modeling of altitude effects on ac flshover of pollute hight voltage insulatos

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 established, 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. gradual 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 relationship 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 voltage 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 pressure range 48-101 H a . It was found that m varied in the range 0.28-0.50 for different pollution levels and insulator 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 polluted insulator is determined by the reignition criterion of the residual arc following a current zero of the critical 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 boundary 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 approximated, 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 characteristic 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 expression 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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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 critical conditions and for determination of the arc boundary 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 determined 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 practical 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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severities as expressed by the average pollution resistance 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 different 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 atmospheric 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 practically 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 pollution 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 efficiency 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 proposed 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 voltage. (29) shows that at high values of EsWEpL, the utilization 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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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 pressure 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 leakage 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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[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", IEEEKSEE Joint Conference on High Voltage Transmission Systems in 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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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.