Behaviour of positive con uctor-rod gaps stressed by impulse voltages in atmospheric air

D.E.Gourgoulis P.N. Mikropoulos C.A. Stassinopoulos C.G.Ya ki nthos

Indexing terms: Conductor-rod gaps, Gap factor, Gap geometry, Impulse voltage, SO% breakdown voltage, Humidity correction factor, Spark paths

Abstract: Results were obtained and evaluated so as to investigate the influence of various parameters on the breakdown mechanism of a 50cm positive conductor-rod gap under impulse voltages. For such a gap it was found that several parameters affect its breakdown characteristics, notably humidity, waveshape of the applied impulse, diameter of the energised conductor and position of the earthed rod with respect to the conductor. Breakdown probability curves have been established, gap factors computed and their dependence on the aforementioned parameters investigated. Finally, the paths taken by the spark channel have been studied. Based on the information gained several suggestions concerning the breakdown mechanism are proposed.

List of symbols

9 LI SI d = diameter of conductor p( U) = breakdown probability curve

Ud Up = crest voltage

(T = standard deviation from a p(U) curve as a

sl U,,, = voltage corrected for air density and humidity

k,

k,,

L

= front duration of the applied voltage = lightning impulse (1.2/50 p) = switching impulse (25012500 ps)

= voltage corrected for air density

= 50% parkover voltage from a p( U) curve

percentage of U,, = the slope of a straight line

= humidity correction factor for 50% breakdown

= humidity correction factor for 5% breakdown

= average length of the projection of the spark

probability

probability

path on the plane of the gap 0 IEE, 1997 ZEE Proceedings online no. 19971250 Paper received 28th October 1996 The authors are with the Aristotle University of Thessaloniki, Department of Electrical and Computer Engineering, High Voltage Laboratory, Building D, Egnatia Street, Thessaloniki 540 06, Greece

0,

eS+ 4;

1 introduction

= standard deviation of L as a percentage of L = length of positive streamer = length of negative streamer

In recent years, to find a way of increasing transmis- sion line voltages above the critical value of 750kV a lot of research has been carried out concerning gap compaction. In this a most helpful concept is that of the gap factor [l] as a working rule describing the geometry of any particular configuration and used for the calculation of clearances in overhead line systems

The conductor-rod gap used has the highest gap fac- tor among the commonly used configurations [4], fur- thermore it has great practical importance since it is a laboratory representation of a conductor-tower clear- ance. The breakdown mechanism of this gap configura- tion was found to depend both on the diameter of the conductor, on the position of the earthed rod, on the waveshape of the applied impulse voltage and on humidity.

[241.

( + ) impulse voltoge r I

50cm 1 2

2cm I

Fig. 1 Schematic representation of gap type

2 Experimental setup

The experimental part of the present work has taken place in the High-Voltage Laboratory of the University of Thessaloniki. The 50cm conductor-rod gap was ver- tically mounted and the axis of the gap was always per- pendicular to the ground. The earthed electrode was an 80cm long cylindrical brass rod having a diameter of 2cm and a hemispherical end. Two conductor diame- ters d = 2cm and d = 3cm and two types of gap config-

209 IEE Proc.-Sei. Meas. Technol., Vol. 144, No. 5, September 1557

urations (axial and non-axial) have been used. Both gap configurations are displayed in Fig. I . The conduc- tor was energised through a lead at midpoint: in the first configuration (axial configuration) the rod was set beneath the midpoint (point l), in the second (non- axial configuration) the rod was set at point 2, l m from midpoint 1.

A four-stage, 560kV, 1 kJ Marx generator produced impulse voltages with the following waveshapes: 1.21 5 0 p (LI), 211700ps, 2511900ps, 50/1950ps, 100/2200ps, 15012200~ and 25012500 ps (Sr). The radiation received by the main conductor-rod gap from the spark gaps of the generator was regarded as negligible. The voltages were measured via a capacitive divider and an oscillo- scope [5]. The humidity in the laboratory varied between 7 and 20gm-3 during the experiments.

For every gap type and waveshape combination the breakdown probability curves p( U) were obtained through the multiple level test method in accordance with IEC [6]. Each voltage level was 2-3% higher than the previous one and consisted of 20 impulses. The p(U) curves were obtained for various values of abso- lute humidity, and from each curve the values of 50% sparkover voltage U,, and standard deviation B as a percentage of UsO were determined. From the U,, the gap factor could be easily computed. All the voltages were corrected for air density [6]. By marking the con- ductor, the position of spark paths passing to it could be determined by visual observation.

3 Breakdown voltages

3.7 Breakdown probability curves The p ( U) curves were fitted with the cumulative normal (Gaussian) distribution for each gap configuration, each applied waveshape and for about six values of absolute humidity. Most of the time the p(U) curves were regular and a good fit has been observed. Typical plots are shown in Fig. 2, for a 50/195Ops impulse volt- age. Furthermore, from this Figure it can be seen that U,, increases with humidity.

95

50

10

99r

-

-

-

I t I I I 250 300 350 LOO L50 500

Up, k V

I3 350

300 Fi .2 Breakdown probability curve: r y l a r shapes for d = 3cm under 502950p and for various values of humi ity -0- -Xgm-3 ....n.. . .

I 18 gm-3

1

-F- 3 - $ - $ - - - _ _ -

-

Sometimes, however, the p ( U) curves tended to be irregular, deviating considerably from the cumulative normal distribution (Fig. 3). The irregular cases are more frequent for waveshapes with ?values of 100 and

210

150ps, with a percentage of -35% of the total. The smallest frequency of irregular distributions was found for LI and SI, displaying a percentage of -13% of the total. Axial geometry shows less irregularities than non-axial and the same is true for the d = 3cm conduc- tor compared with the d = 2cm conductor. The highest percentage of irregular curves (-30% of the total) was found in the non-axial geometry with d = 2cm. Increas- ing humidity also increased the percentage of irregular curves.

9 9 r

11 I I I I I I

300 320 3LO 360 380 LOO L20 Up,kV

Fig.3 axial geometry under 150/2200~ and for various values of humidity

Breakdown probability curve: irregular shapes for d = 2cm and

3.2 Influence of the gap configuration and the impulse shape The average values of U,, with their corresponding 0,

were plotted against tf for all the measured humidities (Fig. 4) with the gap type as parameter. The points relating to the standard impulse LI, although present in the Figures, were not taken into account when drawing the curves, which refer only to impulses with long wavetails.

Fig. 4 shows the following. First, over the range of tf from 2 to 250p for all gap types U,, is almost coii- stant. Second, the standard impulse LI displays a higher U,, than the long tail impulses. Third, U,, increases with increasing d; this becomes more pro- nounced for axial geometry. Fourth, higher U,, occur with axial geometry; this is more obvious with increas- ing d.

500 f

250’ I J 1 10 100 300

t f ‘P ’ s Fig. 4 Average value of U,-,(kV) for all humidities versus +with the gap type as parameter -0- axial, d = 2cm ... O.... non-axial, d = 2cm - -B- - axial, d = 3cm

non-axial, d = 3cm Vertical bars represent the corresponding standard deviation

IEE Proc.-Sei. Meas. Technol., Vol. 144, No. 5, September 1997

It was found that there is a change in the magnitude of the diminution in the sparkover voltages between LI and SI with different gap configurations. The axial geometry and a conductor with d = 3cm give the mini- mum (6%) and the non-axial and the d = 2cm conduc- tor give the maximum (1 5%) diminution.

The values of 0 were found to be almost constant between 4 and 6% with the exception of non-axial geometry with d = 2cm for voltages with short t (LI and 2/1700ps), where values of -3% were obtaineJ

3.3 Influence of humidity Figs. 5 and 6 plot the values of Uso against tf with humidity as parameter, and these show that humidity, in general, causes Us, to increase. The effect of humid- ity on U,, becomes smaller for short-fronted impulses (with tf = 2 and 2 5 p ) and for axial geometry with d = 2cm (Fig. 6). With LI and axial geometry for both d the paradox of increasing humidity causing smaller val- ues of Uso is observed.

500 r

6o

5- J

55

50

I I

10 100 300 t, , PS

0 0 0 - 6 $ . 1 L

0 >

- L; B VI O L

- 0 _......I. ....... J! __._ 0.. 0 ..._ 0 - 2 0 -0

* _ _ _ _ _ L f ..h-.. .----------.I.-. .. .. r...--..l.... - .... I ,'

Fig.5 ters, d = 3cm -0- axial, 18gm-3 ,-.O.... non-axial, 18gm-3 - -.- - axial, 7 g n 6

Vertical bars represent the corresponding standard deviations

U,, (kV) versus tf with the geometry and humidity as param-

non-axial, 7gm-3

250 I I I

1 10 100 300

U,, (kV) versus tf with the geometry and humidity as purame- t f , W

Fig.6 ters, d = 2cm -0- axial, 18gm-3 -...O.... non-axial, 18gm-3 - -.- - axial, 7gm-3

Vertical bars represent the corresponding standard deviations non.axial, 7&

The standard deviation was found to decrease with increasing humidity. The opposite was true for non- axial geometry and d = 3cm.

All the Us, for all gap types and applied impulses were linked with the corresponding values of absolute humidity and linear regressions of Us, over humidity have been calculated. The fit of these regressions was, in general, good except for the cases where the influ- ence of humidity was small, i.e. for short tr:

IEE Proc.-Sci. Meas. Technol.. Vol. 144, No. 5, September 1997

3.4 Humidity correction factors The percentage of correction of the U50 per gm-3 of absolute humidity has been computed by finding a per- centage correction factor k, from the equation:

si! * 100 I C , = ___

In this equation sl is the slope of the straight lines pro- duced via the linear regression of U,, over humidity, and Un5, represents the corresponding values of U,, under normal humidity (1 1 g m 3 ) obtained from these linear regressions. Thus Unso is corrected both for den- sity and humidity. Values of U,,, (in kV), are shown in Table 1.

(1) un50

Table 1: U,, corrected for air density and humidity

tf (PS)

Condition 1.2 2 25 50 100 150 250

Axial, d = 3cm 463 411 411 421 431 431 436

Axial, d = 2cm 400 360 353 353 345 343 346 Non-axial,d=3cm 370 327 321 320 323 320 325

Non-axial, d = 2 c m 367 313 319 319 310 307 308

3.4.1 Influence of the gap type, the impulse shape and the breakdown probability: From the examination of the humidity correction factors k, some conclusions concerning the influence of humidity on U50 can be reached, i.e. for humidity influences Us, more for d = 3cm than for d = 2cm and for non-axial geometries as against axial ones. Study of k, shows that for non-axial geometry with d = 2cm the curve relating k, to tf tends to be U-shaped whereas for all other cases the curve is an inverted U. Additionally, the values of k, with LI were always smaller than with SI.

Study of the p( U) curves shows that the influence of humidity is not equal throughout the full curve. Since low breakdown probabilities are technologically more important, eqn. 1 was modified to refer to 5% break- down probabilities. Thus, values of k,,, corresponding to voltages causing 5% breakdown, were computed. From evaluation of these results it is evident that for the case of non-axial geometry with d = 2cm, kss is greater than k,, this difference tending to increase for longer tr: On the other hand, for all other cases kss is smaller than k, especially for non-axial geometry and d = 3cm.

Fig.7 ~ d = 3 c m

L(cm) and ot (%) versus 9 axiulgeometry, with d as parameter

d = 2cm

3.5 Spark paths and gap factors For axial geometry, both conductor diameters, every voltage level, humidity and applied impulse, and the

21 1

impact points of the sparks at the conductor were determined. From this the projection of the spark path on the plane of the gap has been computed. Its average length L at U,, and its standard deviation 0, as a per- centage of the corresponding L, for the full range of absolute humidity, are plotted in Fig. 7 against with d as parameter. From this figure it can be seen that both L and oL vary little over the full range of the examined impulses. It can also be seen that both L and oL increase for d = 3cm.

For every gap type and impulse shape the gap factor has been calculated from the ratio of its 50% break- down voltage (corrected both for density and humidity) to the U,,, of the positive rod-plane gap under critical 9 For a 50cm gap this was found to be 224kV for a conical rod-plane gap. The resulting gap factors are displayed in Fig. 8 where it can be seen that the highest values are for LI. For long tail impulses they are almost stable except for axial geometry with d = 3cm when they tend to increase with increasing tf Gap fac- tors increase with d = 3cm; both their values and the influence of d are smaller for the non-axial geometry.

I .

’.* t 1 . 0 I I

1 10 100 300

Gap factor versus 9 with the gap type as parameter f f , W

.. non-axial, d = 2cm

non-axial, d = 3cm

For a positive conductor-rod gap with a stressed con- ductor 2cm in diameter for both axial and non-axial geometries and a gap spacing of 50cm under both LI and SI, Allen et al. [4] showed that relatively large neg- ative streamers develop from the rod, especially with axial geometry and under LI. According to these authors, with the assumption that the gap is bridged by both positive and negative streamers with negligible leader growth, U,, can be calculated by the following equation:

where -exf, 4;, E,+ and E,- are the positive and negative lengths and streamer gradients, respectively, at the instant of breakdown. Also, presuming that L is close to the actual length of the spark channel, then:

L = tg + e , ( 3 ) In the present work if E,+ = 5OOkVlm [7] and E; =

1175kV/m [8], then .es+ and 4; can be calculated, the estimates of -es+ and 4; are given in Table 2. Addition of a term E;* e,+ in eqn. 2 to take account of a possi- ble positive leader of length 4; and gradient E$ with about five times the conductivity of E,+ shows that

212

when the calculations are repeated, this results in an addition to the length 4; of the negative streamers. Thus, the estimates of e,- in Table 2 are minimum val- ues. An important parameter is the percentage of the gap that is bridged by either type of streamer. The val- ues of Ujo and L in Table 2 are the average values throughout the range of absolute humidities.

Table 2: Estimation of streamer lengths

Axial, d = 2cm Axial, d = 3cm

U501 L, e:, e,, u50r L e:, er kV cm cm cm kV cm cm cm

1.2/50 400 50.7 29.0 21.7 462 52.9 23.6 29.3

211700 352 51.4 37.3 14.1 416 53.4 31.3 33.1

2511900 355 51.6 37.2 14.4 417 52.6 29.8 22.8

50/1950 358 51.0 35.7 15.3 427 52.7 28.5 24.2

100/2200 350 50.9 36.8 14.1 432 51.4 25.5 25.9

150/2200 350 51.2 37.3 13.9 431 51.9 26.5 25.4

250/2500 350 51.2 37.3 13.9 434 52.0 26.2 25.8

Allen et al. [4] also suggest that at U,, the negative corona starts first and tends to influence the emergence and development of the much more complex and longer positive discharge. This is believed to apply in the present experiments, however, it is also believed that the positive discharge, because of its higher con- ductivity and longer length, plays a more important role in breakdown. Thus the results of this study can be explained in terms of the initiation of negative and the subsequent development of positive corona. The smaller length of the positive streamers when d = 3cm, resulting from the lower geometrical field values at the conductor, does not cancel this mechanism but only slightly diminishes the relative importance of the posi- tive discharge.

4.2 Influence of impulse shape and gap type on

As seen in Fig. 4 LI always displays the highest Use. This is explained by the short times of duration of the impulse, hence the short time available for the develop- ment of the discharge. If LI is compared with long- front impulses the difference between the respective Us0 is accentuated for d = 2cm and for non-axial geometry. This can be attributed to the larger extent and hence contribution of the positive discharge to the breakdown mechanism. The latter is due to the higher geometrical field values at the conductor seen both for smaller d and for non-axial geometry. Further, under long tail impulses tf is seen to have minimal influence on U,, (Fig. 4). It is known [4, 9, 101 that the influence of $-in positive rod-plane gaps becomes smaller as the gap length decreases, thus for a 50cm gap it is negligible except under short front-long tail impulses (e g 211700ps) when a slightly higher U,, is observed. This does not apply in the present experiments, possibly due to the existence of a negative discharge.

The initiation and development of the positive dis- charge and the negative corona is influenced by the val- ues of the field at and around the conductor. Thus the higher values of U50 for axial as against non-axial geometry (Fig. 4) are ascribed to the reduced field in the vicinity of the intersection between the high-voltage lead and the conductor (Fig. 1). Equally, the influence of d on U,, can be ascribed to the lower field values

u50

IEE Proc -Sei Meas Technol, Vol 144, No 5, September 1997

with increasing radius of the conductor. Changes in either the diameter of the conductor or the geometry of the gap result in stronger influence on the values of Us0 in those cases where the value of the field around the conductor is smaller. Therefore, the influence of increasing d on U50 is stronger for axial geometry whereas the differences in the values of U50 between axial and non-axial geometry are accentuated with increasing d.

4.3 Influence of humidity on U,, In general, negative streamers are less influenced by humidity than positive streamers [S, 111. Also, humidity inhibits the detachment of electrons from negative ions [12] which is considered to be the main source of initia- tory electrons for the inception of positive coronas [12- 141. The smaller influence of humidity on U50 for axial geometry can be explained by the greater development of the negative streamers for the latter case. Also, the stronger influence of humidity with increasing d for both geometries is thought to be due to the higher field values with decreasing d that result in easier availability of initiatory electrons. This was also observed by Alli- bone et al. [15] for positive rod-rod gaps.

The lowest influence of humidity is observed for LI; in particular, for axial geometry the influence of humidity reverses so that instead of inhibiting, it actu- ally facilitates breakdown (Figs. 5 and 6). This is ascribed to the first coronas (both negative and posi- tive) that dominate the breakdown mechanism. Here it must be borne in mind that as humidity increases, the density of negative ions increases [12, 161. Thus under conditions of increased negative ions (high humidities) the high fields caused by the higher applied voltages under LI result in a higher probability of electron detachment. This is further facilitated by the greater extent of the negative streamers.

The inverted U-shaped curve relating k, to tf is simi- lar to that relating humidity to the inception of the first corona in positive rod-plane gaps under intermediate tf. Humidity significantly influences the first corona due to the greater importance of primary electrons since the times are not long enough (long tf) nor the field values high enough (short $) for electrons to be readily found [17]. It is thought that since t; is almost constant it is the positive discharge, and especially the first positive corona, similar in mechanism to the first corona of positive rod-plane gaps, that determines the influence of tf on k,.

For the case of non-axial geometry with d = 2cm under long tail impulses the influence of tf on k, (U- curve) can be explained by the emergence of a small positive leader whose development is determined by q [9]. Under long tail impulses (small radius of curvature, positive discharge dominated, i.e. longer e,+) humidity has an influence over a number of successive corona discharges whereas under LI influence occurs over only a single corona; for this reason the lowest value of k, is observed under LI.

The higher values of ks5 than k, for the case of the 2 cm conductor with non-axial geometry can be explained by the easier drift of the injected charge with increasing applied voltage which enhances the probabil- ity of emergence of a small positive leader resulting in less influence of humidity on U50. However, for all other cases where k, > ks5, an increase in the applied voltage, i.e. at higher breakdown probabilities, leads to

IEE Proc.-Sci Meas. Technol., Vol. 144, No. 5, September 1997

easier drift of the charge injected by the first corona from the vicinity of the conductor. This may result in breakdown through a series of coronas involving stronger influence of humidity than for breakdown through a single corona.

5 Conclusions

The sparkover voltage, hence the gap factor of a posi- tive conductor-rod gap depends upon:

the front duration and the wavetail of the applied impulse voltage;

the position of the earthed rod with regard to the lead of the conductor;

the diameter of the conductor; the humidity.

The breakdown mechanism starts with a negative corona, which tends to influence the emergence and development of the much more complex and, in most cases, longer positive discharge; which, mainly because of its higher conductivity, plays a more important role in breakdown.

US0 and k, are determined by the interaction among the availability of initiatory electrons, the structure and complexity of the positive discharge and the extent of negative streamers.

The highest U,, are found under LI, with increasing d and for axial geometry where the longest negative streamers are measured. Of all the gap types examined, the gap with d = 2cm and non-axial geometry, displays the most developed positive discharge with the possible emergence of a positive leader, therefore it tends to behave similarly to a positive rod-plane gap, thus hav- ing the lowest gap factor.

U50 is almost constant under long tail impulses. The influence of humidity is strongest for non-axial geome- try and for d = 3cm.

6 Acknowledgments

The authors wish to thank the Department of Electri- cal and Computer Engineering of the Aristotelian Uni- versity of Thessaloniki for use of the facilities.

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