Electric field distribution in Point-insulating barrier-Plane system using experimental and theoretical method

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Electric field distribution in Point-insulating barrier-Plane system using experimental and

theoretical method

1^st S. Benharat

Electrical and Industrial Systems laboratory (LSEI) University of sciences and technologies Houari Boumediene

(USTHB)

BP 32 El ALLIA 16111, Algiers, Algeria Research center in industrial technologies CRTI

P.O. Box 64, Cheraga 16014, Algiers, Algeria

2^nd S. Bouazabia

Electrical and Industrial Systems laboratory (LSEI) University of sciences and technologies Houari Boumediene

(USTHB) BP 32 El ALLIA 16111,

Algiers, Algeria [email protected] [email protected]

3rd L.Belgacem Research center in industrial

technologies CRTI

P.O. Box 64, Cheraga 16014, Algiers, Algeria

[email protected]

Abstract—The present paper deals with the influence of insulating barriers on the breakdown and the electric field distribution in the Point –insulating barrier- plane air gap system. An experimental investigation on the influence of different parameters such as gap distance between electrodes and barrier dimensions, under AC voltage, have been studied.

The results show that the width and thickness of the insulating barrier effect the electric field variation which increases with increasing applied voltage. The experimental results are compared with a numerical model.

Keywords—Electric field, finite element method, breakdown voltage, insulating barrier, point- plane system.

I. INTRODUCTION

High and medium voltage equipment usually includes mixed structures, combining at least two phases: solid/liquid or solid/gas [1]. This type of insulation is present in equipment such as power transformers and capacitors, circuit breakers and cables as well as in overhead lines.

During putting the electric apparatus into operation of which they form part, these insulating structures may be subjected to different types of constraints and more particularly to electrical constraints. In the presence of an electric field, various phenomena can take birth in the bulk of these materials or on its surface. Indeed, when the electric field exceeds a threshold value, bulk or surface discharges can be generated and lead to the destruction of the insulating structure (following a breakdown of the insulating structure or a bypass of the solid insulation) or even the decommissioning of the system [2-7].

Therefore, knowledge of the conditions of initiation and propagation of these electrical discharges is of great interest for the design, dimensioning and optimization of equipment.

In this paper, the study of the electric field in the point- plane geometry with insulating barrier is presented. For these reasons, an experimental device on a point-plane system with insulating barrier is developed in our Research Laboratory (LSEI). The operating conditions can be simulated with FEMM [8] and Matlab [9] software.

II. EXPERIMENTAL PROCEDURE AND MESURMENT A. Experimental device description

Figure.1 shows the entire experimental setup consisting of a high-voltage power supply, a study system and an acquisition and measurement system (probe and other low- voltage measuring devices).

Fig.1.Schematic diagram of the experimental device

B. System design

The study system consists of a cylindrical steel rod 5mm in diameter, terminated by a conical tip of 2mm in diameter which is the point electrode. The grounded electrode is a steel plane (50 x 36.5 cm²) placed at a distance d from the point electrode. An circular insulating barrier of different diameters (w) and thicknesses (e) is inserted between the two electrodes at a distance x from the point electrode. The set-up is disposed on two wooden insulating supports, one to put the rod-plane system where we can move the plane and the other to hold the barrier is suspended between the point and the plane (Fig.2).

The electric field is measured at the plan electrode using Wilson probe.

1-autotransformer 4-measuring capacitor 2- set-up transformer 5-oscilloscope 3-study system 6-voltmeter

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2 Fig.2 . Rod-plane configuration with insulating barrier

III. MODELING A. Study system model

The study system (Fig.3) consists of an arrangement of point plane electrode gap of d, between which is inserted an insulating barrier of width w, of thickness e and relative permittivity εrsolid, placed at the distance x from the point electrode. The point electrode of radius rp, is connected to the high voltage HV (Uapp) and the planar electrode of width Lp, is grounded. The electric field is measured and calculated on the surface of the plane electrode according to the position x1.

Fig. 3. Study system

To evaluate the effect of the barrier on the behavior of the system, it assumes that a change in the electric field is induced by the presence of the insulating barrier; its distribution depends of dimensions and position of the barrier.

In this paper, the influence of the presence of the barrier on the electric field is evaluated.

B. Electric Filed computation

The field values are obtained by solving the Maxwell equations governing the static state.

= (1)

With :

= (2) D: Electric displacement field, ε : Dielectric permittivity,

ρ: Charge Density, E : Electrical field.

Taking into account the local form of the Ampere law:

= 0 (3) Where:

= − (4) V: Electrical voltage.

Combining equations 1 and 4 gives the Poisson equation in the case of a homogeneous material:

∆ = − (5) Neglecting the space charges and considering the

calculation on the x-y plane, this equation is written as:

^!" + _$ ^!_$" = 0 (6) The resolution of this equation in the study system can be

done only by a numerical calculation. To do this, the FEMM software [8] in MATLAB [9] environment is used, with considering a Neumann boundary condition on a rectangular border around the system:

∂V

∂n = 0 (7) IV. RESULTS AND DISCUSSIONS

A. Voltage effect on the electric field - For different widths

For all, the distance between the 2 electrodes is d=100mm. The results in figures (4 to 7) represent the electric field variation on the plane electrode by varying the applied voltages (Uapp=760V, 1900V, 3040V, 4180V, 5320V), for a fixed diameter, thickness and position of insulating barrier.

Fig .4. Electric field distribution on the plane electrode for different voltages, e=1.2mm, w=23mm and x=8.8mm.

Fig.5. Electrical field distributions on the plane electrode for different voltage, e=1.2mm, w=35.6mm and x=8.8mm.

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

positions(cm)

champ(KV/CM)

Uapp=diff D=23mm

5320V 4180V 3040V 1900V 760V 5320V S 4180V S 3040V S 1900V S 760V S

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

plan cm

E (kV/cm)

U=diff D=35.6

5320V 4180V 3040V 1900 760 5320V S 4180V S 3040V S 1900V S 760V S

x1 (cm)

x1 (cm) Rod

electrode

Insulating barrier

Probe Plan

electrode

Electric field (kV/cm) Electric field (kV/cm)

w

P x1 P1

Plan

x ɛ₀ HV

r_p d

Lp

Insulating barrier e

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3 The curves above show that the field increases with increasing voltage. We note also that the field is maximum near the center of the plane, moving away from this center towards the edge the electric field decreases and tends towards a constant value.

By increasing the voltage, the difference between the two results (simulated and experimental results) becomes more important from 3cm.

Fig.6 . Electrical field distributions on the plane electrode for different voltages, e=1.2mm, w=49mm and x=8.8mm.

Fig .7 . Electrical field distributions on the plane electrode for different voltages, e=1.2mm, d=61.8mm and x=8.8mm.

- For different thicknesses

For a position x = 8.8mm and a diameter w= 23mm, the electric field repartition on the plan for different voltages and thicknesses of the barrier, are given in the figures (8 to 10)

Fig.8 . Electrical field distributions on the plane electrode for different voltages, e=1.2mm, w=23mm and x=8.8mm.

Fig .9 . Electrical field distributions on the plane electrode for different voltages, e=2.4mm, w=23mm and x=8.8mm.

Fig .10 . Electrical field distributions on the plane electrode for different voltages, e=4.2mm, Lb=23mm and x=8,8mm.

Increasing applied voltage induced an increase of the electric field which takes its maximum value near the center of the plane electrode and decreases and becomes constant as it moves away. Note that for the lower applied voltage, more the simulation results agree with those of the experimental ones.

B. Position effect on the electric field distribution

Figures (11 to 15) show the electric field distribution on the plan electrode for different applied voltages for x position of the barrier, thickness e=1.2mm and a width w=49mm.

Fig .11 . Electrical field distributions on the plane electrode for different positions, Uapp=1900V, e=1.2mm, w=49mm

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

position(cm)

champ(kV/cm)

U=DIFF D=49MM

5320V 4180V 3040V 1900 760V 5320V S 4180V S 3040V S 1900V S 760V S

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

positions(cm)

champ(KV/CM)

U=diff D=61.8mm

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

positions (cm)

E (kV/cm)

E=f(D) pour e=1.2mm, Lb=23mm, x=10mm et Upp=diff

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3

positions (cm)

E (kV/cm)

E=f(D) pour e=2.4mm, Lb=23mm, x=7.6mm et Uapp=diff

0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3 3.5

positions (cm)

E (kV/cm)

E=f(D) pour e=4.2mm, Lb=23mm, X=5.8mm et Uapp=diff

0 1 2 3 4 5 6 7 8 9 10

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

position (cm)

E (kV/cm)

E=f(Xp) pour e=1.2mm, Lb=49mm ,x=diff et Uapp=760V

x=88.8mm x=58.8mm x=28.8mm x=8.8mm x=88.8mm S x=58.8mm S x=28.8mm S x=8.8mm S

x1 (cm) x1 (cm)

x1 (cm)

Electric field (kV/cm) Electric field (kV/cm) Electric field (kV/cm) Electric field (kV/cm)

Electric field (kV/cm) Electric field (kV/cm)

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4 Fig.12 . Electrical field distributions on the plan electrode for different

positions, Uapp=1900V, e=1.2mm, w=49mm.

Fig .13 . Electrical field distributions on the plan electrode for different positions, Uapp=3040V, e=1.2mm, w=49mm

Fig .14. Electrical field distributions on the plane electrode for different positions, Uapp=4180V, e=1.2mm, w=49mm.

Fig.15 . Electrical field distributions on the plane electrode for different positions, Uapp=5320V, e=1.2mm, w=49mm.

For the position change, and for experimental results we notice that near the center of plan electrode (under point electrode) the electric field takes its maximum value.

Moving the barrier, the electric field decreases and becomes constant. It has also been found that the values obtained from the simulation are almost equal to those of the experimental between 0 to 40mm of the position x1 on the plane, by exceeding this interval, the difference becomes more important.

CONCLUSION

Experimental and simulation tests in our laboratory allowed us to draw the following conclusions:

The barrier width has a slightly influences on the electric field variation , as soon as the width is increased the field increases, whether by simulation or experimentally.

The thickness has an effect on the electric field distribution. For small thicknesses the electric field does not change, but when the thickness becomes larger the field increases.

It can also be seen that the electric field increases with increasing voltage.

The slight difference between the experimental and simulation results could be due to measurement errors, and also to the chosen simulation conditions (such as not taking into account the space charge).

REFERENCES

[1] S. M. Lebedev, O. S. Gefle and Y. P. Pokholkov, “The Barrier Effect in Dielectrics: The Role of Interfaces in the Breakdown of Inhomogeneous Dielectrics”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 12, No.3; June 2005

[2] A. Boubakeur, “Influence des barrières sur la tension de décharge disruptive des moyens intervalles d’air pointe - plan”, Thèse de doctorat, Politechnika Warszawska, Warsaw, 1979.

[3] A. Beroual and A. Boubakeur,” Influence of Barriers on the Lightning and Switching Impulse strength of Mean Air Gaps in Point/Plane Arrangements”, IEEE Trans. Electr. Insul, Vol .20, No.6, pp.1131- 1991.

[4] Li. Ming, M. Leijion and T. Bengtsson, Ninth international Symposium on High Voltage Engineering, paper 2168. 1995 Graz Convention Center, Austria, 1995.

[5] F. Topalis and I. Stathopulos, “Barrier effect on electrical breakdown in non uniform small and medium air gaps” in Proc. IEE 6th Int.

Conf. Dielectric Materials, Measurements and Applications, Manchester, pp. 439–442, 1992.

[6] S. Sebo, J. Kahler, S. Hutchins and C. Meyers, D. Oswiecinski, A.

Eusebio, and W. Que, “The effect of insulating sheets (barriers) in various gaps the study of ac breakdown voltages and barrier factors”

in Proc. 11th Int. Symposium on High Voltage Engineering, London, Vol. 3 , pp. 144–147, 1999.

[7] S Mouhoubi and A Boubakeur, “Influence des barrières isolantes sur la tension de claquage des intervalles d’air pointe-plan en tension continue et alternative”, International Conference on Electrical System (ICES’06), pp174-177, Oum el Bouagui 2006.

[8] D.Meeker,“Finite Element Method Magnetics”, Version 4.0, [email protected] , May 2004.

[9] “ Matrix laboratory”, livre de matlab math.

0 1 2 3 4 5 6 7 8 9 10

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Positions (cm)

E (kV/cm)

E=f(Xp) pour e=1.2mm, Lb=49mm, x=diff et Uapp=1900V

0 1 2 3 4 5 6 7 8 9 10

0.8 1 1.2 1.4 1.6 1.8 2

Poition Xp (cm)

E (kV/cm)

0 1 2 3 4 5 6 7 8 9 10

1 1.5 2 2.5

Poition Xp (cm)

E (kV/cm)

0 1 2 3 4 5 6 7 8 9 10

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Position Xp (cm)

E (kV/cm)

x1 (cm)

x1 (cm) x1 (cm) x1 (cm)

Electric field (kV/cm) Electric field (kV/cm) Electric field (kV/cm) Electric field (kV/cm)