2F2
(a)
1010
80
4001 L
Measured [1]
Calculated
CCL2F2* Co2
Pd SO0 kPa-cm _ -
*
-
Go
-
--
300
-
,
400
a
40
_-
C200
/
31
0
/
_
0_
.
'-
-
0
.
__-
0
.
I
CJ.
m* 100
300
200
-.
-
.1000
(4)
where M gives the breakdown voltage of CC12F2+N2 mixture as a percentage of the breakdown voltage of
CC12F2 under similar conditions and N is the percentage of CC12F2 in the mixture by volume. Thus if the
relation is to be used for 400 kPa-cm, the breakdown
voltage for CC12F2 from Eq. (3) is obtained as 322.5
kV. In order to find the breakdown voltage of
CC12F2+N2 mixture in which CC12F2 is 40%, N is substituted as 40 in Eq. (4) and M is obtained as 82.52.
Again 82.52% of the breakdown voltage 322.5 kV of
CC12F2 is found to be 266.13 kV as the breakdown voltage of the mixture which agrees very well with that
published in the literature [1]. Calculated and
measured [1] values of breakdown voltages of CC12F2+N2
mixtures are compared in Fig. 1(a) and the agreement
between them is good.
V .
mllx
300
(3)
Equation (3) gives VCCl p in volts when the product
22
pd is in kPa cm. A comparison of the calculated values
from Eq. (3) and the measured data [1] show a reasonable agreement with the error not exceeding ±8%.
M = 38.03
400
_
We have used the breakdown voltages of CC12F2 in
uniform fields from the measurements of Malik and
Qureshi [1] to formulate the Paschen's curve in the
pd range of 100 to 500 kPa- cm. A simple mathematical
expression has been found to fit the data (Appendix 1)
to compute the breakdown voltage of CC12F2 and it is
written as
=
Fa500kPa-cm
_.
METHOD OF ANALYSIS
vCC12F2
- -
-
.
Go
a
cylinders respectively.
* MeGlued [iJ-
_~~~~~~~1
_
0
are the radii of inner and outer
Measured Nl
Calculated
CCL2F2+N2
---
-
435
NO.21
of
0
20
II
40
60
Percentage of CCl2 F2
(b)
so
100
Fig. 1: Measured [1] and calculated values of static
breakdown voltages in mixtures of (a) CCZ2F2+N2
and (b) CCZ2F2+C02 in uniform field
k, a, and b in Eq. (1) are 510, 0.915, and 0.21
respectively.
Similar computations can be made for any other electronegative gas and its mixtures with other gases and
the values of constants k, a, and b can be obtained
as shown in Table 2.
(5)
which gives Vmix in V when the product pd is in kPa*cm.
Thus from the above, it can be seen that the values of
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436
IEEE Transactions
on
Electrical Insulation Vol. EI-17 No.5, October 1982
TABLE 2
MIXTURES OF ELECTRON MODERATING GASES
Constants to be used in the NKH Breakdown
Formula given as Vmi (in V)=k(pd)aNbUc
GAS
k
8P6+air
502.4
3F6+N2
SF6+C02
502.4
330-0
b
SP6+
527.7
0-210
0 *210
0*300
0*210
250-0
0*338
S3F *1,1,1-CE3CF3
566*0
0*160
510*0
0*210
SF6+N20
HF3
3]?6+CF4
CC12Y?2+2
F
2 2
°2
2-C4F68+2l,-CH3CF3
2-C4F8+l9
c-C4F8+CF4
c-0 4F8+N2
c-C4F8tCHP3
c-C 4F8+l,1,1-CH3CF3
250.00*338
335-0
370*0
640 *0
0*300
0*370
Lnni
0250
250-0
0*398
310-0
0"370
310*0
0* 370
540*0
0*250
*
_
Measured [6]
Calculated
SF6+ CO2
V30110
Pds1.0kPa-cm
, ~~~~~
~300__-
0
-20
(1) Always a=0* 915 and cu0o850
2 Equation (1) is applicable when pd 1l
kPa-cm, N> 5.
(3) N=100 gives breakdown voltage of the
first gas.
4) U=l for uiniform fields.
5) In non-uniform fields
(1i) For co-axial cylinders[ 6] -eqn(2)
(ii) For a hemispherical point (radius
=R and plane[7] having a gap d)
[0o6162(d)0*9716+1.l377
U when 0<d8R
Studies on mixtures of electron attaching gases indicate that the contribution of electron attachment
towards inhibiting breakdown has been nearly optimized. Recently [2,3] it has been shown that mixtures of electronegative gases like SF6 with one or
more electron moderating or thermalizing gases serve
to slow down free electrons for more efficient capture, thus improving the breakdown voltage of mixtures. The gases used for this purpose are polar
gases like l,1,1-CH3CF3, CF4, and CHF3. We have
analyzed the breakdown data [2,3] on mixtures of SF6,
c-C4F8, and 2-C4F8 with N2, l,l,l-CH3CF3, CF4, and
CHF3. These measurements have been made at pd values
from 8.454 to 63.437 kPa-cm in uniform field and at
126.65 kPa.cm and 556.73 kPa*cm in case of nonuniform fields using coaxial cylinders of inner and
outer radii of 0.75 and 2.0 cm respectively.
a
0
10 _
,
_ _
0
./
m9*10
__
~ _--100
/
_
~
-0
_
MIXTURES OF CC12F2+N2, CC12F2+C02 AND
_
140
20
60
100
80
Percentage of SF6
]1j
40.
_ _ _
~200
Fig. 2: Measured [6] and calculated values of
breakdown voltages in mixtures of SF6+C02 in
uniform fieZd
SF6+CO2
Breakdown data on CC12F2+N2, CC12F2+C02, and SF6+C02
is available from the recent measurements of Malik
and Qureshi [1,6]. These measurements were carried
out using polished, plane-plane stainless steel electrodes and direct applied voltages for a pressure
range of 50 to 250 kPa with a fixed gap of 2.0 cm.
CC12F2 has slightly higher breakdown strength than
SF6. The uniform field breakdown data of CC12F2 and
SF6 shows that it follows from Eq. (1) when U=1,
N=100 and k and b are as shown in Table 2. Further
analysis of the breakdown voltages of mixtures listed
above shows that Eq. (1) gives reasonably good agreement when N varies from 5 to 100%. The measured
[1,6] and calculated values are shown in Figs. 1 and
2.
> 60
a;
* Measured [2]
---Calculated
SF6+ CF4
Pdx631437kPa-cm_
._ -
>040
-
c
-20
ax
-
_
~~46-520O_
' ._
._
- - - ~0~ - -
-
_,_.
_
. -
20
29-601.
-21.146
*
-_-~
-
_. __
,38062_
_
- -_-
- - - ,-- -
/.0
-
-
Percentage
_
54978
-
_ ~~ _ _
.-
0
static
_
-
_
_
60
of
-
-
-
SF6
_
80
_
_
2
-
6
100
Fig. 3: Measured [2] and calculated values of static
breakdown voltages in mixtures of SF6+CF4 in
uniform field
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Kulkarni,
Nema,
and Husain: Calculation of breakdown voltages of mixttures of
4357
gases
remaining constant. The mixtures
Table 2; a and
of these gases show relatively a higher breakdown voltage compared to the mixtures of SF6 under similar
conditions. Breakdown in 2-C4F8+N2, 2-C4F8+1,1,1CH3CF3, c-C4F8+CF4, c-C4F8+CHF3, C-C4F8+N2 and
c-C4F8+l,l,l-CH3CF3 shows that Eq. (1) gives reasonably accurate values of breakdown voltages as shown
in Figs. 6-9.
c
* Measured [2]
---Calculated
60~
Pdm63*437kPa-cm 54l978
SF6+ CHF3
0
0%
a
,A-~-
3:
-'
-
aX 20
t
a#
0
_--
_ -p. -
-
- -
~
___~--
- -
-@
- -~~~~
-
IV
46.520
_--
-
O'- 40
..~
- - - -,
38-062
- - -
29604
MeasuredD2
.146
- -I~~~~21
x
.
51
.
60
40
20
100
80
Percentage of SF6
(a)
measured
[3]
-.-.-Calculated ,
80
0
Uniform field
Calculated ,
s0
Non-uniform field
5F6+1,1,1- C:H3CF3
S 60
at
63-437
x~~~
4-
,._
_,-
.3.
1
300
.1
a2o
_
x
,
-2_
_-
12-687
010o
x
20
'0i00
Go
I-o
x
I
_
-
0
Percentage of SF6
s0
-100I
Fig. 5: Measured [2,3] and calculated values of
static breakdown voltages in mixtures of
SF6+1, 1,1-CH3 CF3 in uniform and non-uniform field
and R0=2. 0 cm)
(coaxial cylinders, RI=O. 75
Pd:126-65kPa-cm
_
5o
40
x
0
CD
21-146
-
_, _-
x-
3
38 062 _ _ _
Pds 556-73kPa-cm _
.G. 200
0
_
-
13]
---Calculated
SF6+ CHF3
0
L46-52
__--29-60L
', '
,
20
m
_-~
-*
,
Measured
54,978__
_-
0
c0
x
Pd126-65kPa-cm
x
x
x-
x
_
I
20
_
_
_
_
_
_
_
_
cm
a
60
40
Percentage of SF6
(b)
s0
-
I100
Fig. 4: Measured [ 2, 3] and calculated values of
static breakdown voZtages in mixtures of SF6+CHF3
(a) in uniform field and (b) in non-uniform field
(coaxial cylinders, R.=O. 75 cm and R =2. 0 cm)
0
Pdx126*6SkPe.cm
120
a#
0%
0-
0 s0
CX
-
Mixtures with SF6
The breakdown voltage of SF6 at different pd can be
obtained from Eq. (1) in uniform field conditions
when U=1 and N=100 with k and b values shown in Table
2. Analysis of the relative breakdown voltage ratios
in SF6+CF4, SF6+CHF3, and SF6+l,l,l-CH3CF3 shows that
Eq. (1) yields breakdown voltages of these mixtures
in uniform and non-uniform fields with the values of
k and b also shown in Table 2. It is to be noted
that the values of a and c remain constant in all
cases.
The calculated and measured [3] values have
been plotted in Figs. 3, 4 and 5 and are in good
agreement.
Mixtures with c-C4F8 and
2-C4F8
a
81
X.x
./'
40
GI
co
I
d
2-
e
x 2-C4 F t 1,1,1-CH3 CF3
-2- C,4FS
4-1N2
Measured (3]
-.--2-C4, FS+1,.1 -CH3CF3 Calculated
I
I
I
1 '
u-.I
40
20
80
~0
Percentage of
2-C4FS
100
Fig. 6: Measured [3] and calculated values of static
breakdown voZtages in mixtures of 2-C4F8+N2 and
2-C4F8+1,1,1-CH3CF3 in coaxiaZ electrode systems
(R =0. 75 cm and R~~~0=2. 0 cm)
c-C4F8and 2-C4F8 have higher dielectric strengths
than SF6 and their breakdown voltage is related to pd
by Eq. (1) with appropriate values of k and b from
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438
IEEE Transactions on Electrical Insulation Vol. EI-17
No.5,
80.
* Measured [2J
---Calculated
-X 60
*
Pdr 63-437kPa-cm
_.
~_ ~54-978__
c-C4F8+ CF4
a;
CY%
-
_
_o
0
3:
--r
*_
~-. -,
:0
_
__
0
a.20
296041
r
(I
-- _ -
- - -.
__
-1
12-667
I
I
I
I
20
40
60
80
Percentage of c-C4F6
-
u -,
-0
100
-
__-.--
-
S~~~~~~~J
-
38-062 _ _
~
29-604
- , ' --21-146
,-_
20
20
-
- -
.', -'- _-
:0
Go
L
,
o
,'-
0
.46520___-
, _
-
46-520_
.
54 978
*
. 60
-
a
.-
m
Pdu631437 kPa-cm
Measured(2]
----Calculated
c-C4F+ CHF3
-,
October 1982
-,'~
_-12
-.-
20
40
687
60
Percentage of C-C4 F8
100
80
(a)
Fig. 7: Measured [2] and caZculated vaZues of static
breakdown voZtages in mixtures of C-C4F8+CF4 in
uniform fields
lull
--
a
DISCUSSION
It is important to note that Eq. (1) synthesizes
three factors which can be separated by appropriately
splitting k into kl and k2 (k=klk2) and writing
Vi
=
* UbUc
k, (pd)a.*k}
(7)
The first part k (pd)a gives breakdown of the main
gases illustrated by Eq. (3) in the case of CC12F2.
Secondly, it incorporates in itself an expression
k2Nb such as Eq. (4) which tells what percent of the
breakdown voltage of the main gas can be realized for
a particular mixture and thirdly it includes U'c as
the effect of non-uniformity of the electrode system.
The first part of the equation can be correlated to
the ionization property of the gas leading to breakdown as shown in Appendix 2 [5]. It is thus possible
to replace this part of the empirical Eq. (1) with an
equation which is based on fundamental properties of
a gas. The second part of the equation will have to
be based on the effective electron attachment property
of the gas and its relative efficiency in a mixture.
Quantitative data on attachment is not yet available
in electronegative gases over the full pd range discussed here. The third part of Eq. (1) is analytical
in nature and is based at present on considerations
of maximum and average electric field (Emax and Eav)
in different electrode systems and their effect on
the breakdown voltage.
With some limitations Eq. (1) has however been
applied earlier quite successfully in dc and power
frequency ac breakdowns [4] over a wide range of pd.
Studies reported here are available in a limited pd
range and only in dc voltage. On the basis of
earlier comparison it may be said that power frequency
ac breakdown voltages in the mixtures reported in
this paper will not be much different than dc voltages,
thus Eq. (1) will be valid with small modifications
in numerical values of k and b in most of these cases.
80
Pd1126*65kPa-cm
or
-.0
O 60
V3
~~~0
x
o
X./*
X
0 20
~0
C1.F$4CHF3}
C4F+ N2
---c
-.-
20
Measured 131
C C1F.CHF3
C C sF8+N2
c-
mnU-'
.~
.-
1.0
J
Calculated
60
Percentage of c-C4F8
-.80
100
(b)
Fig. 8: Measured [2, 3] and calculated vaZues of
static breakdown voZtages in mixtures of (a)
c-C4F8+CHF3 in uniform field and (b) C-C4F8+CHF3
and c-C4F8+N2 in non-uniform field (coaxiaZ
cyZinders, R.=O. 75 cm and R =2. 0 cm)
0
SUMMARY
Table 2 summarizes the full analysis of the breakdown in electron attaching gases and their mixtures
for all the measurements discussed in this and the
earlier [4] paper. Calculated and measured values of
breakdown voltages are found to be in good agreement
in all these cases. This analysis illustrates that
the breakdown voltage data on gas-mixtures can be
formulated and similar measurements in gas mixtures
not analyzed here can easily be understood by using
this analysis. It should, however, be noted that
there is a need of devising a standard test cell and
procedure to ascertain variability in experimental
measurements and make this analysis more accurate.
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Nema, Kulkarni, and Husain: Calculation
of breakdown voltages of mixtures of gases
APPENDIX
Measured [2] Uniform field
----Calculated j
1ooF
Measured[3)1. Non-uniform
x
Pdv126650kPo-cm _.
x
x
601
._*
_.
-,K-.,
63-437?
- .-. -.--
_
.5I
x --,
,-
_ _ _
_
4S4978
i.e. that
__
VCC1
ln
I.6*520
*. _
1
BREAKDOWN VOLTAGE OF CCl2F2
The breakdown voltage of a uniform field gap in
CCl2F2 for pd values of 100, 200, 300, and 400 kPa-cm
from the data of Malik and Qureshi [1] is shown in
Fig. 10. On a log-log scale the data follows a
straight line showing an equation of the form y--mx+n
field
Calculated J
c- C4 F8 +11 - C H3 C F3
-
439
=
m
ln (pd) +
(8)
n
be fitted to these data. Numerical values of
m and constant n are determined by considering
any two points on the line. The values determined
by us are m=0.915 and n=ln 1341 which therefore
can
slope
0
O0~
:00
m
,-' ,
"
,' ,-a
_-
-
-,
oz,
'
- - _ --
.38-062 _ 0
_-_
29-604_____
-- - ~*
-146
- -
81
21-*46
20~
,'
yields Eq. (3).
,_
BREAKDOWN OF MIXTURE OF CC12F2+N2
_12 687
--.-.--T
uI
0
20
40
60
Percentage of c-C4F8
1!
80
Fig. 9: Measured [2,3] and calculated values
static breakdown voZtages in mixtures of
C-C4F8+1,1,1-CH3CF3
in uniform field and non-
uniform field (coaxiaZ cyZinders,
R
of
R =0.
5
cm
and
=2.0 cm)
0
As stated in the text, the breakdown voltage of a
mixture containing CC12F2 is a certain fixed percentage of the breakdown voltage of CCl2F2 itself. Also
any correlation between the mixture proportion and
the breakdown voltage obtained from measurements at
a particular pd also holds for other pd values.
Average values of percentage breakdown voltages of a
mixture relative to CCl2F2 from measurements at 100,
200, 300, 400, and 500 kPa,cm are obtained from the
published data [1] and are shown in Fig. 11 against
percentage (5 to 100) of CC12F2 in the mixture.
These average values follow an approximate straight
line on a log-log scale indicating that Eq. (8) can
be applied in this case also. The numerical values
of m and n determined by us here are 0.21 and 38.03
respectively, yielding Eq, (4),
ACKNOWLEDGMENTS
Thanks are due to the Chairman of the Department
of High Voltage Engineering, Indian Institute of
Science, Bangalore for permission to publish this
analysis. One of us (EH) is thankful to UGC (India)
for funds and Aligarh Muslim University for leave
under Q.I.P.
I
1000
90
s0
4
70
4
460
m a4
Ow
41 so_
U.
zo
Uz
I.Oi
350
cn
a
0
o
4
6
2
8 10
PERCENTAGE OF
250
_
20
CC12F2
_
30 40
60
.-
IN
-
CC12F2 +
of% d%
a f%
80
100
N2
Fig. 11: Percentage breakdown voltage of CCZ2F2+N2
as a function of percentage of CCl2F2 in the
150
0
mixture
a
m 100
90
_
100
I
200
pd, kPa
Fig. 10:
11
200
c
3
I30
w
> 300
w
40
I
300
-cm
I
o00
Breakdown voltage of CCZ2F2 at different pd
Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY BOMBAY. Downloaded on December 30, 2008 at 00:23 from IEEE Xplore. Restrictions apply.
IEEE Transactions on Electrical Insulation Vol. EI-17 No.5, October 1982
440
REFERENCES
APPENDIX - 2
On the basis of Townsend breakdown criteria for
electron attaching gases
y
(cam
[exp(-r-n)d
-
1]
=
1,
[1]
N. H. Malik and A. H. Qureshi, "Sparking potentials for CCl2F2-CO2 and CC12F2-N2 gas mixtures"
Int. Symp. on Elect. Insul., (IEEE), June 9-11,
1980, pp. 38-40.
[2]
D. R. James, L. G. Christophorou and R. A.
Mathis, "New Unitary and Multicomponent Gaseous
Dielectrics", Proc. 1Ind Int. Symp. on Gaseous
Dielectrics, Knoxville, Tennessee, 1980,
pp. 115-127.
[3]
C. C. Chan, M. 0. Pace and L. G. Christophorou,
"DC Breakdown Strengths of some Multicomponent
Gas Mixtures in Concentric Cylinder Geometries",
Proc. IInd Int. Symp. on Gaseous Dielectrics,
Knoxville, Tennessee, 1980, pp. 149-159.
the breakdown voltage is given as
Vb =
Bpd
ln[
(9)
Apd
ln (1 + in)
ny
where p is pressure, d is gap distance, Cl, y, n are
primary ionization, secondary ionization, and attachment coefficients respectively, and A and B are constants related to molecular properties of the gas.
Eq. (9) may be rewritten as
Vb
Bpd
- lln p d +
[4]
SF6-Gas mixtures in uniform and non-uniform
Electric fields", IEEE Trans. on Elect. Insul.,
Vol. EI-17, No. 1, Feb. 82, pp. 70-75.
(10)
Kk
where
R. S. Nema, S. V. Kulkarni and Ekram Husain,
"Calculation of sparking potentials of SF6 and
[5]
Ekram Husain and R. S. Nema, "Analysis of
Paschen curves for air, N2 and SF6 using the
Townsend breakdown equation", IEEE Trans. on
Elect. Insul., Vol. EI-17, No. 4, (1982),
pp. 350-353.
Also: Ekram Husain, Ph.D. Thesis, Indian
Institute of Science, Bangalore, India,
July 1981.
[6]
N. H. Malik and A. H. Qureshi, "Breakdown gradients in SF6-N2, SF6-air and SF6-CO2 mixtures",
IEEE Trans. on Elect. Insul. Vol. EI-15, 1980,
pp. 413-418.
[7]
Using Eqs. (10) and (11), it is possible to evaluate Vb in V at any pd for SF6 in the pd range of
0.3 to 1200 kPa*cm.
A. A. Azer and R. P. Comsa, "Influence of field
non-uniformity on the breakdown voltage characteristics of SF6" , IEEE Trans. on Elect. Insul..,
Vol. EI-8, No. 4, 1973, pp. 136-141.
[8]
It is thus possible to replace the first part of
Eq. (7) with a fundamental equation of the form as
given by Eq. (10) and the same can be written as
A. H. Cookson, "Electrical breakdown studies of
SF6/CO2/fluorocarbon mixtures", Proc. IInd Int.
Symp. on Gaseous Dielectrics, Knoxville,
Tennessee, 1980, pp. 169-177.
[9]
M. S. Bhalla and J. D. Craggs, "Measurement of
ionization and attachment coefficients in sulphurhexafluoride in uniform fields", Proc. Phys.
Soc., Vol. 80, 1962, pp. 151-160.
ln[
K=
ln (1+ -n)
cty
Eq. (10) may be used for evaluating the breakdown
voltage V if B is known and if it is possible to
evaluate k for all pd values. It has been made possible by us [5] in the case of SF6 by obtaining B
2189.25 V/kPa-cm from published literature [9] and
computing K from
K =
ln[6.4541(pd)-0.8374] for 3.0 < pd < 1200 kPa-cm
and K = ln[4.1227(pdY0.-4331] for0.3- pd ' 3.0 kPa-cm
(11)
V
Mrnx
Bpd
ln pd + K
k2
Nb* Uc
(12)
Manuscript was received 26 February 1981, in final
form 10 ApriZ 1982.
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