INFLUENCE OF ELECTRODE SURFACE DEFECTS ON DISCHARGE VOLTAGE IN AIR

V. D. Kuchin

Sharp protrusions on the surface of electrodes create local distortions of the electric field. These distortions may cause premature corona discharge and energy losses. The question of the influence of electrode surface defects on the discharge voltage is of great practical interest, since high-voltage structures have sharp corners, bolts, rivets, and so forth, which cause a local increase in field intensity. The influence of electrode surface defects on the discharge voltage is explained as follows [1]. The presence of a protrusion on the surface of an electrode causes an increase in the field intensity. The magnitude of the change in field intensity depends not on the number of protrusions but on their dimensions. The field intensity will be greater at the protrusion that has the smaller radius of curvature. As the dimensions of the protrusion decrease, the region of increased electric-field intensity decreases, while similarity is preserved in the distribution of the lines of force. The onset of an independent discharge occurs in the region of increased electric-field intensity.

The phenomenon of air breakdown between electrodes with a disturbed surface under direct voltage was investigated by Scheibe (1938). The electrodes were in the form of paraboloids with a radius of curvature at the apex of 18 cm. The distance between the apices of the paraboloids remained constant and equal to 20 mm. From the apex of one electrode a wire was advanced into the interelectrode gap. The dimensions of the point (length and diameter) could be varied. Figure 1 presents the dependence of the discharge voltage on the size of the point. On the basis of the results of Scheibe’s experiments, it is asserted that the presence on the electrode surface of points up to 3 mm long does not cause a significant reduction in the discharge voltage under direct voltage. Analyzing the results of Scheibe’s measurements, Kossel concludes that on the surface of a high-voltage electrode in a uniform field small or sufficiently sharp protrusions of a “critical” length up to 3 mm are permissible; these will not affect the magnitude of the discharge voltage.

This conclusion is in contradiction with experimental data on breakdown in a nonuniform field (for example, the point–plane electrode system). In explaining the phenomenon of breakdown, Kossel does not take into account the role of space charges formed as a result of the change in the configuration of the electric field. Space charges cause a sharp increase in the field intensity in some of its parts. For spark gaps within the limits of a uniform field, the breakdown intensity of the electric field has a definite value independent of the distance between the electrodes. With an increase in the length of the gap of a spherical discharger, the electric field becomes nonuniform and the breakdown field intensity decreases. It has been established that a discharge can arise only in the case when the intensit-

the field strength reaches a critical value in a limited space [4]. Such a phenomenon will most likely occur at disruptive protrusions. A spark, having arisen in this region, may propagate farther into the interelectrode gap, despite the fact that the electric-field strength in the gap has not reached the critical value. Owing to ionization of the gap, a space charge is formed. The electrons, having reached the anode, are absorbed by it, while the remaining positive ionic charge in the discharge gap is distributed in such a way that the principal part of it is concentrated near the anode. Such a distribution of the space charge will lead to still greater distortion of the initial field. When the critical strength is reached in the disturbed region of the electric field, partial breakdown of the gap will occur. The ions in the region of partial breakdown may be regarded as a conductor that is a continuation of the point (a streamer). In a point–plane electrode system,

Fig. 1. Dependence of the breakdown voltage on the size of a point on the electrode surface under constant voltage according to Schäibe.

the streamer develops more readily when the point is positive. Consequently, the breakdown voltage for negative polarity of the point will be higher than for positive polarity. In order for the discharge to continue at negative polarity, it is necessary to increase the surface field strength, i.e., to raise the voltage. The streamer lengthens and, at a certain voltage, connects the two electrodes by a conducting channel. The distortion of the field by the space charge causes a lowering of the breakdown voltage. Thus, taking into account the influence of space charges, a self-sustained discharge occurs at a reduced voltage. The discharge voltage decreases especially noticeably in a sharply nonuniform field, where space charges play a very significant role, and the discharge voltage depends strongly on the polarity of the electrodes [3].

Up to the present time, the question of the influence of disturbances of the electrode surface on the discharge voltage has not been sufficiently studied, although it is of great importance. Experimental data are lacking on the influence of disturbances of the electrode surface on the discharge voltage under impulses. At ultra-

…high electric voltages and large distances between electrodes, new physical phenomena and features in the operation of installations are encountered which are not taken into account or do not occur at lower voltages. Therefore, complex devices are used to regulate the field in order to obtain the usual operating potential gradients in the designs of apparatus and installations for extra-high voltages. An increase in operating gradients and a reduction in the overall dimensions of installations are achieved by uniform loading of the insulation through the creation of a favorable configuration of the installation’s electric field. The task was set to investigate the influence of disturbances of the electrode surface on the dc and impulse discharge voltage in air and oil, and to give practical recommendations for the treatment of the surfaces of high-voltage apparatus and equipment.

The discharge voltage was measured between spheres of diameter \(d_{\text{sphere}} = 50\) mm with a disturbed surface under dc and impulse voltages in air. The disturbing protrusion was a wire of various lengths and various diameters, which was passed through the sphere. The treatment of the end of the wire is immaterial, since under impulses it melts slightly. In the experiments the distance between the spheres remained constant and equal to 20 mm. For such a length of the discharge gap, the field between spheres with \(d_{\text{sphere}} = 50\) mm may be considered uniform. The diameter of the spheres remained constant; only the dimensions of the point were varied. The voltage was measured with sphere gaps.

Fig. 2. Dependence of the breakdown voltage on the magnitude of the point on the electrode surface in air. Dc voltage.

\(U_{\text{br. max}}\)—breakdown voltage.
\(\triangle\) \(l\)—length of the point.
1—wire of diameter 0.07 mm; point (−). 2—wire of diameter 0.07 mm; point (+). 3—wire of diameter 0.18 mm; point (−). 4—wire of diameter 0.18 mm; point (+). 5—Schaibe dependence (wire of diameter 0.075 mm). 6—Schaibe dependence (wire of diameter 0.2 mm).

On Fig. 2 is shown the dependence of the discharge voltage on the length of the point for different wire diameters under dc voltage. For comparison, Schaibe’s dependences are given for identical wire diameters. From our experiments it follows that the magnitude of the discharge voltage is affected more by the length of the point than by its diameter. With a decrease in the wire diameter, the influence of the polarity of the point on the magnitude of the discharge voltage is smaller. Breakdown of the gap is preceded by the formation of a corona around the point. The corona inception voltage was determined visually and by sound. With an increase in the length of the point from 0.5 mm to 15 mm, the corona inception voltage decreases, respectively, from \(0.73\,U_{\text{br. max}}\) to \(0.44\,U_{\text{br. max}}\). The dependence of the corona inception voltage on the length of the point is presented in Fig. 3.

An investigation was carried out of the influence of disturbances of the electrode surface on the discharge voltage under impulses. From experiments on the distribution of the voltage drop under impulses in the interelectrode gap, kindly provided by V. S. Dmitrevskii, it is known that the greatest voltage drop occurs in the region near the high-voltage electrode, if the electrodes are symmetrical. Disturbance of the field by a foreign object in this region will lead to a discharge at a lower voltage than when other regions of the interelectrode gap are disturbed. If the point is on the grounded electrode, then the increase in the field strength near the grounded electrode is less than in the case when the point is on the high-voltage electrode; therefore, with a grounded point the discharge voltage is higher than with an ungrounded one.

Fig. 3. Dependence of the breakdown voltage on the size of the point on the electrode surface. Impulse voltage.

1—wire of diameter 0.07 mm; point (−). 2—wire of diameter 0.18 mm; 0.38 mm; point (−). 3—wire of diameter 0.07 mm; 0.18 mm; 0.38 mm; point (+). 4—corona-inception voltage for the point (−). 5—corona-inception voltage for the point (+).

Figure 3 shows the dependence of the magnitude of the discharge voltage on the length of the point for various wire diameters under impulse voltage. The difference in discharge voltages for different polarities of the point under impulses is many times greater than under direct voltage. The thinner the wire, the more significant the influence of polarity.

From a comparison of the results of investigations under impulse and direct voltage (Figs. 2 and 3), it is seen that the discharge voltage for negative polarity of the point under impulses is 25% higher than under direct voltage (Fig. 4). Correspondingly, for positive polarity of the point it is higher by 10–15%. However, it cannot be asserted that disturbance of the electrode surface does not affect the magnitude of the discharge voltage under impulses. As can be seen from Fig. 4, a point 0.5 mm long and 0.07 mm in diameter already lowers the impulse discharge voltage by 10% when the point is negative. If the point is positive, the breakdown impulse voltage decreases by more than 40%. The assertion that “...it is not necessary to avoid sharp corners, as is done at normal frequency, in the designs of impulse generators, since under impulses sharp edges, corners, etc. have a higher discharge voltage than rounded parts,” is not confirmed by our experiments [2].

Figure 5 presents the dependence of the discharge impulse voltage on the magnitude of the capacitance in the “strike” for a point of positive polar-

of a certain length (6 mm). With an increase in the capacitance in the “surge,” the discharge voltage decreases, and the amount of energy entering the gap, equal to

\[ W_{\mathrm{dis}}=\frac{C U_{\mathrm{br.\,max}}^{2}}{2}\ \mathrm{W\,sec}, \]

Fig. 4. Comparison of the results of studies at direct and impulse voltages. Wire diameter 0.07 mm.

1, 4—impulse voltage.
2, 3—direct voltage.

increases, since when the capacitance in the “surge” is increased by a factor of 3, the breakdown voltage decreases by only 12%. For a point of negative polarity, the influence of the capacitance in the “surge” is smaller.

Fig. 5. Dependence of the impulse breakdown voltage on the magnitude of the capacitance in the “surge.”

\(C\)—capacitance in the “surge.”

1—dependence of the breakdown voltage on the magnitude of the capacitance in the “surge.”

2—dependence of the energy

\[ \frac{C U_{\mathrm{br.\,max}}^{2}}{2}, \]

entering the gap, on the magnitude of the capacitance in the “surge.”

Experiments were carried out on the flashover of large interelectrode distances up to 100 mm in air (Fig. 6). Planes with rounded edges were used as electrodes. The dependence of the discharge voltage on the magnitude of the disturbing protrusion (a point made of wire) does not differ from the dependences obtained for small interelectrode distances. At

Fig. 6 presents the dependence of the discharge voltage on the length of the point for different pulse polarities. The influence of pulse polarity for points of small size (3–5 mm) is considerable and reaches 25%.

Fig. 6. Dependence of the breakdown voltage on pulse polarity.

1, 2—positive pulse.
3, 4—negative pulse.

On the basis of our experimental data, the average and maximum discharge potential gradients were calculated for points of various sizes during discharge under direct and impulse voltages. The average and maximum voltage gradients were determined as the ratio

\[ E=\frac{U_{\text{br. max}}}{S}\,\frac{\text{kV}}{\text{cm}}, \]

where \(U_{\text{br. max}}\) is the discharge voltage, \(S\) is the distance between the end of the point and the sphere, and also as the tangent to the curve of the dependence of the discharge voltage on the length of the point. The calculated average gradient depends little on the type of voltage (direct, alternating, impulse) and does not depend on the length of the point (and therefore on the length of the gap), with the exception of very small lengths (up to 1.5 mm), at which it increases by approximately 10%.

Figure 7 gives the dependence of the average and maximum calculated gradients on the wire diameter. As is seen from the graph, the average discharge gradient for negative polarity of the point is 25% lower than the discharge gradient of a uniform field. With increasing wire diameter, the average and maximum discharge voltage gradients decrease. An exception is the dependence of the maximum gradient on the wire diameter for positive polarity of the point, which probably increases up to a certain limit and then, evidently, will decrease.

On the basis of the experimental data obtained, it may be concluded that a disturbance of the electrode surface in the form of sharp protrusions or points, with a ratio of point diameter to sphere diameter from 0.0014 to 0.016, lowers the discharge voltage in air. Therefore, the surfaces of high-voltage structures should be carefully polished and sharp protrusions should be avoided.

In conclusion, I consider it my duty to express my gratitude to the supervisor of the work, Professor Doctor A. A. Vorob'ev, for suggesting the topic, and for valuable guidance and critical comments during its execution.

Fig. 7. Mean and maximum calculated potential gradients as a function of wire diameter.

\(E\)—voltage gradient.
1—maximum gradient; point \(( - )\).
2—maximum gradient; point \(( + )\).
3—mean gradient; point \(( - )\).
4—mean gradient; point \(( + )\).

LITERATURE

1. Kossel W. Bemerkungen über elektrostatische Maschinen. Zeit. für Physik, 1938—1939, Bd. 111, Heft 3—4, S. 264—280, mit 9 Fig.

2. Edited by Prof. A. M. Zalesky. Manual for Laboratory Work in High Voltage. ONTI, Kubuch, 1934.

3. Vorob'ev A. A. High-Voltage Engineering. GEI, 1945.

4. Frenkel' Ya. I. Theory of Atmospheric Electricity Phenomena. GITTL, 1949.