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The Influence of the Inhomogeneity of the Field, the Effect of Grounding and the Corona Current to the Dielectric Behaviour of Small Air Gaps Athanasios Maglaras Electrical Engineering Department Technological Educational Institute of Larissa T.E.I. of Larissa Larissa, 41110, Greece Frangiskos V. Topalis School of Electrical and Computer Engineering National Technical University of Athens Iroon Politechniou 9, Athens, 15780, Greece +306936858768, +302410610803. maglaras@teilar,gr ABSTRACT: The influence of the inhomogeneity of electric field, the effect of grounding, and the corona current to the dielectric behaviour of the rod-plate air gaps is investigated in the present paper. The ground effect occurs due to the fact that in the air gap arrangements one electrode is usually grounded. The maximum and the average value of the field strength and the field factor of the gap were resulted by simulation. The corona onset voltage, the corona current and the breakdown voltage of correspondent experimental arrangements were measured. It is resulted that (a) the effect of grounding has a significant influence to the electric field distribution, and hence to the corona onset and the breakdown voltage of small air gaps and is valid for both polarities of the applied voltage, and (b) the inhomogeneity of the field determines the evolution of the dielectric behaviour of the gap. Keywords: Air Gap, Field Strength, Breakdown, Corona, Ground Effect, Polarity Effect. I. INTRODUCTION Small air gaps are widely used in several applications like ozone production and chip construction, in electrostatic filters, electrostatic painting, loudspeakers, etc. The dielectric behaviour of these arrangements and especially the corona onset and the breakdown voltage, as well as the corona current is of great importance. The mostly used air gaps are the rod-plate (or the pointplate), and the rod-rod (or point-point) air gaps, [1] - [9]. The corona effects and the polarity effect are well known phenomena and thoroughly studied, while their influence to the dielectric behaviour of air gaps has been investigated for many applications [1] – [12] The most determinant factor for the dielectric behaviour and especially for the dielectric strength of an air gap is the inhomogeniety of the electric field, and especially the maximum value of the field strength in the gap, which usually appears on the sharper edge of the electrodes, mostly on the tip of a rod, and the field factor across the axis of the gap. Other factors are the polarity and the form of the applied voltage as well as the corona effects, which take place when the field strength exceeds some specific value [6] - [14]. In less homogenous electric fields like the small air gaps with relatively big diameters of the electrodes, the corona effects do not appear before breakdown. The values of the breakdown voltage depend on the grade of the field’s inhomogeneity. The more inhomogeneous the field is the lower the breakdown voltage becomes [15[, [16]. In longer air gaps the field is more inhomogeneous and corona effects and hence a corona current through the gap occur before breakdown. The intensity of the corona effects depend on the grade of the field’s inhomogeneity. The more inhomogeneous the field is the higher the corona current becomes. The corona current influences the breakdown voltage positively [16]-[19]. It is well known that the grounding of one of the electrodes influences the values of the breakdown voltage of the spark gaps, especially in the vertical arrangements (Fig. 1). This is due to the fact that the distribution of the electric field is influenced by the parasite capacitances between the electrodes and the grounded surroundings [1] – [3]. In a rod-plate gap the influence also depends on the electrode chosen to be grounded [18] – [19]. It is also well known that on the tip of a stressed rod the corona effects start when the value of the field strength at the tip exceeds some specific value, given by empirical equations. The value depends on the radius of the rod’s tip and the polarity of the applied voltage. In rod-plate air gaps it also depends on the gap length, and the plate’s diameter [1] – [4]. ( x, y) 2 : rr y rr , , R1 2 2 2 2 a rr G 2 rr y x rr G 2 rr y G 2 G ( x, y) : 2 x 2 b, . P 2 2 2 2 r b b x G b y r b b x G b p p 2 2 2 2 2 2 2 2 (7) (8) y Shield R Figure 1. Spark gaps Plate 2rr Rod rpl a rpl x II. THEORETICAL In the present paper the influence of the grounding of one of the electrodes to the field distribution and the dielectric behaviour of horizontal rod-plate air gaps has been analytically and experimentally investigated. Especially investigated is the way in which the inhomogeneity of the field influences the appearance of the corona or the breakdown in a rod-plate air gap. What need to be clarified is if it is possible, using exclusively simulation analysis, and not experiments, to predict whether in a gap stressed by high voltage corona effects or breakdown is expected. Special models of rod-plate and rod-rod air gaps have been analyzed with the Finite Element Method. All the analyzed models are axisymetric, with a spherical boundary shield big enough in diameter. The influence of the grounding to the electric field distribution in air gaps has been investigated. Special software has been used for the simulation analysis of the air gap models. It is based on the Finite Element Method with the use of Poisson’s equation 2V , (1) and the Dirichlet boundary conditions V=0, in order to solve two-dimensional problems of axisymetric models. The initial conditions of a rod-plate air gap are given by the following equations (Fig. 2) a) For the arrangements with the rod grounded, while the plate is stressed by 1V: V ( x, y) 0, if ( x, y) R1 , (2) V ( x, y ) 2, if ( x, y ) P (3) b) For the arrangements with the plate grounded, while the rod is stressed by 1V: V ( x, y ) 0, if ( x, y ) P , (4) V ( x, y) 1, if ( x, y) R1 , (5) where ( x, y) 2 : x 2 y 2 R 2 , (6) G/2 G/2 b Figure 2. The rod-plate model. One electrode is stressed, whereas the other is grounded. R>>G. III INVESTIGATION PROCEDURE The differences between equations (2), (3), and (4), (5), for the initial conditions, are significant, and lead to differences in the electric field distribution. The maximum value of the field strength in the gap, and the average value of the field strength and the field factor along the axis of the gap have been resulted from analysis, listed and analyzed. The corona onset, the corona current and the breakdown voltage of correspondent experimental horizontal laboratory arrangements have been measured. The influence of the ground effect to the corona onset and the breakdown voltage of small air gaps have been investigated. Special attention has been given to the investigation of the way in which the average value of the field strength and the field factor across the axis of the gap influence the phenomena of corona and breakdown. The arrangements, which have been modeled, analyzed, and experimentally studied, are typical rod-plate air gap arrangements of different electrode geometry. The rod electrode is a cylinder long enough, with a relatively small diameter (4-14 mm) and a hemisphere tip, and the plate electrode is a disk up to 150 mm in diameter. High DC voltage of negative or positive polarity is applied to one electrode while the other is at earth potential (grounded), or both electrodes are symmetrically charged with opposite 190 Field strength on the rod (V/m). and equal voltages. A.C. and lightning Impulse voltage have also been used. The influence of the surrounding is minimized, by keeping relatively big distances between the models and the boundary shielding, as well as between the experimental arrangements and the grounded elements of the laboratory. All the analyzed models are axisymetric with a spherical boundary shield big enough in diameter (at least 200 times bigger than the gap’s length) at earth potential (Fig. 2). In the experimental models the grounded surroundings are at a distance of at least 20 times longer than the gap’s length. The average value of the field strength, along the axis of an air gap (Fig. 2 ) is defined by equation: av V G (9) Rod 10 mm Plate 100 mm 1V 150 110 70 30 1 2 3 4 5 6 7 8 Gap length (cm) The field factor (or efficiency factor) n is a net number, which defines the inhomogeneity of the field in the gap and is expressed by equation: nE E max av , (10) where V is the applied voltage, G is the gap length, Emax is the maximum value of the field strength (on the tip of the rod), and Eav is the average value of the field strength along the axis of the gap. For a rod-plate air gap, with a very big plate, the field factor is given by equation [1,2]: 2G , if G>>rr, (11) n r ln( G r ) r r where and rr is the radius of the rod. The plate’s diameter is big enough. The polarity of the applied voltage affects the maximum values of the field strength at corona onset and breakdown, the influence depending on the rod’s and the plate’s diameter (polarity effect) [1] – [4]. IV. THE SIMULATION RESULTS The simulation analysis with the Finite Element Method has shown a significant influence of the ground effect to the field distribution in rod-plate air gaps. The differences between the arrangements with the rod or the plate grounded, or with symmetrically charged electrodes are obvious as shown in Figures 3, and 4. The effect of grounding is intense when the gap length is relatively big and the plate’s and rod’s diameters are relatively small. In the air gaps with the rod-grounded (rgr) the field is less inhomogeneous than in the plategrounded (pl-gr) arrangement, (Figure 4). The maximum values of the field strength on the rod and the values of the field factor along the axis are relatively lower in the arrangements with the rod grounded (r-gr), and higher in the arrangements with the plate grounded. In the arrangements with symmetrically charged electrodes the values are somewhere in between, (Figure 3) Figure 3. The maximum values of the field strength on the rod and the field factor along the axis of rod-plate air gaps, for the different arrangements with the rod (r-gr), or the plate grounded (pl-gr), either with symmetrically charged electrodes (symm.). Plate-grounded. Symm. charged Rod-grounded Figure 4 Field strength distribution in rod-plate air gap models for the different arrangements. V. THE EXPERIMENTAL RESULTS The grounding of one electrode influences the corona onset and the breakdown voltage of the rod-plate air gaps greatly. The corona onset voltage is higher in the less inhomogeneous arrangement with the rod grounded and lower in the arrangement with the plate grounded. The grade of the differences depends on the gap length, as well as the rod’s and the plate’s diameter. When the applied voltage is negative the effect of grounding to the corona onset voltage is intense, as shown in Figure 5. In the rod-grounded arrangement the field is less inhomogeneous and there are no corona effects before the breakdown, and thus the breakdown voltage is 80 70 60 50 40 30 20 10 0 overlapped. This is the effect of the corona current to the breakdown voltage [19]. 100 Vbr, r-gr Corona onset voltage (KV) Volta ge (KV) compared to the corona onset voltage of the plate-grounded arrangement. Vc , pl-gr 1 2 3 4 5 6 7 8 9 10 80 R-gr, Vbr, DC(-) Rod (+) 60 40 Pl-gr, Vc, DC(+) 20 0 G a p le ngth (c m ) 1 2 3 4 45 40 35 30 r-gr 25 pl-gr 20 15 10 1 2 Ga p le ngth, c m 3 Corona Ons et Voltage (KV) 70 60 50 40 30 20 10 0 r-gr pl-gr 1 2 3 4 5 6 7 8 9 Gap length (cm) 6 7 8 9 10 11 60 50 40 V, r-gr, DC (-) Rod (-) 30 V, pl-gr, DC (+) 20 10 0 1 (b) Breakdown voltage Figure 5. The effect of grounding to the corona onset and the breakdown voltage of rod-plate air gaps stressed by DC negative voltage. 5 Gap length (cm) Breakdown voltage (KV) Bre akdown voltage, KV (a) Corona onset and breakdown voltage 2 3 4 5 Gap length (cm) Figure 7. The effect of grounding to the corona onset and the breakdown voltage, when the polarity of the rod is the same (positive or negative) compared to the plate. The effect of grounding is also valid when the applied voltage is DC of positive polarity, (Figure 6). The effect of grounding is clearer for the cases in which the rod has the same polarity (positive or negative) compared to the plate. The corona onset and the breakdown voltage are analogically higher in the arrangement with the rod grounded than in the arrangement with the plate grounded in small and longer air gaps (Figure 7), as it is expected from Figure 3. In these arrangements there is no polarity effect. (a) Corona onset voltage Breakdown Voltage (KV) 80 70 60 Rod-plate 10-100 mm DC(+) r-gr VI. THE INFLUENCE OF THE AVERAGE VALUE OF THE FIELD STRENGTH 50 40 30 pl-gr 20 10 0 1 2 3 4 5 Gap length, (cm) (b) Breakdown voltage Figure 6. The effect of grounding to the corona onset and the breakdown voltage of rod-plate air gaps stressed by DC positive voltage. The corona current minimizes the effect of grounding to the breakdown voltage. The corona current, appears earlier in the plate-grounded arrangement, than in the arrangement with the rod-grounded, and changes the field distribution, making it less inhomogeneous. The maximum value of the field strength decreases and the breakdown voltage increases, (Figure 5). The effect of grounding is The average value of the field strength across the axis of a rod-plate air gap at corona onset or breakdown, given by equation (9), decreases as the gap length increases, the value also depending on the gap’s geometry. From figure 9 it can be resulted that breakdown occurs without corona when the average value of the field strength across the gap is higher than a specific value Eav1>11 KV/cm. Otherwise, and under the circumstance that the maximum value of the field strength is higher than the appropriate value Ec, corona appears before breakdown. It can also be resulted that the breakdown occurs before corona when the gap’s length is smaller than 2 - 4 cm, the value depending on the rod’s diameter also. Air gaps with two different rod’s diameter of 4 and 12 mm, and a plate diameter of 100 mm, have been chosen. The results of gaps with bigger diameter of plate, or with rod’s diameter between 4 and 12, are somewhere between. In the graphs of Figure 9, two different areas can be clearly separated: the left area, in which breakdown occurs without corona, and the right area, where corona appears (right bottom area) before breakdown (top right area). Average field strength (KV/cm) 20 18 R-gr, (+) 16 14 12 Breakdown after corona Brekdown without corona pl-gr, (-) 10 R-gr, (+) 8 pl-gr, (-) 6 Corona 4 2 r(-) It can be generally concluded from Figures 9 and 10 that in rod-plate air gaps stressed by high voltage: a) The gap is led to breakdown without corona when the average value of the field strength along the axis of the gap is higher than 11 KV/cm, and the value of the field factor is lower than 3.5, b) the gap is led to breakdown after corona when the average value of the field strength along the axis of the gap is higher than 11 KV/cm, and the value of the field factor is higher than 3.5, and c) corona occurs when the average value of the field strength along the axis of the gap is lower than 11 KV/cm, and the value of the field factor along the axis is higher than 4.5. These results are valid for air gaps with a rod’s diameter between 4 and 12 mm. 0 1 2 3 4 5 18 6 16 Gap length (cm) Corona and breakdown 14 Field factor 25 20 15 Breakdown after corona Brekdown without corona Average field strength (KV/cm) (a) Negative rod 4 mm, plate 100 mm 12 10 R-gr 8 6 4 Brekdown without corona 2 pl-gr, (-) 0 R-gr, (+) 1 10 2 3 4 5 6 7 8 R-gr, (+) Gap length (cm) pl-gr, (-) 5 pl-gr r(-) Corona (a) Rod 4 mm, plate 100 mm 0 7 1 2 3 4 5 6 6 Gap length (cm) The dashed lines of the graphs show the values of average value of the field strength, for which breakdown occurs before corona effects. The polarity of the applied voltage influences the results greatly. VII. THE INFLUENCE OF THE FIELD FACTOR The value of the field factor across the axis of a rod-plate air gap at corona onset or breakdown, given by equation (10), increases as the gap length increases, the value also depending on the gap’s geometry. From Figure 9 it can be resulted that breakdown occurs without corona when the value of the field factor across the axis is lower than a specific value FF1<3,5 or 4,5, the value depending on the rod’s diameter. Otherwise, and under the circumstance that the maximum value of the field strength is higher than the appropriate value Ec, corona appears before breakdown. The influence of the polarity of the applied voltage is not significant. In figure 10, two areas can be clearly separated. In the bottom area the gap is led to breakdown without corona, though in the top area corona effects are followed by breakdown. Field factor (b) Negative rod 12 mm, plate 100 mm Figure 9. The average value of the field strength at corona and breakdown. Pl-gr Corona and breakdown 5 4 3 Brekdown without corona 2 r-gr 1 0 1 2 3 4 5 6 7 8 Gap length (cm) (b) Rod 12, plate 100 mm Figure 10. The values of the field factor at corona and breakdown.. VIII. CONCLUSIONS 1) The grounding of one of the electrodes has a significant influence to the electric field distribution, the maximum value of the field strength in the gap, as well as the average value of the field strength and the value of the field factor across the axis of the gap. 2) The ground effect also influences the corona onset and the breakdown voltage of relatively small air gaps and is valid for both polarities of DC applied voltage (positive or negative). 3) The average value of the field strength and the field factor across the axis of the gap are determinant factors for the corona and the breakdown of the gaps. 4) When the average value of the field strength is lower than 11 KV/cm and the field factor is higher than 4.5 corona appears before breakdown. 5) When the average value of the field strength is higher than 11 KV/cm and the field factor is lower than 3.5 the gap is led to breakdown without corona. VIII. ACKNOWLEDGMENT The project is co-funded by the European Social Fund and & National Resources. IX. REFERENCES E. Kuffel, W. Z. Zaengl, J. Kuffel, High voltage engineering. Fundamentals, Newnes Oxford, 2000 . [2] M. Khalifa, High voltage engineering, Theory and practice, Marcel Dekker inc., New York, 1990 [3] M. S. Naidu, V. Kamaraju, High voltage engineering, Mc Graw Hill, New York, 1996. [4] P. N. Nikolopoulos, High voltages, National Technical University of Athens, 1990. [5] “Der elektrische durchshlag von luft im unhomogenen feid“, E. Marx, Arch. F. El., vol. 24, 1930, pp. 61f. [6] “Point to plane corona in dry air”, H. Bandel, Physical Review, 1951. [7] “From the glow corona into the breakdown”, K. Feser, H. Singer, ETZ-A Bd 93, H 1, p 36-39, 1972. [8] “Negative corona in air using a point/cup electrode system, IEEE Transactions on Dielectrics and Electrical Insulation”, Er-ning Li, J. M. K. MacAlpine, Vol. 7 No 6., December 2000. [9] “A comment on the methods of calculation of corona onset voltage”, M. Salama, H. Parekh, K. Srivastava, 1976. [10] M. Abdel-Salam, N. Allen, “Onset voltage of positive glow corona in rod-plane gaps as influenced by temperature”, IEEE Proceedings Science, Measurement and Technology, 2005. [11] “Application of a corona onset criterion to calculation of corona onset voltage of stranded conductors”, Kenichi Yamazaki, Robert G. Olsen, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 11, No 4, 2004 [12] “Computing the corona onset and the utilization factor of rod-plane electrode by using charge simulation method, Ozcan Kalenderli, Emel Onal, Ozkan Altay, IEEE, 2001 [13] “Method for measuring field in space charge by means of Pockel’s device”, K. Hidaka, T. Kouno, J. Electrostatics vol. 11,1982, pp. 195-211, (1982) [14] “Negative Corona in Air Using a Point/Cup Electrode System”, Er-ning Li, J. M. K. MacAlpine, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 7, No 6, 2000. [15] Li Ming, Mats Leijon and Tord Bengtsson, “Factors influencing barrier effects in air gaps”, Ninth International Symposium on High Voltage Engineering, Graz, Austria, 1995. [16] A. Maglaras, “Numerical analysis of electric field in air gaps, related to the Barrier Effect”, 1st IC-SCCE Athens, 2004. [17] A. Maglaras, L. Maglaras, “Numerical Modeling and Analysis of electric field distribution in rod – plate air gaps, with or without barrier, stressed by breakdown voltages”, 1st IC-EpsMsO, Athens, 2005. [18] A. Maglaras, L. Maglaras, J. Drigojias, “ Modeling and analysis along with experimental investigation of the Ground Effect in rod-plate air gaps with or without barrier”, 5th WSEAS/ IASME International Conference on Electric Power Systems, High Voltages, Electric Machines, (POWER’05), Tenerife, 2005.. [19] A. Maglaras, L. Maglaras, “The ground effect, the polarity effect, and the mirror effect in small rod-plate and rod-rod air gaps stressed by DC voltage, 15th Symposium of ISH, Ljubljana, Slovenia, 2007 [1] IV. BIOGRAPHIES Athanasios Maglaras (M’85-93, M’06) was born in Greece in 1948. He received the Electrical and Mechanical Engineering degree from the National Technical University of Athens, in Greece, in 1971, the M.Sc. degree in 1985, and he is a Ph.D. student in National Technical University of Athens, in Greece. Since 1980 he is an Associate Professor of Technological Education Institute (T.E.I.) of Larissa in Greece. He was Head of the Electrical Engineering Department of the T.E.I. of Larissa for 6 years, and he is the Head of the High Voltage and CAD/CAE Laboratory in the T.E.I. of Larissa since 1990. He is a member of the Technical Chamber of Greece, the IEEE, and the CIGRE. The main research interests are High Voltages, Electromagnetic Field Analysis, and CAD/CAE. He was supervisor and partner in many European research and educational projects. He is author of 5 books concerning High Voltages, Electric Fields, CAD/CAE, and more than 20 papers in scientific magazines and conferences. Frangiskos V. Topalis (M’90) received the Diploma in Electrical and Mechanical Engineering and the Ph.D. from the National Technical University of Athens (NTUA) in 1979 and in 1990 respectively. Since 2007 he is Professor of the School of Electrical and Computer Engineering of National Technical University of Athens His research interests concern high voltages, harmonics, lighting and rational use of energy. He is a member of the Technical Chamber of Greece and of IEEE. He is an author of 5 books and 4 technical brochures concerning high voltages, lightning and electrical measurements and more than 100 papers in scientific journals and conferences.