Cigré 33-01 (TF13-01) 04 IWD - 36 WG11/Renard/70

A simplified statistical method for the qualification of insulators for polluted environments C.S. Engelbrecht STRI Sweden

Summary

1. evaluation of the type and severity of the pollution at the site 2. Specification of a laboratory test that is the most representative of the pollution at the site 3. Selection of insulators that show a good behaviour under this test. Unfortunately this procedure is not described in further detail to guide the potential user how to select the method for the evaluation of the site severity, the test method or how to determine the test severity or even how to use the test results to select insulator dimensions.

1

The aim of this paper is to provide a simple method, based on a statistical dimensioning procedure, to qualify insulators for polluted environments using a laboratory simulation of natural pollution.

Introduction

Methods for the selection and specification of insulators have been the subject of many studies with a host of statistical and deterministic methods described in literature[1]. Perhaps the most popular dimensioning method, is the deterministic procedure of IEC 60815[2], which is based on the specific creepage distance concept. It has however been shown that the use of this method is not advisable as it does not consider all factors that may influence the behaviour of the insulator under polluted conditions.

2

The statistical dimensioning method

IEC 71[3] proposes a statistical method for the dimensioning of air insulation with respect to switching surges. This method can be applied with some changes, for the dimensioning of insulators under polluted conditions as is shown in Fig 1[4][1]. The variation in the pollution stress of the environment is shown by the probability density function “S”, which is a combination of the amount of pollution on the insulator and the wetting conditions. This stress curve is determined by pollution severity measurements at the site where the insulators are to be installed.

Another approach, which is in fact recommended by IEC 60815, is based on the laboratory simulation of natural pollution. Examples of such laboratory methods are the Solid Layer and Salt-Fog methods. This method has three steps[2]:

-1-

a pollution event is defined as a time period when a polluted insulator is exposed sufficiently long to wetting so that the pollution layer can go into solution. For each event a risk for flashover is calculated based on the conductivity measurements during that event and the insulator strength, as was determined under a selected laboratory test. This method requires an automated device for insulator conductivity measurements.

A cumulative distribution function, “W”, represents the strength characteristic of the insulators as a function of the pollution stress, assuming constant applied voltage. This function can be determined through laboratory pollution tests on the insulator. (P) Strength (W)

A different approach was put forward by Suzuki et al.[6]. In this case the insulator stress is represented by a two dimensional distribution function. The dimensions being amount of pollution, given by the Equivalent Salt Deposit Density (ESDD) and the wetting, represented by the relative humidity. This method requires that the insulator strength also be determined as a function of relative humidity and pollution deposit, information that is not provided by the presently available laboratory test methods. These two methods are not generally used as they are regarded as rather complicated.

Probability for flashover (S*F) Risk for flashover

Pollution Stress

Fig 1

Designing insulation by a risk analysis [4][1].

The convolution of these two functions gives the probability for flashover of the insulator in the given environment as a function of the pollution stress. The insulator performance is expressed by the risk for flashover, which is represented by the area underneath the (S*F) curve. The risk for flashover is the fraction of pollution events that will lead to flashover.

A much simpler way, which is also widely accepted is the use of ESDD[7][8][9] for site severity measurements. The advantage is that it is also the severity parameter of the clean-fog test. When this approach is followed some assumptions about the wetting of the insulator needs to be made to enable a statistical dimensioning process. These are (1) The frequency of occurrence of the wetting events and (2) The distribution of the severity of wetting.

Another way to express the insulator performance is by the average number of events between flashovers or the return time. The return time is the inverse of the risk for flashover.

Reported experience[5] show that the frequency of critical pollution events may range from ten to thirty events per year, while the wetting severity can conservatively be assumed to be the worst possible (i.e. that simulated in the artificial pollution test) each time.

2.1. Selection of a stress parameter

The selection of the stress parameter will not be discussed in too much detail as the report by Cigré 33.13.03 will cover this. From the statistical dimensioning point of view the following points should be considered: • A suitable stress parameter (“S” in Fig 1) must be determined. This parameter should give an unambiguous indication of site severity and wetting. Requirements for this parameter are that it should be easily measurable and it must also be correlated to a laboratory test severity. • For the available standardised laboratory tests, the stress function “S” (most often quantified by ESDD measurements) is different for different insulators in the same environment. • It can take several years to obtain a reliable stress distribution function. • The sample interval should be such that it is in the same time order than variations in site severity. This is to ensure that peaks in the site severity are captured with certainty.

Various probability density functions were used in the past to approximate the distribution of site severity. The most often used ones are log-normal[10], normal[11] or gamma distribution[1] functions. An example of typical measurements from a site and a fitted log-normal distribution function is shown in Fig 2.

Probability of exceding absyssa

1

100

0,9

90

0,8

80

0,7 0,6

70

Cumulative probability function Probability density function

60

0,5

50

0,4

40

0,3

30

0,2

20

0,1

10

0 0,001

Probability density

Stress (S)

0 0,01

2

0,1

Equivalent Salt Deposit Density (mg/cm )

Fig 2

One approach to characterise the pollution at a site was presented by ENEL[5]. For the risk of failure calculation -2-

Typical results from pollution site severity measurements and a fitted log-normal distribution.

The resemblance between these distribution functions are remarkable as is shown in Fig 3.

2.2. Selection of the distribution function for insulator strength

In pollution testing, the probability of flashover is normally expressed as a function of voltage for a constant pollution stress. This is because it is much easier to vary the voltage during the pollution test than it is to vary the pollution severity[13]. To enable a statistical dimensioning procedure the probability for flashover is required as a function of pollution stress for a constant voltage. The flashover characteristics of insulators under polluted conditions are usually characterised by a cumulative Gaussian distribution with the 50% flashover voltage, U50, and the standard deviation, σ as its two parameters. There is however some evidence from experimental data[1] that the probability distribution for flashover is truncated. In other words that for a particular pollution stress, there exist a voltage below which flashover is not possible, i.e. zero probability. This truncation is best described by a three parameter Weibull distribution function given by[14][15]:

P(U) = 1 – e

U – U0 k –  ---------------- βU 0

Fig 3

For the dimensioning process the flashover probability is required as a function of the pollution severity. If the laboratory or field test results are not available in such a form (i.e. the usual case) then the following relationship can be used to convert [1]:

(1)

The three parameters being U0, k and β. These can be described in terms of the fifty percent flashover, U50, the standard deviation, σ, and the truncation parameter, n, as follows[3][14]:

U o = U 50 – nσ

(2)

1,38 k = ---------------------n ln  ------------  n – 1

(3)

nc β = ----------------------------------k ( 1 – nc ) ( ln 2 ) σc = -------U 50

Comparison of distribution functions derived for polluted insulators. Experimental data from [15] are included.

CL U ( γ ) = ------- • γ –α A

(6)

A and α are constants obtained from laboratory testing, CL is the creepage length and γ is the pollution severity parameter, typically ESDD. For a constant applied voltage, the probability for flashover becomes: k

γ 50 – α 1  1 –  --- -------------------  ------ – 1  β ( 1 – nc ) γ  (7) P(γ) = 1 – e 

(4) (5)

With γ50 corresponding to the pollution severity with a 50% probability for flashover. This distribution function is also truncated and the SDD at truncation can be determined as follows:

The U50 and σ are usually available from laboratory tests but the value of n cannot easily be determined. In IEC 71 the assumption is made that the truncation occurs at 4σ below U50 (i.e. n=4) for the disruptive discharge probability of external insulation.

γ 0 = γ 50 ( 1 – nc ) 1 ⁄ α

(8)

2.3. Effect of number of insulators of the installation

For polluted insulators, however, it was found from experimental data that the value of ‘n’ is significantly lower than 4. Results on cap and pin insulators from a natural pollution testing station[16][14] showed that n=2.1 (c=0.088). A statistical flashover study, comprising 2800 tests on artificially polluted post insulators[15], indicated that the truncation occurs at n=2.5 (c=0.084).

Various papers[9][15][14] indicate the importance of taking account of “parallel” insulators. Parallel insulators are considered as identical insulators, which are subjected to the same pollution conditions and can be considered as behaving statistically independently - i.e the behaviour of one insulator does not influence the others. It was shown[9] that, considering a normal distribu-3-

same as the 10% flashover severity in the case of many parallel insulators, refer Fig 5.

tion, the withstand voltage (taken here as a 5% flashover probability) of a group of 120 insulators is 78% that of a single insulator. This effect is illustrated in Fig 4.

As for slow-front overvoltages the stress distribution is characterised by the statistical severity, γs2, which is the pollution severity having a 2% probability of being exceeded[3]. If the monthly pollution severity measurements cover a period of less that 4 years this severity should be estimated.

1

Probability for flashover (p.u.)

0.9 0.8 0.7 0.6 0.5 0.4 0.3

The relationship between the statistical severity γs2 and the co-ordination withstand severity γcw is given by the statistical co-ordination factor Kcs[3]:

Constant pollution stress

1 Insulator 10 Insulators in parallel 120 Insulators in parallel

0.2 0.1 0 0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

γ cw = K cs • γ s2

1.5

Voltage stress over insulator (p.u. of 50% stress value)

Fig 4

Effect of parallel insulators on the probability for flashover of the whole system. c=0.10

The statistical co-ordination factor can consist of several components. Some are: • The severity measurement needs to be corrected if it was performed for a differently shaped insulator than the one being specified[1]. • The severity measurement needs also be corrected if the severity measurements were performed on nonenergised insulators, or if a.c. severity measurements are used for the dimensioning of a d.c. installation[1]. • If sufficient severity measurements are available, e.g. four years, Kcs = 1, but it can be chosen higher to compensate for too few severity measurements.

Statistically the effect of “i” parallel insulators is described by:

Pi = 1 – [ 1 – P ]

i

(9)

Where Pi is the flashover probability of “i” insulators and P the flashover probability of one insulator. The effect of parallel insulators on the truncated distribution function (i.e. equation (7) in section 2.2.) is shown in Fig 5 for one, ten and a 120 parallel insulators.

Insulators can be qualified to withstand the co-ordination withstand severity by field trials or laboratory pollution tests. Laboratory tests are necessary if no previous service experience are available or if there is no time to perform field trials. As this is quite often the case, it is necessary to consider the qualification of insulators with a pollution withstand test.

1

Probability for flashover (p.u.)

0.9 0.8 0.7 0.6 0.5 0.4

One Insulator

0.3

10 Insulators in parallel 120 Insulators in parallel

0.2

Laboratory testing to qualify an insulator can either be a pollution withstand test[17] or a range of pollution tests to determine the insulator’s flashover characteristic. The former is preferred as it requires a maximum of four pollution tests to qualify the insulator.

0.1 0 0.01

Fig 5

(10)

SDD (mg/cm2)

0.1

Probability distribution function as a function of SDD. The applied voltage is constant. ( γ50=0,03, c=0,084, n=2,5 and α=2,17).

3 2.4. Simplified statistical method for polluted insulators

The nomencalture in the following simplified method is adapted from IEC 71[3], on which this method is based.

Qualification of insulators with a pollution withstand test

3.1. The pollution withstand test

A withstand pollution test is used to “prove” that the insulator has an acceptable performance in a certain environment[4]. The pollution severity at which the test is performed -- named the withstand pollution severity - is selected based on actual pollution measurements at the site for which the insulators are intended (see section 2.4.), or from published guidelines or given by the customer. According to IEC 60507[17] the pollution test is

The aim of the statistical dimensioning is to select the strength of the insulation to obtain an acceptable risk of failure. For the purposes of the statistical design, the strength of the insulation is characterised by the co-ordination withstand severity. For the truncated distribution function the co-ordination withstand severity γ cw is taken as equal to the truncation severity γ 0 given by equation (8). This value is preferred as it is practically the -4-

test giving the wrong result. This is however an expensive solution, due to the costs associated with pollution testing,

considered as a withstand, when a maximum of one flashover in four tests occurs. 3.2. The success rate of a pollution withstand test Proba bility of pa ssin g the with stand test

1

A withstand test is aimed at verifying that the insulator has at most a 10% flashover probability at the withstand pollution severity[3]. The result of the test is either “passed” or “failed”, so no details are obtained about the actual flashover voltage. An ideal withstand test would pass a insulator if its flashover probability is below 10% and fail it if it is above.

0 .9

1 fla s h o ve r o u t o f 4 tes ts

0 .8

3 fla s h o ve rs o u t o f 1 5 tes ts

0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 0

However, because of the limited number of tests performed in the withstand test, the outcome is not so exact. With the help of the binomial distribution the probability of passing the withstand test can be calculated for the whole range of insulator flashover probability[4]. The result is presented in Fig 6.

0.2

0.3

0.4

0.5

0 .6

0 .7

0 .8

0.9

1

Probab ility of in sula tor flashing ove r

Fig 7

•

From the curve it can be seen that an insulator with a 10% flashover probability has a 95% chance of passing the test, while one with a 50% flashover probability has a 30% chance of passing the test. It is therefore possible that an insulator with a higher than 10% flashover probability can pass the withstand test, or in other words there is a risk that an insulator has passed the test when it actually should have failed.

The probability of passing a pollution withstand test as a function of the flashover probability of the insulator: The effect of the number of tests.

Use the same withstand test to qualify the insulator for a higher flashover probability, for instance 50%. The chance for the withstand test to give a wrong result is then only 4,4%. This effect is illustrated in Fig 8. Compare the shaded area to that of Fig 6. P ro b a bility of pa s s in g the w ith sta n d te s t (p .u )

1

1

P ro b a bility o f pa s s in g the with sta n d te s t (p .u )

0.1

0 .9 0 .8 0 .7

0 .9 0 .8 0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 0

0 .6

0.1

0.2

0 .3

0.4

0.5

0 .6

0.7

0.8

0 .9

1

1.1

P ro b ab ility of in s ulator flash in g o v er 0 .5

Fig 8

0 .4 0 .3 0 .2

The probability of passing a pollution withstand test as a function of the flashover probability of the insulator: The effect of qualifying the 50% flashover probability instead of the 10%.

0 .1

3.3. The required withstand severity

0 0

0.1

0.2

0 .3

0.4

0.5

0 .6

0.7

0.8

0 .9

1

1.1

P ro b ab ility of in s ula tor flas h in g o v er

Fig 6

To compensate for the few pollution tests performed to qualify a insulator, it is suggested that required withstand severity γrw be derived from the co-ordination withstand severity as follows:

The probability of passing a pollution withstand test as a function of the flashover probability of the insulator. The risk of a insulator passing the test when it should not is illustrated by the shaded area.

This risk is given by the shaded area in Fig 6 and it is calculated to be 0,302. This means that there is a 30% chance that the withstand test gives a wrong result! This is assuming, of course that the insulators for the test are selected at random.

γcw γ rw = --------------------------1⁄α ( 1 – nc )

(11)

This equation is derived from (8) and it means that the withstand test is no longer used to qualify the withstand pollution severity, but to qualify it for the severity that

There are various ways to improve the “success” rate of the withstand test. Some are: • The chances of a good test result can be improved by performing more than the required 3 of the withstand test pollution tests. Fig 7 shows that allowing 3 flashovers out of 15 tests, instead of one flashover in 4 tests, lead to a significant reduction in the risk of the -5-

standard deviation σ. Some published values are listed in table 1. An extensive table can also be found in [20].

has 50% flashover probability, for the reasons explained in the previous section. 1

50

table 1

Probability Density Function

0.9

γcw

40

γrw

: Reported standard deviations for solid layer tests

0.8

Type of insulator

Norm. standard deviation (c)

[9]

Standard shape disc

0.10

[16]

Anti-fog disc

0.088

[15]

Porcelain post insulators

0.084

[12]

Post insulators

0.06

An example of the selection of the pollution test severity based on a risk analysis of the insulation performance.

[18]

IEEE disc anti-fog disc

0.01-0.11 0.04-0.15

Fig 9 illustrates this principle. As an example, a typical pollution density function is shown for a light to medium polluted environment -- see Fig 2. It is the solid line in the figure, plotted against the left axis. The dashed curve represents the insulator strength characteristic, which was selected according to section 2.4. to withstand this environment. The co-ordination withstand severity was selected as 0,06 mg/cm2 . Using equation (11), while assuming α=0,22, c=0,08 and n= 2,5, the required withstand severity is calculated as 0,18 mg/cm2 as is indicated in Fig 9.

[19]

Standard shape disc (Artificial tests)

0.06

[19]

Standard shape disc (Naturally polluted artificially wetting)

0.13

[19]

Standard shape disc (Natural tests)

0.20

30

0.6 0.5

20

0.4 0.3

10

Cumulative probability

Source

0.7

0.2 ESDD Probability Density function

0.1

Strength of one Insulator 0

0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

2

Equivalent Salt Deposit Density (mg/cm )

Fig 9

4

The results in the table indicate that the standard deviation can vary to a large extent, depending on the type of insulator, test procedure and laboratory setup. In most cases reported above, an up-down test procedure was followed, which is known to produce a less accurate estimation of the standard deviation.

A summary of the simplified method

The simplified method can be summarised in the following steps:

5.2. Selection of alpha

1. Perform pollution severity measurements at the intended site.

Hilleman[4] provides a summary of published values for α in equation (6). The A constant is valid for:

2. Plot the measurements as a cumulative distribution function and estimate the statistical severity, γs2, which is the pollution severity having a 2% probability of being exceeded. 3. Calculate the co-ordination withstand severity from: γ cw

SCL = A • γ α

(12)

Where SCL is the Specific creepage length defined as the mm per kVrms line to ground voltage. The tables are repeated below:

γcw

= K cs • γ s2

4. Determine the required withstand severity γrw from:

table 2

γ cw γ rw = --------------------------1⁄α ( 1 – nc )

Disc insulators, solid layer method procedure B a[4]

Insulator configuration

Range mg/cm2

A

α

5. Specify a withstand pollution test with a test severity of γrw.

I-string

0,02-0,1

86,5

0,374

I-string

0,1-0,3

51,4

0,158

5

V-string

0,02-0,1

52,9

0,274

V-string

0,1-0,3

37,1

0,122

I-string

0,02-0,4

66

0,223

I-string

0,02-0,4

48

0,220

Supporting information

5.1. Selection of the standard deviation

Laboratory pollution test results are often provided as an estimate of the U50, but normally without the -6-

table 2

Disc insulators, solid layer method procedure Ba[4]

Insulator configuration

Range mg/cm2

A

α

I-string

0,02-0,4

54,4

0,232

[6]

a. Severity parameter is the salt deposit density (SDD) table 3

[7]

Disc insulators, solid layer method procedure Aa[4]

Insulator configuration

Range µS

A

α

I-string

2,5-80

14,2

0,387

I-string

2,5-80

14,2

0,28

[8] [9]

a. Severity parameter is the layer conductivity table 4

[10]

a

Disc insulators, salt fog method [4]

Insulator configuration

Range kg/m3

A

α

I-string

3,5-100

23,4

0,224

I-string

3,5-100

16,6

0,28

[11]

[12]

a. Severity parameter is the test salinity. table 5

[13]

Post insulators, solid layer method procedure Ba[4]

Insulator average diameter, mm

Range mg/cm2

A

α

200

0,01-0,1

63,0

0,220

300

0,01-0,1

75,8

0,226

400

0,01-0,1

87,4

0,229

500

0,01-0,1

103,2

0,240

600

0,01-0,1

115,6

0,240

[14]

[15]

[16]

a. Severity parameter is the salt deposit density (SDD) 6

References

[17]

[1] Cigré task force 33.04.01: “Polluted insulators: a review of current knowledge”, Cigré technical publication 158, June 2000. [2] IEC: “Guide for the selection of insulators in respect of polluted conditions”, Publication 60815, First edition 1986. [3] IEC: “Insulation Co-ordination”, Publication 71. [4] Hilleman, A. R.: “Insulation co-ordination for power systems”, Book, Marcel Dekker, 1999. [5] Sforzini, M., Cortina, R., Marrone, G.: “Statistical approach for insulator design in polluted areas”,

[18] [19] [20]

-7-

IEEE Trans. on Power Apparatus and Systems, Vol. PAS-102, 1983, pp. 3157-3166. Suzuki, Y., Fukuta, T. Mizuno, Y., Naito, K.: “Probabilistic assessment of flashover performance of transmission lines in contaminated areas”, IEEE Trans. on Dielectrics and Electrical Insulation, Vol. 6 No. 3, June 1999, pp.337-341. IEEE Working Group on Insulator Contamination, Lightning and Insulator Subcommittee: “Application of insulators in a contaminated environment”, IEEE Trans. on Power Apparatus and Systems, Vol. PAS-98, No. 5, Sept./Oct., 1979, pp. 16761695. NGK: “Technical Guide”, Cat. No. 91R, First revision, 1989. EPRI: “Transmission Line Reference Book 345 kV and above”, Book, Second edition, Electric Power research institute. Naito, K.: “A review on pollution test procedures and performance assessment of insulators”, NGK Review, No.10, pp. 14-23. 1986. Gutman, I., Hartings, R., Vosloo, W.L.: “Longterm testing of insulators at a coastal test station in South Africa”, Accepted for the International Symposium on High-Voltage Engineering in India, 2001. Sklenicka, V., Vokalek, J., Kunt, J., Vachek, V., Zeman, I.: “Selection of insulators for polluted areas”, Cigré 1990 session, Paris, Paper 23-301. Lambeth, P.J.: “Variable-voltage application for insulator pollution tests”, IEEE Trans. on Power Delivery, Vol.3, No.4, Oct. 1988, pp. 2103-2111. Rizk, F.A.M.: “A systematic approach to high voltage insulator selection for polluted environment”, The second regional conference in Arab countries Amman, Jordan, 1997 May 12-14. Ivanov, V.V., Solomonik, E.A.: “Statistical flashover voltage studies of wet polluted high voltage insulators”, 9th International Symposium on High Voltage Engineering (ISH), Graz, Austria, Paper 3227, Aug. 28-Sept. 1, 1995. Houlgate, R.G., Lambeth, P.J., Roberts, W.J.: “The performance of insulators at extra and ultra high voltages in a coastal environment”, Cigré 29th session, Paris, Paper no. 33-01, 1982. IEC: “Artificial pollution tests on high voltage insulators to be used on a.c. systems”. Standard 60507, Second edition, 1991. 86 IEEE/Cigre round robin (Clean Fog) Naito, K.: “Insulator pollution - general aspects”, Looms, J.S.T.: “Insulators for High Voltages”, Book, IEE Power Engineering Series 7, Peter Peregrinus, 1988. pp.154-155.