-
810 ' IEEE Transactions on Power Delivery, Vol. 12, No. 2, April
1997
~ o d ~ l i ~ g of Alt~tude Effects on AC lashover of ~ ~ l l u
t e d igh Voltage ~nsulators
Farouk A.M. Rizk A.Q. Rezazada Fellow IEEE Non-member Institut
de recherche d'Hydro-QuCbec (IREQ) Varennes, QuCbec, Canada J3X
1S1
General Motors of Canada Ltd. London, Ontario, Canada N6A
4N5
Abstract - The Paper i n t l " z j a new Physical approach to
account for the effect of reduced air density on the flashover
voltage and critical leakage current of polluted high voltage
insulators. The analysis starts by updating the mathematical model,
previously estab- lished, of power frequency flashover of polluted
insula-
critical flashover voltage U,(.,, p ) can be expressed in terms
of the corresponding value at 1 atm, U, (os, 1) by:
(1) U c ( o s , p ) = K d Uc ( 0 ~ 7 1 ) tors at normal
atmospheric pressure. It then proceeds to introduce the effect of
ambient pressure on the physical parameters of the dielectric
recovery equation. The effect of reduced pressure on the arc
boundary radius is investigated. The combined effect of humidity
and
where Kd is an air density correction factor which, in general,
varies with the type of voltage stress, insulator profile and
pollution severity.
Kd has often been expressed in the form [8991: reduced air
density on the dielectric strength at ambient temperature is also
accounted for. The above analysis results in a new expression for
the reignition voltage which includes ambient pressure effects.
The analytical findings are then used to investigate the effect
of reduced air density on the critical leakage current and
flashover voltage of simple-shaped polluted insulators. The effect
of more complex profiles is sub- sequently introduced.
The model results are compared with experiments and the
agreement established is quite satisfactory. Finally simple
practical altitude correction factors for polluted insulators are
proposed.
Several investigations? mostly experimental, have already
addressed the problem of altitude effects on pollution flashover of
high voltage insulators [l-91. For a given severity, measured in
terms of the specific layer conductivity os and ambient pressure p
atm, the
96 % 104-0 PWRD A paper recommended and approved by the IEEE
Transmission and Distribution Committee of the IEEE Power
Engineering Society for presentatlon at the 1996 IEEE/PES Winter
Meeting, January 21- 25, 1996, Baltimore, MD. Manuscript submitted
August 1, 1995; made available for printing December 5, 1995.
where p is the ambient pressure in atm and the exponent m
depends in general on the type of voltage stress, insulator design
and pollution severity.
During laboratory tests, it appears that m also depends on the
mode of voltage application (e.g. grad- ual rise, constant
application, etc.) [9].
Rudakova and Tikhodeev [8] reviewed the Russian literature on
the subject, including field, laboratory and vacuum chamber tests.
It was found that in moun- tainous regions there is a general
tendency for lower pollution severity the higher the altitude.
Furthermore, it was reported that the dependence of the critical
flashover voltage on severity in the range 2-14pS is practically
independent of ambient pressure, which leads to the conclusion that
the exponent m above is rather insensitive to severity. It was also
found that for a standard insulator, in the majority of studies,
the exponent m above could be taken as 0.5. The relation- ship
between ambient pressure in atmospheres and the altitude H in km
was taken as [SI:
p = (1 - H I 44.3)5.25 ( 3 )
This yields an altitude correction formula [8]:
Kd = 1 - 0.059 * H (4) For insulators with deep ribs and small
rib spacing,
the exponent m increases to reach 0.8, as the insulator
performance is influenced by air breakdown between ribs [SI.
0885-8977/97/$10.00 0 1996 IEEE
NAE55099Resaltado
-
E111
A model meeting the above requirements lis introduced below.
BASIC MODEL
Mercure [9] analyzed the results of several investigations of
the dependence of the flashover voltage of cap-and-pin insulators
on ambient pressure. Ishiis AC results [6] yielded m = 0.50 for
standard and m = 0.55 for antifog insulators. The 50% flashover
volt- age was determined by the wet contaminant technique, using
the up-and-down method.
AC pollution tests [7] were performed on four types of
cap-and-pin insulators in 3-unit strings in the pres- sure range
48-101 H a . It was found that m varied in the range 0.28-0.50 for
different pollution levels and insu- lator types with an average of
0.44. It was also found the critical AC voltage gradient and the
critical current can be related by [7]:
(V/cm, A, atm) (5) a-0.67 0.65 Ec=C1, p
where the constant C varied according to the insulator type in
the narrow range of 345-376 VA0.67/cm.
AC artificial pollution tests [lo] were carried out in an
evacuated chamber in the pressure range 0.67- 1.0 atm and confirmed
that for simple shaped insulator (standard IEEE disc) the exponent
m can be taken as 0.5. For a more complex shaped pin type insulator
(NEMA 56-1) the exponent was as high as 0.8.
AC solid layer tests were carried out [ l l ] on a smooth
cylindrical insulator 1 1.9 cm diameter and 85 cm length as well as
5 other porcelain supporting insulators in a fog chamber in the
pressure range 50- 101 kPa and ESDD in the range 0.03-0.40 mg/cm2.
For the simple insulator profile m was found to be about 0.40
independently of severity. For other insulators m varied with
severity, being low at low severity and low again at high severity,
exhibiting a maximum in between. The above tests, however, were
carried out with gradual voltage rise to flashover.
Despite the above experimental work and a few empirical attempts
[ I l l , there is no physically based mathematical model available
to account for altitude effects on AC flashover of polluted
insulators.
A physically based model should be able to: - determine the
dependence of reignition voltage of
an AC arc on ambient pressure, for the current range of interest
to pollution flashover,
- account for the variation of critical distance and leakage
current with air density,
- derive an expression for the critical AC flashover voltage, at
a given pollution severity, as a function of altitude,
- quantify the dependence of altitude effects on insulator
profile.
In the model introduced by Rizk [12, 13, 141, the minimum
voltage necessary for AC flashover of a pol- luted insulator is
determined by the reignition criterion of the residual arc
following a current zero of the criti- cal leakage current. The
criterion for arc motion lis taken as necessary but not sufficient
and assumed to be satisfied at a lower voltage as in the DC case.
The problem becomes essentially to solve the energy balance
equation [12] of the residual hot gas, which starts with a
temperature of typically 3000 K at current zero. Cooling of the
residual hot gas takes place by generalized thermal conduction
involving kinetic and dissociation energies and the effect of
convection is indirectly expressed by the arc boundary radius. Thie
latter is a function of the peak arc current and the quasi- static
arc E-I characteristics used as one of the bound- ary
conditions.
Introducing the thermal flux function S due to Maecker [ 151
:
T S = j x d t 0
where K is the coefficient of thermal conductivity and T the
axial gas temperature, assuming cylindrical symme- try, S can, in
the range 300 K-3000 K, be expressed as
(7)
where p is a constant. The thermal diffusivity k = rdscp (6 is
the gas
density and Cp is the specific heAt) can also be approxi- mated,
again in the range 300-3000 K, by:
S = const T P
k = a * S (8) where a* is a constant.
Solution of the energy balance equation [12] yielded the
following expression for the variation of the minimum breakdown
voltage ud of the residual arc column with time t subsequent to
current zero:
21 r1P U, = U& { 1 + (so / s, - l)/[l + 4a*(So - s,) t /
r,
where udu is the breakdown voltage at ambient temperature is the
thermal flux function at t = 0 So (T = 3000 K)
-
812
2500
8 2000
p, 1000-
. -3 & 1500 >
Sb
rb
is the thermal flux function at ambient temperature (T = 300 K)
is the arc boundary radius.
- -
- -
- -
- 0 ,\
The boundary radius was obtained from Maecker's solution of the
energy balance equation of the static arc 1151, at the peak of the
AC leakage current.
The critical situation is reached a quarter cycle from current
zero ( t = d2a) when the circuit voltage reaches the dielectric
recovery voltage ud.
For an arc of length x the critical reignition voltage resulting
from the above analysis takes the form:
ucx = x Eda f < i m > (10)
500
where i, is the peak leakage current and Eda is the dielectric
strength at ambient temperature.
Combining the reignition equation (10) with the circuit
equation:
(11) U,, = x No / ig + rp ( L - x ) i, where No and n are
constants from the static arc charac- teristic E ik = N o , rp is
the average pollution resistance per unit length and L is the
leakage path and searching for the critical point results in the
critical arc length x,, critical current i, and critical voltage
U,. As is well known rp is related to the specific layer
conductivity os by the relationship rp = f /(Lo,), where f is the
insulator form factor.
- x MODEL . Empirical [18]
I I I I I I I I I
UPDATING OF MODEL PARAMETERS
Revised thermal conductivity of air at temperatures of 2000 K
and above were taken from Ref. [16], while the more common values
in the range 300-1500 K were obtained from [17].
Numerical integration of (6) yielded the following values:
at T = 3000 K, SO = 350.8 J1m.s; at T = 300K, Sb= 5.34Jlm.s.
Regression analysis resulted in the exponent in (7): p = 1.778
and in (8) above U* = 3.78 x 10- m /J.
Substituting the numerical values in (9):
6 3
with t in s and rb in cm.
The dependence of the boundary radius on current was found
as:
(cm, Ape&> (13) e0.663 q, = 0.497 I ,
Substituting for U&, t = 5 ms (50 Hz) and rb from (13) into
(12):
(Vpeak, Ape&, cm) (14) Within the range 0.05-1.00 A,
regression analysis shows that (14) could be expressed as
(Vpeak, cm, Ape&) (15) .OS26 U,, = 716 x l i ,
This yields values very close to the following expres- sion
given by Claverie and Porcheron [18] based on experimental
results:
U,, = 800 x/& (16)
as shown in Fig. 1 representing the dielectric gradient Ed = U,,
/ X .
3000 :
Fig. 1 Variation of the dielectric reignition voltage gradient
with arc current at atmospheric pressure in a resistive
circuit.
EFFECT OF PRESSURE ON BASIC PARAMETERS
For the limited pressure range of 0.6-1 atm and for the
temperature range of 300-3000K, the effect of pressure on thermal
conductivity of air can be neglected. Also the initial temperature
of the dielectric recovery period was assumed practically constant
at 3000 K. Therefore, the values of SO, Sb and p defined
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813
At 20C, H, = 17 g/m3 and (20) can be approximated as :
Ed,(P) = Ed,(l) * p *
above will remain the same, independent of pressure in the range
of interest.
The specific heat is also practically constant in that range,
while the density is proportional to ambient pressure. This means
that the thermal diffusivity k is inversely proportional to ambient
pressure and the same follows for the parameter a * which
represents the slope of the k-S line.
The variation of the quasi-static voltage gradient with pressure
is needed both for the circuit equation at criti- cal conditions
and for determination of the arc bound- ary radius, required for
the dielectric recovery equation. With a static characteristic of
the form:
E in = No pmo
there is some uncertainty about the variation of m, and n with
pressure [2, 6, 191.
With m, = 0.2, which is roughly a mean value of the measurements
for arcs in air in the current range 20mA-4A and pressure range
20-150kPa [19], our calculations showed that:
% Oc P-0.465
The exponent of -0.465 compares with -0.38 deter- mined by Suits
[20] for arc currents in the range 1- 10 A.
The variation with pressure of the dielectric gradient at
ambient temperature, Ed,, comprises two factors: - a simple
proportionality to the ambient pressure - a factor that has to
account for the effect of
humidity, which during laboratory tests in a fog chamber is at
saturation.
From IEC Publication 60-1, it follows that the humidity
correction factor Kh for power frequency voltage, at constant
temperature:
Kh = 1 + 0.012 (: - 1 1) where Hu is the absolute humidity,
g/m3
P is the ambient pressure, atm
It follows that:
Ed,(P) = E&(l) * p * 1 + 0.012 - - 11 [ (7 )I (20) / [1+
0.012 ( H , - 1 l)]
BASIC EQUATIONS AT VARIABLE PRESSURE
Introducing the above pressure dependency of thle different
parameters into (9), the dielectric reignition equation takes the
form:
UCx(p)=5233x*p* 1+0.2 --1 * [ (: I1 [1+ 64.69/(1+ 1.057 I (iL326
* p0.07))]0'562
(22) Within the range 0.05-1 .OO A and ambient pressurle
range 0.6-1 .O atm, regression analysis yields the muclh
simpler, though approximate, reignition equation:
0.77 -0.526 Ucx(p) = 716 x p I I,,, (Vpeak, cm, Atm, Ape&)
(23)
At any pressure, the circuit equation takes the form:
Ucx(p) = x No pmo I ik + r- ( L - x) im (24.) Solving (23) and
(24) and searching for the criticall
point (% = 0) yields the critical arc length xc, critical
current i, and critical voltage U,.
NUMERICAL RESULTS AND COMPARISON WITH EXPERIMENTS
SIMPLE INSULATOR SHAPES
For simple insulator shapes, where the ratio of the insulator
leakage path L to height h is not high, it is assumed that at any
pressure, within the range of prac- tical interest, the arc follows
the leakage path, without bridging of adjacent ribs or consecutive
sheds.
Critical Voltage
Solution of (23) and (24) above gives the dependence of the
critical voltage per unit leakage length UJL on ambient atmospheric
pressure p , for different pollution
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814
severities as expressed by the average pollution resis- tance
per unit leakage length rp as shown in Fig. 2.
For a cap-and-pin insulator with L = 38 cm and form factor f =
0.75, the above rp range (1000-6000 Rlcm) corresponds to a specific
layer conductivity range of 3- 20 ,US. For a long rod insulator
with L = 180 cm andf= 6.3 the corresponding range is 6-35 ,US.
loo0 L 800 -
E 0 -
600 - a - > i 400 - . 5 -
200 - - x r p = 1000 ohdcm U rp = 3000 ohmkm + rp = 6000
ohdcm
Fig. 2 Dependence of critical voltage per unit leakage length on
atmospheric pressure, for different pollution severities expressed
in average pollution resistance per unit leakage length.
Fig. 3 shows the variation of U J L with rp for dif- ferent
values of atmospheric pressure in the range 0.6- 1 atm.
loo0 >
+ p = 1.0Atm + p = 0.8 Atm * p=0.6Atm
3
Fig. 3
I I I I I I 0 1000 2000 3000 4000 5000 6000
rp , ohm/ cm
0
Variation of the critical voltage per unit leakage length with
average pollution resistance per unit leakage length, for different
values of the ambient atmospheric pressure.
Regression analysis shows that UcL can be expressed as:
(25) a m U, I L = const. rp p
Within the rp range of 1000-6000 Wcm and ambient pressure range
of 0.6-1.0 atm, the exponents a and m amounted to 0.355 and 0.466
respectively. The model value of m = 0.466 is in excellent
agreement with the value of m = 0.50 most quoted from experiments
on simple shaped insulators [8, 91.
Critical current
Fig. 4 shows model results of the variation of the critical
current i, i.e. the maximum current that can flow without
flashover, as function of ambient pressure in the range 0.6-1.0
Atm, at different severities. It is shown that the critical current
is more sensitive to ambient pressure than the critical voltage.
For the same severity, the critical current decreases significantly
with altitude.
-3 a d 0 .3
0.6
0.4
I I I I I I I I I I
x r p = 1000 ohdcm +- rp = 3000 ohdcm + m = 6000 ohdcm
0.2 C L 0 0.5 0.6 0.7 0.8 0.9 1 .o
P , Atm
Fig. 4 Critical leakage current as function of atmos- pheric
pressure, for different pollution severities.
Regression analysis shows that for a fixed severity, the
critical current can be expressed as:
i, = const. pmc (26)
where m, is a constant, which varies slightly with severity. For
example m, = 0.576 at rp = 1000 Wcm and reaches 0.635 at rp =
6000Rlcm, so that an
-
815
approximate mean value of m, = 0.6 can be used within that
range.
Critical Distance
Experimental results and mathematical models show that if the
arc burning on a polluted insulator surface bridges about 2/3 of
the leakage path, flashover is prac- tically assured [14]. The
effect of ambient pressure on such critical distance x, is
presented in Fig. 5.
0.541 ; rp; 1 0 0 C l o h y l I I , , 0.50
cl rp = 3000 ohdcm + rp = 6000 ohmkm 0.5 0.6 0.7 0.8 0.9 1
.o
P , Atm
Fig. 5 Critical distance per unit leakage length as function of
atmospheric pressure, for different pollution severities.
It is shown that, practically independent of the pollu- tion
severity or ambient pressure, the critical distance:
x, 0.65 L (27)
LONG LEAKAGE PATH INSULATORS
For long rod insulators with closely spaced sheds or cap-and-pin
insulators with deep and close ribs, there is a possibility of arc
bridging by sparkover in air across some highly stressed gaps,
instead of following the leakage path, as indicated in Ref.
[21].
Cheng and Nour [22] have shown experimentally that for an
insulator with rib width w and depth d the effi- ciency of
utilization of the leakage path can be expressed as:
4 w l d q = l - e
where c' depends on severity.
In the present analysis it is suggested that the phe- nomenon of
arc bridging and accordingly the efficiency of utilization of the
leakage will depend on: - the insulator geometry as explained above
- the pollution severity; as it is expected that with
lower severity and accordingly higher voltage stress arc
bridging will be more likely
- ambient pressure; since as shown above the streamer gradient
in air is more sensitive to ambient pressure than the pollution
gradient.
Guided by the empirical expression (28), it is pro- posed that
for an insulator of height h and leakage length L:
-cES hlEpL q = 1 - e (29)
where E, is the streamer gradient in air
ED C is a constant
is the pollution flashover gradient
i.e. the variable that determines bridging is not only geometry
but is the ratio of the streamer sparkover voltage of the insulator
to its pollution flashover volt- age. (29) shows that at high
values of EsWEpL, the utili- zation factor will approach unity,
which is physically sound. Such high value can be due to, for
example,, high pollution severity resulting in low Ep values.
Introducing the dependence of Es and Ep on pressure, (29) takes
the form:
-cE,1 hpo.331Epl L q = l - e (30)
where Esl and Epl refer top = 1 atm. For any insulator design at
a given pollution severity.,
the leakage path utilization efficient ql at p = 1 atm follows
from (30):
-C Esl hl EP1 L q1=1-e (31)
It follows that the efficiency at any pressure p , q(p)., is
related to q1 by:
(32)
q1 can be measured at p = 1 atm, at any requiredl severity, by
comparing the insulator flashover voltage: with that of a smooth
insulator of the same leakage pathL and form factor. (32) remains
valid even if h in (29) is replaced by another parameter such as
the insulator d i m e ter .
Introducing q(p) in (25):
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816
U J P ) = r l (P) . Pm . / rll (33)
which for a given insulator shape can be expressed as:
U&> = pme . UJ1) (34)
where m, is an effective pressure exponent. Fig. 6 shows the
variation of m, with 771 in the range
0.6-1.0. Here m, increases from 0.47 at = 1.0 (smooth cylinder)
to 0.68 at q1 = 0.6. The latter value of q1 is indicative of a poor
insulator design with too deep ribs or too close sheds.
In experimental results on antifog insulators the pres- sure
exponent varied from 0.55 [6] to 0.8 [8] in good agreement with the
above model results.
I I I I I I I I I I
0.5 0.6 0.7 0.8 0.9 1 .o ETA1 , pu
Fig. 6 Variation of the effective pressure exponent me with 771
characterizing the insulator profile.
ALTITU~E CORRECT1
From the above analysis, it is clear that the altitude
correction factor Kd will be a function of not only altitude but
also the insulator design represented above by the parameter
171.
Table 1 shows calculations of Kd from proposed values of m,.
Although antifog insulators (low ql) are more severely derated
at high altitude as shown in the Table, such insulators can still
be used advantageously when warranted by pollution severity.
Table 1
Altitude Correction Factor for Polluted Insulators with
Different 771
1 .oo 0.95 0.85 0.70 0.60
1.
2.
3.
4.
5.
6 .
7.
CONCLUSIONS
A new, physically-based method is introduced to account for the
effect of altitude on AC flashover voltages of polluted insulators.
The parameters of a previously introduced model for flashover of
polluted insulators at sea level have been updated, based on
revised values for thermal properties of air at high temperature
and the resulting reignition voltage calculations are in excellent
agreement with experiment. The critical AC withstand voltages of
polluted simple-shaped insulators vary approximately with the
square root of ambient pressure. The critical current is somewhat
more sensitive to ambient pressure than the critical voltage, the
pressure exponent being 0.6 for insulators of simple shapes. The
critical arc length amounts to 65% of the leak- age path,
practically independent of pollution severity or ambient pressure.
A new formula for the efficiency of leakage path utilization has
been derived, which includes the effects of insulator geometry,
pollution severity and ambient pressure, and which is in good
agreement with experimentally obtained flashover voltages at
different altitudes. New altitude derating factors of polluted
insulator performance are presented and account, for the first
time, for insulator geometry.
REFERENCES
[ l ] J. Fryxell and' A. Schei, "Influence of High Altitude on
the Flashover Voltage of Insulators, Elteknik, Vol. 9, No. 1, 1966,
pp. 1-3.
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817
[2] R. Wilkins, "Characteristics of Low Current Arcs Relevant to
Pollution Flashover", Second Int. Conf. on Gas Discharges, IEE,
1972, pp. 206-208.
[3] G.A. Lebedev, E.I. Ostapenko, "Effect of Air Pressure on
Dielectric Strength of Wet Contaminated Insulators",
Elektrotekhnik, No. 1,
[4] V.I. Brobroskii and 1.0. Ordokov, "A Study of the Electrical
Strength of External Insulation under Mountain Conditions", Soviet
Power Engineering,
[5] T. Kawamura, M. Ishii, M.Akbar and K. Nagai, "Pressure
Dependence of DC Breakdown of Contaminated Insulators", IEEE Trans.
on Electrical Insulation, Vol. EI-17, No. 1, 1982,
[6] M. Ishii, K. Shimada, T. Kawamura and T. Matsumoto,
"Flashover of Contaminated Surface under Low Atmospheric Pressure",
4th ISH, Athens, 1983, Paper No. 46.02.
[7] Z. Tiebin, Z. Renyu and X. Jiaqi, "The Influence of Pressure
on AC Flashover Characteristics of Contaminated Insulators",
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China, Beijing, Oct. 17-22, 1987,
[8] V.M. Rudakova and N.N. Tikhodeev, "Influence of Low Air
Pressure on Flashover Voltages of Polluted Insulators: Test Data,
Generalization Attempts and Some Recommendations", IEEE Trans. on
Power Delivery, Vol. 4, No. 1, January
[9] H.P. Mercure, "Insulator Pollution Performance at High
Altitude: Major Trends", IEEE Trans. on Power Delivery, Vol. 4,
1989, pp. 1461-1468.
[lo] Anibal de la O., Jorge Glez de la Vega, "Performance of AC
Insulators under Low Pressure Fog Chamber Tests", 7th ISH, Dresden,
1991, Paper No. 44.19.
[ 111 H. Chaofeng, G. Zhicheng and Z. Renyu, "Influence of Air
Pressure on AC Flashover Voltage of Polluted Post Insulators", 8th
ISH, Yokohama, Japan, 1993, Paper No. 46.01.
[ 121 F.A.M. Rizk, "Analysis of Dielectric Recovery with
Reference to Dry-Zone Arcs on Polluted Insulators", IEEE Conference
Paper No. 7 lCPl34- PWR, presented at the Winter Power Meeting, New
York, N.Y., 1971.
1972, pp. 56-58.
NO. 7, July 1978, pp. 428-430.
pp. 39-45.
pp. 291-294.
1989, pp. 607-613.
[ 131 F.A.M. Rizk, "A Criterion for AC Flashover of Polluted
Insulators", IEEE Conference Paper N~D. 71CP135-PWR, presented at
the Winter Power Meeting, New York, N.Y., 1971.
[ 141 F.A.M. Rizk, "Mathematical Models for Pollution
Flashover", Electra, No. 78, 1981, pp. 71-103.
[ 151 H. Maecker, "Uber die Charakteristiken zylindrischer
Bogen", Zeitschrift fur Physik, 15'7,
[16] J. Yos, "Revised Transport Properties for High Temperature
Air and its Components", AVCO Report, Lowell, Mass., 1967.
[17] V. Isachenko, V. Osipova, A. Sukomel, "Heiit Transfer",
Book, Moscow, 1974, p. 562.
[18] P. Claverie, Y. Porcheron, "How to Choose Insulators for
Polluted Areas", IEEE Trans., Vol. PAS-92, No. 3, May/June 1973,
pp. 1121-1 131.
[ 191 J.P. Novak and G. Ellena, "Arc Field Measurement with a
Simple Experimental Arrangement", .I.
[20] C.G. Suits, H. Poritsky, "Application of Heat Transfer Data
to Arc Characteristics", Phys. Rev.,
[21] D.A. Hoch, D.A. Swift, "Flashover Performance of Polluted
Insulation: An Assessment of the Influence of Air Density", AFRICON
9Z!, Swaziland, 22-24 September 1992.
[22]T.C.Cheng and H.I.M. Nour, "A Study on the Profile of HVDC
Insulators", IEEE Trans. on Electrical Insulation, Vol. 24, No. 1,
February
1959, pp. 1-29.
Phys. D: Appl. Phys. 20 (1987), pp. 462-467.
Vol. 55, 1939, pp. 1184-1191.
1989, pp. 113-117.
BIOGRAPHY
Farouk A.M. Rizk (Fellow 82) is Fellow Research Scientist at
IREQ, Chairman of E C Technical Committee 28: Insulation
Coordination and Convener CIG& WG 33.04: Insulator
Contamination.
A.Q. Rezazada holds a B.Sc. Eng. degree from Kabul University in
Afganistan and an M.Sc. degree from McGill University, Montrkal,
Canada. Mr. Rezazada is presently a reliability engineer at General
Motors Canada.
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818
Discussion
Gu Leguan (Chongqing University, PRC): I should like to
congratulate the authors on a very valuable paper which should of
interest to utilities
in high altitude regions. This paper for the first time makes a
systematic study on modeling of altitude effects on AC flashover of
polluted high voltage insulators. I would pay my respect to the
effort of the authors and add the following comments.
Is the critical distance x, 0.65L (27) independent
of the arc bridging and the types of specimens, that is, the
standard polluted insulator, and the polluted insulators with deep
ribs and small rib spacing?
When discussing "Long leakage path insulators" the authors state
that "-the pollution severity; as it is expected that with lower
severity and
accordingly higher voltage stress arc bridging will
be more likely". Clarifying this point would be
appreciated.
D. A. Swift (University of Natal, R.S.A.): Dr. Rizk and his
colleague are to be congratulated on extending the mathematical
model of AC flashover across a polluted and wetted hydrophilic
insulator to take air density into account. One wonders if this new
model can be of more general use for coping with problems in this
important research area.
For various reasons, especially cost, there is a growing need to
be able to calculate - more accurately than is currently the case -
the flashover voltage of practical shapes of high voltage
insulators. To achieve this aim, one should note that it seems
likely that air-gap discharges between the ribs of a shed and
between sheds play a not insignificant role in this overall
process. Therefore, the next generation of flashover models need to
address this problem. As the authors have shown that
M.Moreno and M.Ramirez (LAPEM-CFE, Irapuato, Mexico) :
Mathematical Models for pollution insulators has been a subject of
much interest. The authors should be congratulated for their timely
paper which introduces a new physical approach to account for the
effect of reduced aidensity on the flashover voltage of polluted
insulators. This subject is important for Mkxico and especially for
CFE with transmission sistems at high altitude.
In Mexico we have done some experimental work at LAPEM (Irapuato
1710 ma.s.1.) and at Topilejo (H.V.Experimenta1 Station at 3000
m.a.s.1.) and part of this data was presented in ref. [l].
We have made a comparison between our results and your
Mathematical Model results (fig.2) and we have comments and
questions as follow:
The tendency (low U,(p)/L values with reduced p) for Standard
and Fog insulators with rp middle values is quite acceptable,
however, for Standard insulator with rp=9600 Q/cm and with fog type
insulators with rp=500 !U cm the slope or tendency is less
pronounced. Could you comment on this?.
The method used for the solution of eqs. (23) and (24) and
searching for x, , i, ,U, is not clear enough, could you put the
description of the procedure into words ? . How is the fbntion U,,
(p) around the point x,?. dU, /dx=O means a maximun or a minimun
point ? and how would it be interpreted ?.
In eq. (30) there is an exponent equal to 0.33 for the pressure,
where does it come from ?.
Would you be so kind as to answer the above questions and make
additional comments ?.
REFERENCE
[ 11 D. Serrano, M. Ramirez and M. Moreno " High Altitude A.C.
Standard Tests on Polluted Insulators " CIGRE 33-94 (WG- 04) 28
IWD. Ludvika, Sweden, 1994.-
Manuscript received February 12, 1996.
N.N. Tikhodeev, E.A. Solomonik, NIIPT, St. Peterburg, Russia:
The paper is of great scientific and practical interest for
selection of line insulation of HV and EHV AC overhead power
transmission lines running at high altitudes of 1OOOm to 4000m
above the sea level. A number of experimental studies, including
that by NIIPT authors [8], used comparative tests of wet polluted
insulator units of different types at varying relative air
pressures p to derive a correction
air density affects air gap discharges to a greater extent than
it does surface discharges, we have a variable that could be
employed to good effect for getting the weightings that have to be
apportioned to these two components of the flashover mechanism.
successfully.
Therefore, I ask the authors if they have given any thought to
this broader scope that may now be opened up.
factor K~ p m , m tending to be higher for units of more
elaborate shapes. These findings had no theoretical explanation;
now this paper bridges the gap
J p o r K~
Here are some comments and questions:
1.The authors calculate U, from Eq. (24), whose
-
819
second term takes into account the resistance Ri of the polluted
unit's wet zone 3 after the dry zone 2, with the current applied to
zone 3 pointwise by the partial arc 1 of length x (see the insert).
The authors of the paper are indubitably aware that the resistance
can be found from the equation Ri(x) = rp(L - x ) only roughly,
which makes the U, calculation very approximate.
i
.-
The resistance of the wet zone at p = 1 was studied in detail in
two NIIPT papers, one of which dealt with cap- and-pin insulators
(E.A. Solomonik, Re- sistance of polluted insulator units with and
without partial arc on their surface, NIIPT Proceedings, No. 1 1
,
1965, pp. 74-104) and the other, with rod units (J. Yu. Gutman,
Methodology of calculation of flashover voltages of polluted rod
insulators 7th ISH, R. 43.18, 1991). In these papers the magnitude
of RzT was determined more stringently on the basis of calculations
and simulation of respective electrostatic fields (a ring with one
pointwise current application and a cylinder with two such inputs).
In both cases it was found that with the current applied pointwise
the resistance Rz* ( x ) is 1.5 to 2.5 times as high as Ri ( x )
determined from the linear model. In addition &* ( x ) depends
non-linearly on x , especially at d L c 0 . 3 and x/L>O.8. In
our opinion, use of the simplistic linear model yields lower
flashover voltages which substantially different from those found
experimentally. Calculation of the ratio U, ( p ) / U,(1) may
partly compensate the errors
resulting from the neglect of non-linearity of Rz* ( x ) and the
pointwise current application to the wet zone in its critical point
(XJL = 213). At any rate, use of the reported linear model instead
of the Rt: ( x ) approach should be additionally validated.
2. The allowance for the absolute humidity in Eqs. (19) through
(21) is not supported by experimental findings. Why is the
reference temperature taken to be 20C? As a flashover develops the
ambient temperature near the insulator surface and in the partial
arc zone rises much higher.
3. Summarized in Fig. 6 and Table 1 are the basic
recommendations of the reported study. On the whole they are
corroborated by USSR test findings. It could be to a greater
advantage of the paper if the authors related the parameter to os
more rigidly and
correlated it with the geometry of insulators, including
porcelain and composite rod units.
Manuscript received February 22, 1996.
Farouk A.M. Rizk: I would like to thank the discussers for their
compliments, valuable interest in the paper and for many pertinent
questions. Particularly noteworthy is the fact that all the
discussers have: previously contributed to the subject matter of
the: paper.
To Prof. N.N. Tikhodeev and E.A. Solomonik
The discussers request validation of the use of the linear model
Rp(x) = rp(L-x) and I am pleased to respond.
Let us approximate the exponent of i, in (23) by 0.5 to express
U,,@) as:
U,, ( p ) = A x p0'77 I & (23)' For simplification let us
also take n=OS in the static
arc characteristic so that:
U,,, = x No pmo I & This simplification, as will be shown
later, will have
insignificant effect on the result. Let us express the pollution
layer resistance in the
general form Rp(x), so that the circuit equation becomes:
V , , ( p ) = x No pmo I&+ R p ( x ) i , (24)'
Equating (23)' and (24)', with m, = 0.2:
A x p0.77 I & = x No po.2 I&+ R p ( x ) i , (35)
From which:
( A p0.77 - N o p o e 2 ) x = R, ( x ) i, Jm
:. i, = ( A p 0.77 - No p0.2)2'3 x2l3 R,-2/3(x) (36)
Substitute for i, in (23)':
-
820
~ ~ 2 1 3 0.77 R2./3(x) P p0.77 - No p ~ . 2 ) " 3
permit full recovery of dielectric strength. Therefore the
humidity corrections were applied as for any other gap at ambient
temperature, taken as 20C, using IEC Standard 60- 1. Experimental
support and explanation of this correction approach are given in
ref. [25], [26]. However in the vicinity of arc current zero, the
temperature of the column is obviously much higher than ambient and
the effect of temperature on dielectric strength is accounted for
by the thermodynamic function multiplied by U,, in (9) or byf(i,)
in (10).
elaborate further on the proposed expression for the
(37) U , ( P ) =
The critical distance xc is found from solving:
-(x d 213 R, 113 (x))=O dx (38)
and has nothing to do with ambient pressure as long as no
significant arc bridging takes place (see response to Gu Leguan
below). Substitute x=xc in (37):
Finally at the request of the discussers, 1 will
Substituting in (31) and recognizing that Esl is a From (39),
independent of whether Rp(x) is linear or nonlinear, it is obvious
that the dependence of U,@) on
constant:
pressure can be expressed by:
p0.77 (1 - No / A y f 3 (40) Substituting for 'i, in terms of q,
it follows that: 0.77 - p0.2 No / uc (PI 1 UC(1) =
(43) -const. 0: hl f " L1-" q = l - - e
which from regression analysis in the range 0.6 I p 5
where m = 0.478, very close to the value of 0.5 most quoted from
experiments on simple shaped insulators and to the value of m =
0.466 obtained above from the linear model.
Note that the static arc characteristics have insignificant
effect on the ambient pressure dependence of the insulator critical
withstand voltage. For example if N,P'.~/A is completely neglected
in (40), the exponent m would be 0.513.
As for the second point brought by the discussers, the
assumption made is that the dielectric withstand voltage of the
residual arc gap at any temperature T is
As previously mentioned, for cap and pin insulator units, the
outside diameter D may replace the spacing h in the formulae for q.
It may even be more appropriate to replace L by the protected
leakage path L, and h by the minimum distance in air between two
consecutive discs. Further comments on 71 are given in the response
to Prof. Swift.
To Prof. Gu Leguan
Let the arc length x, be related to the length x of bridged part
of the polluted insulator by:
related to that at ambient temperature T, by Ud(T) = Ud(T,) *
T,IT, independently of the prevailing ambient humidity at T,. This
relationship is supported by experiments in ref. [23]. [24]. U&
= Ud(T,) = xEd, is defined as the dielectric withstand voltage of
the gap concerned at ambient temperature i.e. either without any
arcing or after very long time following arcing to
where A ( x , p ) is in general a function of x and the ambient
pressure p .
With the resistance of the unbridged part expressed by the
genera' expression R ~ ( x ) , it can be shown, following the
simplifications introduced above, that the critical voltage
corresponding to any x:
-
82 1
,y ( ) = ~ ~ 2 / 3 x2/3 0.77 113 Details of the derivation of
the recovery and circuit equations and their solution are given in
Ref. [12-141 and need not be repeated here.
The exponent of 0.33 in (30) is justified as follows. From (21)
Eda or E, is proportional to po'80. From
cx P P R, ( x > l
(A p0.77 - No p0.2)1/3 (45)
(25) E, is proportional to p0*47. It follows that E,/Ep is
proportional to p0.33.
The critical voltage U,@) corresponds to a critical distance x,
obtained from:
d 213 1/3 - (il2l3 (x, P ) * R, = o (46) dx To Prof. D.A.
Swift
This means that in general the critical length x, will depend on
both the distribution (nonuniformity) of the pollution layer
surface resistance as well as on the bridging factor il and may
therefore differ from xc 0.65 L .
On the other hand for insulators with insignificant arc bridging
of the ribs (ilZ1) or insulator designs where the bridging factor
il can be considered reasonably independent of x (A = q p ) ) the
linear model then predicts: x, 2 0.65 L independently of pollution
severity or ambient pressure as given in conclusion ( 5 ) of the
paper.
The statement concerning voltage stress is clarified as follows.
At lower pollution severity, it is clear that the insulator
withstands higher voltage. This means that there will be more
voltage available for bridging of the air gaps i.e. the air gaps
will be more stressed at lower pollution severity, making bridging
more likely.
To M. Moreno and M. Ramirez
As mentioned in the paper, the model results of Figures 2 to 5
apply to insulators without bridging of adjacent ribs or
consecutive sheds. The discussers mention that their experimental
results confirm the findings of Fig. 2 within the range of r,
indicated (1000 - 6000 Wcm). The statement concerning the results
of r,= 9600Wcm and 500SZ/cm is not clear and it is difficult to
comment without seeing the actual results. My guess is that the
discussers compared a point
Yes, I gave some thought to the broader problem of the effect of
insulator shape on its pollution performance. I agree that the
model described in the paper may serve as a starting point for more
detailed future investigations of that subject. I will include here
only some brief comments.
Previous investigations on the efficiency of utilisation of the
leakage path of cap and pin insulators [27] resulted in the
empirical formula (using symbols of the present paper):
771 =1/[1+0.5(L/D-l)] (47)
for UD I 1.55.
(using the symbols of this paper) For long rod insulators ref.
[28] gives the relationship
vi = 2.86 / [1+ L / h] (48)
Comparison of these relationships with (42), (43) shows that our
formulae go farther than (47) and (48) in that they indicate that
is a function of not only insulator geometry but decreases at low
pollution severity, as can be concluded from experiments of Fig. 5
in Ref. [29]. Furthermore, they show that for constant r,, 771 is a
function WL for long rod insulators or their replacement quantities
for cap and pin units. On the other hand, for constant q, as is
frequently the case in experimental comparisons, the form factor f
also plays a role in determining 771, for the same h and
corresponding to rp = 500 Wcm obtained on an antifog L- Finally
in (31) the assumption that c is independent insulator with r, =
9600 CYcm obtained from a standard of h/L may be valid only for a
limited range of that disc and found the tendency less pronounced
than in parameter. If wL however varies within a wide range,
for the very low Pollution severity (rp=9600wcm7 cylinder), the
nature of the parameter c should be 0, 22@) , at an altitude of
1710m, Some arc further investigated both theoretically and
bridging was already taking place on the standard experimentally.
This comment however has no effect insulator. This would account
for the less pronounced on (32), which remains valid even if c
becomes a variation. function of WL.
Fig. 3. If @less is correct then this mean that e.g. from WL =
1/3 (antifog rod) to WL = 1 (smooth
-
822
eferences
[23] L.L. Alston, "High Temperature Effects on Flashover in
Air", Proceedings IEE, Vol. 105, Part A, December 1958, pp.
549-553.
[24]A.H. Sharabaugh, P.K. Watson, D.R. White, T.H. Lee, A.
Greenwood, "An Investigation of the Breakdown of Nitrogen at High
Temperature with Use of a Shock Tube", AJEE Trans., Vol. 80,
Part
[25] K. Feser, A. Pigini, "Influence of Atmospheric Conditions
on the Dielectric Strength of External Insulation", Electra, No.
112, 1987, pp. 83-95.
[26] N.L. Allen, J.R. Fonseca, H.J. Geldenhuys, J.C. Zheng,
"Influence of Air Humidity on the Dielectric Strength of External
Insulation", Chapter 8, CIGRE Monograph "Guidelines for the
111, 1961, pp. 333-344.
Evaluation of the Dielectric Strength of External
Insulation".
[27] G.N. Alexandrov, J.M. Gutman, V.L. Ivanov, V.E.
Kiesewetter, A.S. Maikopar, S .D. Merkhalev, A.A. Philippov, V.S.
Rashkes, N.N. Tikhodeev, "Dielectric Strength of Line Insulation",
CIGRE 1966, Paper No. 417.
[28] S .D. Merkhalev, E.A. Solomonik, "Selection and Operation
of Insulators in Regions with Polluted Atmospheres", Book,
Energoatomizdat, Leningrad, 1983, p. 65.
[29] F.A.M. Rizk, A.El-Sarky, A.A. Assaad, M.M. Awad,
"Comparative Tests on Contaminated Insulators with Reference to
Desert Conditions", CIGRE 1972, Paper No. 33.03.
Manuscript received May 29, 1996.