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Prediction of the dielectric strength for c-C4F8 mixtures with CF4, CO2, N2, O2 and air by
Boltzmann equation analysis
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2014 J. Phys. D: Appl. Phys. 47 425204
(http://iopscience.iop.org/0022-3727/47/42/425204)
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Journal of Physics D: Applied Physics
J. Phys. D: Appl. Phys. 47 (2014) 425204 (9pp)
doi:10.1088/0022-3727/47/42/425204
Prediction of the dielectric strength for
c-C4F8 mixtures with CF4, CO2, N2, O2 and
air by Boltzmann equation analysis
Xingwen Li1 , Hu Zhao1 , Shenli Jia1 and Anthony B Murphy2
1
State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, No 28
Xianning West Road, Xi’an, Shaanxi Province 710049, People’s Republic of China
2
CSIRO Materials Science and Engineering, PO Box 218, Lindfield NSW 2070, Australia
E-mail: [email protected]
Received 18 June 2014, revised 16 August 2014
Accepted for publication 21 August 2014
Published 18 September 2014
Abstract
The dielectric strength of c-C4 F8 , and mixtures of c-C4 F8 with CF4 , CO2 , N2 , O2 and air, is
studied through solution of the Boltzmann equation. The reduced ionization coefficient α/N
and reduced attachment coefficient η/N are calculated, allowing the reduced effective
ionization coefficient (α–η)/N and the critical reduced electric field strength (E/N )cr
(the reduced electric field for which (α–η)/N = 0), to be determined. A high value of (E/N )cr
for an electronegative gas, such as those considered here, indicates good insulating properties.
It is found that c-C4 F8 –N2 and c-C4 F8 –air have very similar (E/N )cr values, higher than those
of the other three mixtures, and superior even to that of pure SF6 for c-C4 F8 concentrations
above 80%. Comparison of the results obtained for c-C4 F8 and c-C4 F8 –N2 with experimental
values from the literature supports the validity of the approach taken here and the parameters
used.
Keywords: arc, dielectric strength, circuit breaker
(Some figures may appear in colour only in the online journal)
greatly limits the application of SF6 in cold areas, such as
Siberia, western Canada and northeastern China. Therefore,
comprehensive investigations of possible environmentally
friendly substitutes for SF6 have become more urgent and
important for new high-voltage electric apparatus design [2].
In the search for an environmentally friendly substitute for
SF6 , most previous studies have concentrated on mixtures of
SF6 and another gas [3–16]; unfortunately, none has yet been
found to have insulating properties comparable to SF6 . It is
consequently necessary to investigate other potential gases and
gas mixtures. Recently, CF3 I [17–25], c-C4 F8 [26–33] and
their mixtures have been suggested and studied as potential
substitutes for SF6 , due to their relatively high dielectric
strength and low global warming potential. In a previous paper
[34], the authors studied the insulating characteristics of CF3 I
mixtures with CF4 , CO2 , N2 , O2 and air theoretically. This
paper aims to numerically investigate the insulating properties
of c-C4 F8 mixtures.
1. Introduction
Sulfur hexafluoride (SF6 ) was, for many decades, considered
an ideal insulating medium by the electric power industry,
owing to its outstanding properties. Currently, nearly 50% of
SF6 produced is used in the power industry, with approximately
80% of this gas being utilized in high-voltage switchgear
equipment. However, two problems are becoming increasingly
significant when SF6 is used as an insulating medium in
high-voltage equipment, such as gas-insulated transmission
lines (GIL), gas-insulated switchgear (GIS) and gas-insulated
transformers (GIT). One is its extremely high global-warming
potential of 23 900 over 100 years [1], which means that
the application of SF6 may cause great potential danger to
the environment. Consequently, SF6 was designated as a
regulated gas at COP3 (Third Session of the Conference of
the Parties to the United Nations Framework Convention on
Climate Change) in 1997. The other is the higher liquefaction
temperature of SF6 relative to other common gases. This
0022-3727/14/425204+09$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
Table 1. Property comparison of different gases [32, 37].
CF4
CO2
N2
O2
SF6
0
8700
−8
0
6300
−128
0
1
−78.5
0
0
−195.8
0
0
−183
0
23 900
−64
6
(α-η)/N (×10-21m2)
ODP
GWP
Tliqu
c-C4 F8
8
ODP—ozone depleting potential; GWP—global warming
potential; Tliqu —liquefaction temperature at 0.1 MPa (◦ C).
The sparkover voltage of c-C4 F8 is about 1.3 times that
of SF6 at atmospheric pressure for an ac waveform, and the
lightning impulse voltage is 1.3–1.4 times that of SF6 [32].
The critical reduced electric field strength (E/N)cr , where
E and N represent the electric field and the particle number
density respectively, was determined to be 359 Td, 392.6 Td,
414.3 Td and 434 Td by Naidu [35], Xiao [31], Urquijo [27]
and Wen [36], respectively. The value of (E/N)cr of SF6 of
362 Td is clearly inferior to that of c-C4 F8 . Table 1 compares
the critical properties of c-C4 F8 with those of CF4 , CO2 , N2 ,
O2 and SF6 . c-C4 F8 is non-toxic, and has no ozone-depleting
potential and good thermal stability. However, the liquefaction
temperature of c-C4 F8 (−8 ◦ C at 0.1 MPa) is much higher
than that of SF6 (−64 ◦ C at 0.1 MPa), which is likely to limit
the application of pure c-C4 F8 in high-voltage apparatus. In
commercial GIS, SF6 at 0.5 MPa is widely used; unfortunately,
the use of pure c-C4 F8 at such high gas pressures is not possible.
To address this issue, mixing of the c-C4 F8 with a buffer gas
with a lower liquefaction temperature has been proposed.
Yamamoto [32] experimentally studied the insulating
strength of c-C4 F8 mixtures as an insulating medium in GILs
with sphere-plane and needle-plane electrode systems. It was
found that the mixtures had good insulating strength under
quasi-homogeneous conditions and were even superior to SF6 –
N2 under inhomogeneous conditions. Naidu [35] and Urquijo
[27] each measured the electron swarm parameters of pure
c-C4 F8 . Novak [38] determined a set of cross-sections for
c-C4 F8 , and calculated the transport coefficients of c-C4 F8
and c-C4 F8 –N2 mixtures by Boltzmann equation analysis.
Subsequently, Christophorou [33] modified and constructed
the collision cross-sections, providing the fundamental data
required for calculation of the insulating properties of gas
mixtures containing c-C4 F8 . There have been, however, few
studies of the insulating characteristics of mixtures of c-C4 F8
with other gases of interest, such as CF4 , CO2 , N2 , O2 or air.
The aim of this paper is to address this problem by presenting
calculations of the insulating characteristics of mixtures of cC4 F8 with CF4 , CO2 , N2 , O2 and air, and by comparing the
properties of the different mixtures with each other and with
those of SF6 .
We first calculate and analyse the reduced ionization
coefficient α/N , reduced attachment coefficient η/N and
reduced effective ionization coefficient (α–η)/N of c-C4 F8 and
its mixtures with the other gases. We then determine the
critical reduced electric field strength (E/N )cr , i.e., the value
of E/N for which (α–η)/N = 0. We also compare our results
with experimental data in the literature for pure c-C4 F8 , and
mixtures of c-C4 F8 with N2 .
Note that all percentages used are mole percentages.
4
Present calculation
Urquijo [27]
Yamaji [29]
Naidu [35]
Wen [36]
2
0
-2
-4
200
300
400
E/N (Td)
500
600
Figure 1. Reduced effective ionization coefficients (α–η)/N as a
function of E/N in c-C4 F8 , with results from the literature plotted
for comparison.
2. Method of calculation and parameters
In this paper, the insulating properties of c-C4 F8 mixtures are
analysed by solving the Boltzmann equation under the zerodimensional two-term spherical harmonic approximation. A
set of accurate collision cross-sections for all species in the
mixtures is required. The collision cross-sections for the cC4 F8 molecule were taken from Christophorou [33], and the
data for CF4 , CO2 , N2 and O2 were from the Plasma Data
Exchange Project [39]. The validity of the calculation method
and parameters adopted will be checked using comparisons of
results calculated with data from the literature.
The Boltzmann equation is strongly nonlinear for
electronegative gases, and its solution requires an iterative
procedure. The two-term approximation is a widely used
and convenient approach. It is sufficiently accurate when
two conditions are satisfied: the anisotropies caused by the
influence of the electric field are small, and the elastic process
contributions dominate those of inelastic processes [40, 41].
For the range of conditions considered here, E/N has relatively
low values, and the elastic collision cross-sections for all
species in c-C4 F8 and its mixtures are large enough to ensure
that the two-term approximation is valid.
The plasma module of the COMSOL 4.3 software
was used to perform the calculations. The gas number
density was set to 2.5 × 1019 cm−3 , corresponding to one
atmospheric pressure at 300 K. A number of assumptions were
required because of limitations on the availability of data.
Excited states of all species were neglected. Furthermore,
due to the relatively low gas number density and the
low ionization degree, three-body collisions and Coulomb
interactions between charged particles were not considered.
Finally, following a collision that results in ionization, the
secondary and ionizing electron were assumed to have equal
energy.
Figure 1 shows the calculated reduced effective ionization
coefficients (α–η)/N as a function of E/N in c-C4 F8 , with
data from the literature [27, 29, 35, 36] plotted for comparison.
2
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
10-20
10-20
10-21
α/N (m2)
α/N (m2)
10-21
20%c-C4F8-80%N2
40%c-C4F8-60%N2
60%c-C4F8-40%N2
80%c-C4F8-20%N2
100%c-C4F8
10-22
20%c-C4F8-80%CF4
40%c-C4F8-60%CF4
60%c-C4F8-40%CF4
80%c-C4F8-20%CF4
100%c-C4F8
10-22
10-23
10-23
200
300
400
E/N (Td)
500
200
600
300
400
E/N (Td)
500
600
Figure 4. Dependence of reduced ionization coefficients α/N on
E/N in different c-C4 F8 –N2 mixtures.
Figure 2. Dependence of reduced ionization coefficients α/N on
E/N in different c-C4 F8 –CF4 mixtures.
10-20
10-20
10-21
α/N (m2)
α/N (m2)
10-21
20%c-C4F8-80%CO2
40%c-C4F8-60%CO2
60%c-C4F8-40%CO2
80%c-C4F8-20%CO2
100%c-C4F8
10-22
10-23
200
300
400
E/N (Td)
500
20%c-C4F8-80%O2
40%c-C4F8-60%O2
60%c-C4F8-40%O2
80%c-C4F8-20%O2
100%c-C4F8
10-22
10-23
600
200
Figure 3. Dependence of reduced ionization coefficients α/N on
E/N in different c-C4 F8 –CO2 mixtures.
300
400
E/N (Td)
500
600
Figure 5. Dependence of reduced ionization coefficients α/N on
E/N in different c-C4 F8 –O2 mixtures.
Generally, good agreement was found between the calculated
values obtained here and the literature values, with our values
falling in between the results presented by different authors.
In addition, figure 1 indicates that (E/N)cr of c-C4 F8 , the
value at which the balance reaches between the total ionization
rate coefficient and the total attachment rate coefficient, is
about 409.3 Td, similar to Urquijo’s experimental value of
414.3 Td.
The aim of the calculations is to study the insulating
properties of c-C4 F8 mixtures, in particular by comparing
the values of (E/N)cr . In the gas breakdown process,
especially for the case of an electronegative gas, collisional
ionization and the collision attachment reactions between
electrons and other particles play key roles. Thus, the reduced
ionization coefficient α/N , reduced attachment coefficient
η/N and reduced effective ionization coefficient (α–η)/N will
be analysed in the following sections for different c-C4 F8
mixtures.
10-20
α/N (m2)
10-21
20%c-C4F8-80%air
40%c-C4F8-60%air
60%c-C4F8-40%air
80%c-C4F8-20%air
100%c-C4F8
10-22
10-23
200
300
400
E/N (Td)
500
600
Figure 6. Dependence of reduced ionization coefficients α/N on
E/N in different c-C4 F8 –air mixtures.
CO2 , N2 , O2 and air, respectively. In general, α/N increases
with E/N because of the acceleration of electrons in the
increased electric field. In addition, the values of α/N in
all these c-C4 F8 mixtures increase with the reduction of
3. α/N of c-C4 F8 mixtures
Figures 2–6 present the calculated reduced ionization
coefficient α/N of different mixtures of c-C4 F8 with CF4 ,
3
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
10-20
10
-22
α/N (m2)
10
η/N (m2)
10-21
-21
c-C4F8
20%c-C4F8-80%CF4
20%c-C4F8-80%CO2
20%c-C4F8-80%N2
20%c-C4F8-80%O2
20%c-C4F8-80%air
10-22
20%c-C4F8-80%CO2
40%c-C4F8-60%CO2
60%c-C4F8-40%CO2
80%c-C4F8-20%CO2
100%c-C4F8
10-23
10-23
200
300
400
E/N (Td)
500
200
600
300
400
E/N (Td)
500
600
Figure 9. Dependence of reduced attachment coefficients η/N on
E/N in different c-C4 F8 –CO2 mixtures.
Figure 7. Dependence of reduced ionization coefficients α/N on
E/N in 20% c-C4 F8 mixtures with CF4 , CO2 , N2 , O2 and air.
10-21
η/N (m2)
η/N (m2)
10-21
20%c-C4F8-80%CF4
40%c-C4F8-60%CF4
60%c-C4F8-40%CF4
80%c-C4F8-20%CF4
100%c-C4F8
10-22
10-22
20%c-C4F8-80%N2
40%c-C4F8-60%N2
60%c-C4F8-40%N2
80%c-C4F8-20%N2
100%c-C4F8
10-23
10-23
200
300
400
E/N (Td)
500
200
600
300
400
E/N (Td)
500
600
Figure 10. Dependence of reduced attachment coefficients η/N on
E/N in different c-C4 F8 –N2 mixtures.
Figure 8. Dependence of reduced attachment coefficients η/N on
E/N in different c-C4 F8 –CF4 mixtures.
c-C4 F8 concentration, because of the lower ionization crosssection of c-C4 F8 molecules relative to that of the other
molecules.
Figure 7 shows α/N in mixtures of 20% c-C4 F8 with CF4 ,
CO2 , N2 , O2 and air. It is found that α/N of the c-C4 F8 –N2
mixture is the smallest of these mixtures, and the value of cC4 F8 –air mixtures is slightly larger. This is a consequence of
two properties of N2 : its relatively low ionization cross-section
and its high vibrational excitation cross-sections, which lead
to a reduction of the electron kinetic energy.
η/N (m2)
10-21
20%c-C4F8-80%O2
40%c-C4F8-60%O2
60%c-C4F8-40%O2
80%c-C4F8-20%O2
100%c-C4F8
10-22
4. η/N of c-C4 F8 mixtures
10-23
200
The variation of η/N in different mixtures of c-C4 F8 with CF4 ,
CO2 , N2 , O2 and air is presented in figures 8–12 respectively.
Elevating E/N increases the proportion of high kinetic energy
electrons, which makes attachment to the particles more
difficult. Consequently, the η/N of c-C4 F8 mixtures decreases
significantly with increased E/N .
It is also found that increasing c-C4 F8 concentration
markedly enhances η/N . c-C4 F8 is a strong electronegative
300
400
E/N (Td)
500
600
Figure 11. Dependence of reduced attachment coefficients η/N on
E/N in different c-C4 F8 –O2 mixtures.
gas, and has a larger attachment cross-section than that of the
other gases.
Another notable point is that for relatively low
concentrations of c-C4 F8 , such as 40%, η/N of c-C4 F8 –N2
4
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
Attachment cross section (10-22m2)
3
η/N (m2)
10-21
10
10
-22
20%c-C4F8-80%air
40%c-C4F8-60%air
60%c-C4F8-40%air
80%c-C4F8-20%air
100%c-C4F8
2.5
CF4
2
1.5
O2
1
0.5
CO2
-23
200
300
400
E/N (Td)
500
0
600
4
Figure 12. Dependence of reduced attachment coefficients η/N on
E/N in different c-C4 F8 –air mixtures.
6
8
Electron energy (eV)
10
12
Figure 14. Attachment cross-section data for CF4 , CO2 , O2
molecules [39].
12
25
20%c-C4F8-80%CF4
40%c-C4F8-60%CF4
60%c-C4F8-40%CF4
80%c-C4F8-20%CF4
100%c-C4F8
8
(α–η)/N (×10-21m2)
15
η/N (×10-22m2)
10
40%c-C4F8-60%CF4
40%c-C4F8-60%CO2
40%c-C4F8-60%N2
40%c-C4F8-60%O2
40%c-C4F8-60%air
20
10
5
6
4
2
0
-2
-4
200
300
400
E/N (Td)
500
-6
600
200
Figure 13. Dependence of reduced attachment coefficients η/N on
E/N in 40% c-C4 F8 mixtures with CF4 , CO2 , N2 , O2 and air.
300
400
E/N (Td)
500
600
Figure 15. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in different c-C4 F8 –CF4 mixtures.
12
and c-C4 F8 –air is clearly higher than that of the other mixtures
for E/N below 280 Td, as shown in figure 13. However, for
larger values of E/N , η/N is largest for c-C4 F8 –CF4 . The
former is mainly attributed to the large vibrational excitation
cross-sections of N2 , and the latter is because CF4 has a larger
attachment cross-section than that of CO2 , N2 , O2 for higher
electron energies (7–10 eV), as shown in figure 14.
10
20%c-C4F8-80%CO2
40%c-C4F8-60%CO2
60%c-C4F8-40%CO2
80%c-C4F8-20%CO2
100%c-C4F8
(α–η)/N (×10-21m2)
8
5. (α–η )/N of c-C4 F8 mixtures
6
4
2
0
-2
Based on the values of α/N and η/N , the reduced effective
ionization coefficient (α–η)/N , from which the critical reduced
electric field strength (E/N )cr can be predicted, is obtained.
Figures 15–19 show the calculated (α–η)/N of c-C4 F8
mixtures with CF4 , CO2 , N2 , O2 and air for different ratios,
respectively. With increasing E/N , the increase in α/N
and the reduction in η/N leads to a clear rise in (α–η)/N .
Additionally, because of the large attachment cross-section
and small ionization cross-section of c-C4 F8 molecule, the
value of (α–η)/N in these mixtures decreases strongly with
increasing c-C4 F8 concentration. This helps to prevent
-4
-6
200
300
400
E/N (Td)
500
600
Figure 16. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in different c-C4 F8 –CO2 mixtures.
the electron avalanche and subsequently the occurrence of
dielectric breakdown.
In addition, (α–η)/N of 40% c-C4 F8 mixtures with CF4 ,
CO2 , N2 , O2 and air are plotted in figure 20 for comparison.
5
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
12
10
10
20%c-C4F8-80%N2
40%c-C4F8-60%N2
60%c-C4F8-40%N2
80%c-C4F8-20%N2
100%c-C4F8
6
40%c-C4F8-60%CF4
40%c-C4F8-60%CO2
40%c-C4F8-60%N2
40%c-C4F8-60%O2
40%c-C4F8-60%air
8
(α–η)/N (×10-21m2)
(α–η)/N (×10-21m2)
8
4
2
0
-2
6
4
2
0
-4
-2
-6
200
300
400
E/N (Td)
500
200
600
400
E/N (Td)
500
600
Figure 20. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in 40% c-C4 F8 mixtures with CF4 , CO2 , N2 , O2
and air.
Figure 17. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in different c-C4 F8 –N2 mixtures.
450
12
10
350
(E/N)cr (Td)
6
Present calculation
Chan [42]
James [43]
400
20%c-C4F8-80%O2
40%c-C4F8-60%O2
60%c-C4F8-40%O2
80%c-C4F8-20%O2
100%c-C4F8
8
(α–η)/N (×10-21m2)
300
4
2
0
300
250
200
-2
150
-4
100
-6
200
300
400
E/N (Td)
500
20
600
12
(α–η)/N (×10-21m2)
6
80
100
(α–η)/N of c-C4 F8 mixtures with N2 and air are found to be
very similar, and both are much lower than those of the other
mixtures.
20%c-C4F8-80%air
40%c-C4F8-60%air
60%c-C4F8-40%air
80%c-C4F8-20%air
100%c-C4F8
8
60
[c-C4F8] (%)
Figure 21. Dependence on c-C4 F8 concentration of critical reduced
electric field strength (E/N)cr in c-C4 F8 –N2 mixtures, compared
with experimental results from the literature.
Figure 18. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in different c-C4 F8 –O2 mixtures.
10
40
6. (E/N)cr of c-C4 F8 mixtures
4
(E/N )cr is a critical quantity for evaluating the performance
of electronegative gases as insulators. The dependence of
(E/N )cr in c-C4 F8 –N2 mixtures on c-C4 F8 concentration is
shown in figure 21; the experimental results of Chan [42] and
James [43] are given for comparison. Our calculated results
agree well with the experimental results.
Figure 22 presents the (E/N )cr of mixtures of c-C4 F8
with CF4 , CO2 , N2 , O2 and air respectively, with (E/N)cr
of SF6 –N2 and SF6 –CO2 mixtures shown for comparison. It
is apparent that (E/N )cr in all the c-C4 F8 mixtures increases
approximately linearly with c-C4 F8 concentration. In addition,
(E/N )cr in c-C4 F8 –N2 and c-C4 F8 –air mixtures are similar,
and both are significantly larger than that of the other mixtures.
2
0
-2
-4
-6
200
300
400
E/N (Td)
500
600
Figure 19. Dependence of reduced effective ionization coefficients
(α–η)/N on E/N in different c-C4 F8 –air mixtures.
6
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
Table 2. Parameters of fitted critical reduced electric field strength
(E/N )cr in c-C4 F8 –N2 and c-C4 F8 –air mixtures.
450
400
a
b
c
d
68.644
139.918
1.922
−0.832
60.383
6.113
0.195
0.881
350
c-C4 F8 –N2
c-C4 F8 –air
250
2.2
c-C4F8-CF4
c-C4F8-CO2
c-C4F8-N2
c-C4F8-O2
c-C4F8-Air
SF6-CO2 [12]
SF6-N2 [15]
200
150
100
50
2.0
0
20
40
60
[c-C4F8] or [SF6] (%)
80
c-C4F8-N2
c-C4F8-air
SF6-N2
SF6
1.8
Gas pressure ratio
(E/N)cr (Td)
300
100
Figure 22. Dependence on c-C4 F8 concentration of the critical
reduced electric field strength (E/N)cr in c-C4 F8 mixtures with CF4 ,
CO2 , N2 , O2 and air, and SF6 mixtures with CO2 and N2 .
1.6
1.4
1.2
1.0
450
0.8
20
Calculated value for c-C4F8-N2
Fitting value for c-C4F8-N2
Calculated value for c-C4F8-air
Fitting value for c-C4F8-air
400
(E/N)cr (Td)
350
40
60
[c-C4F8] or [SF6] (%)
80
100
Figure 24. Ratio of pressure of the gas mixture to that of pure SF6
gas required to give the same insulating strength.
commercial software MATLAB to the expression:
300
(E/N )cr = a + bx + cx d ,
250
where x represents the concentration of c-C4 F8 in c-C4 F8 –
N2 or c-C4 F8 –air mixtures. Table 2 gives the parameters of
fitted (E/N )cr in c-C4 F8 –N2 and c-C4 F8 –air mixtures, and the
accuracy of the fits is shown in figure 23.
The insulating strength of the two gases can be compared
by using the assumption that the insulating performance of any
gas is proportional, at a given gas temperature, to its pressure.
The pressure of c-C4 F8 –N2 and c-C4 F8 –air mixtures that is
required to give the same insulating strength as SF6 is shown
in figure 24 (in the form of the ratio of the mixture pressure
to that of SF6 ). The ratio of SF6 –N2 mixture pressure to SF6
pressure is plotted for comparison.
The ratios for c-C4 F8 –N2 and c-C4 F8 –air are very similar.
For c-C4 F8 concentrations above 80%, the required gas
pressure for the two mixtures is lower than that for SF6 –N2 ,
and the values of (E/N )cr are larger than that of pure SF6 .
However, the problem of the high liquefaction temperature of
the mixtures must be kept in mind. According to Yamamoto
et al [32], for an ambient temperature between −20 ◦ C and
40 ◦ C, the concentration of c-C4 F8 must be below 15% and
12% for gas pressures of 0.4 MPa and 0.5 MPa, respectively.
From the present calculations, it is found that (E/N )cr of cC4 F8 –N2 for c-C4 F8 concentrations of 15% and 12% (mole
fraction) are 200.3 Td and 190.3 Td respectively, which is
clearly higher than the air value of 121.4 Td [44]. This
indicates that the performance of c-C4 F8 mixtures with N2
or air is likely to be superior to dry air as an insulating
medium for high-voltage apparatus. It is known that the global
warming potential (GWP) of c-C4 F8 mixtures becomes higher
200
150
20
40
60
[c-C4F8] (%)
80
(1)
100
Figure 23. Fitted critical reduced electric field strength (E/N )cr in
c-C4 F8 –N2 and c-C4 F8 –air mixtures.
This suggests that c-C4 F8 –N2 or c-C4 F8 –air have greater
potential as a substitute for SF6 than the other mixtures.
A gas used for insulation in power apparatus should have
as high a value of (E/N )cr as possible, especially from the
viewpoint of miniaturization of the components. (E/N )cr in
c-C4 F8 is calculated to be 409.3 Td, and the values of (E/N )cr
in the c-C4 F8 –N2 and c-C4 F8 –air mixtures are superior even
to that of pure SF6 for c-C4 F8 concentrations beyond 80%.
(E/N )cr in c-C4 F8 –CO2 is the lowest of the c-C4 F8 mixtures
considered.
7. Discussion
The analysis presented in section 6 predicted c-C4 F8 –N2 and
c-C4 F8 –air mixtures to have insulating performance superior
to the other three mixtures. To allow easy use of the results
in engineering applications, the dependence of (E/N )cr on cC4 F8 concentration in the two mixtures was fitted using the
7
J. Phys. D: Appl. Phys. 47 (2014) 425204
X Li et al
for an ambient temperature between −20 ◦ C and 40 ◦ C. The
results obtained here indicate that (E/N )cr of c-C4 F8 –N2 for
c-C4 F8 concentrations of 15% and 12% are 200.3 and 190.3 Td,
respectively, clearly higher than the value for air of 121.4 Td.
Thus, a conclusion may be drawn that the performance
of the c-C4 F8 mixture with N2 or air as an insulating
medium for high-voltage apparatus is likely be superior to
dry air.
1.2
Pure SF6
1.0
SF6 mixtures with CO2, N2, O2 and air
c-C4F8 mixtures with CO2, N2, O2 and air
c-C4F8-CF4
SF6-CF4
GWP (a.u.)
0.8
0.6
0.4
Acknowledgments
0.2
The work was supported by National Natural Science
Foundation of China (51221005 and 51222704) and Fok Ying
Tung Education Foundation (131058).
0.0
0
20
40
60
[c-C4F8] or [SF6] (%)
80
100
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Figure 25. GWP of gas mixtures relative to pure SF6 .
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We have compared the insulating properties of mixtures of cC4 F8 with CF4 , CO2 , N2 , O2 and air using Boltzmann equation
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8
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