STUDY OF BREAKDOWN OF AIR-GAPS AT HIGH VOLTAGES

Autumn Sem 2010 Report submitted in partial fulfillment of the requirements for

the degree of

Master of Technology In

Power System Engineering

Submitted by: Saswata Sekhar Roy

(09EE6314)

DEPARTMENT OF ELECTRICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY

KHARAGPUR Nov 2010

1

Abstract

Corona inception and breakdown are investigated in air for point-to-Sphere, sphere-to-sphere, rod(square)-to-sphere gaps under 50-Hz ac voltages. The Breakdown Voltage increases if the Gap Distance increases. The equations of Breakdown Voltage as a function of Gap Distance are obtained from the Curve fitting method.

2

Contents Abstract..................................................................................…………………..1 1 Introduction 1

1.1 Types of Mechanism for Breakdown………………………………………………………………………………………………3 1.1.1 Townsend Theory………………………………………………………………………………………………………………………..3 1.1.1.1 Current Growth in the Presence of Secondary Processes…………………………………………………………4 1.1.1.2 Townsend’s Criterion for Breakdown……………………………………………………………………………………….5 1.1.2 Streamer Theory of Breakdown in Gases…………………………………………………………………………………….5 1.2 Paschen’s Law………………………………………………………………………………………………………………………………..7 1.3 Paschen’s curve………………………………………………………………………………………………………………………………7

2 Experimental Techniques 2

2.1 Circuit Diagram……………………………………………………………………………………………………………………………….8 2.2 Test procedures………………………………………………………………………………………………………………………………9 2.3 Air Density Correction factor…………………………………………………………………………………………………………..9 2.4 Humidity Correction Factors……………………………………………………………………………………………………………9 2.5 Standard Reference Atmosphere……………………………………………………………………………………………………9 2.6 According to IEC 60052 (2002) ………………………………………………………………………………………………………..9

3 Work done so far 3 3.1 Calculation……………………………………………………………………………………………………………………………………..12 3.2Results…………………………………………………………………………………………………………………………………………….13 3.2.1 Breakdown voltage in respect to gap distances of SPHERE-SPHERE…………………………………………….13 3.2.2 Breakdown voltage in respect to gap distances of SPHERE-POINT………………………………………………14 3.2.3 Breakdown voltage in respect to gap distances of POINT- SPHERE………………………………………………16 3.2.4 Breakdown voltage in respect to gap distances of ROD(SQUARE)- SPHERE…………………………………18 3.3 Conclusion………………………………………………………………………………………………………………………………………20 4 Future Work 4 4.1 Future Work…………………………………………………………………………………………………………………………………….21

3

1 Introduction

Various phenomena occur in Air dielectric when a voltage is applied. When low voltage is applied, small current flows between the electrodes and the insulation retains its electrical properties. If the applied voltage is large, the current flowing through the insulation increases very sharply and an electrical breakdown occur. A strongly conducting spark formed during breakdown, practically produces a short circuit between the electrodes. The maximum voltage applied to the insulation at the moment of breakdown is called the breakdown voltage. For a uniform gap, the effect of humidity on the breakdown voltage is negligible. For non-uniform gaps such as rod-sphere, sphere-sphere like gaps the influence of humidity is found to be of significant. A correction procedure recommended by IEC is commonly used for converting the measured voltage or the test voltage from non-standard to standard reference atmosphere. So the result in analysis is then corrected into the standard reference conditions [in STP].

1.1 Types of Mechanism for Air Breakdown

There are two types of mechanism for Air breakdown i. Townsend Theory ii. Streamer Theory 1.1.1 Townsend Theory

Townsend conducted experiments on the growth of these currents which led to breakdown under d.c. voltage conditions, and he proposed a theory to explain the phenomenon named as Townsend’s Current Growth Equation.

4

Assuming n0 electrons are emitted from the cathode and when one electron collides with a neutral particle, a positive atom and electron formed. This is called as ionization by collision.

If be the average number of ionizing collisions made by an electron per centimeter travel in the direction of the field where it depends on gas pressure p and E/p, and is called the Townsend’s first ionization coefficient. At any distance x from the cathode when the number of electrons, nx , travel a distance of dx they give rise to ( dxnx ) electrons. Then, the number of electrons reaching the anode at x=d, nd will be

00

xxnn ………………………………....1

xx n

dxdn

or xx enn

0 ……………………….2

And, at x=d. xd enn

0 ………………………......3

Then, the number of electrons reaching the anode(x=d) will be-

…………………………….4

Therefore the average current in the gap, which is equal to the number of electrons traveling per second is

………………………….5

Where I0 is the initial current at the cathode.

1.1.1.1 Current Growth in the Presence of Secondary Processes

When the initial set of electrons reach the anode the single avalanche process is completed. Townsend’s secondary ionization coefficient in the same way as , as the net number of secondary electrons produced per incident positive ion, photon, excited particle or metastable particle and the total value of due to the three different processes is 321 and is a function of gas pressure p and E/p. Following Townsend’s procedure for current growth, it may be assumed that

'0n Number of secondary electrons produced due to secondary processes.

Let, ''0n total number of electrons leaving the cathode.

0

0

1d dn nen

0dI I e

5

Then '

00''

0 nnn …………………………………..6 The total number of electrons n reaching to the anode becomes, denn ''

0denn )( '

00 ……………………….7 And )]([ '

00'0 nnnn …………………………..8

Eliminating '0n ,

)1(10

d

d

eenn

or

)1(10

d

d

eeII

…………..9

1.1.1.2 Townsend’s Criterion for Breakdown

Eqn. 9 give the total average current in a gap before the occurrence of breakdown. As the distance between the electrode d is increased the denominator of the equation tend to zero and at some critical distance d=ds 0)1(1 de ………………………………..10 For values of d<ds, I is approximately equal to 0I and if the external source for the supply of 0I is removed, I becomes zero. If d=ds, I and the current will be limited only by the resistance of power supply and the external circuit. This condition is called Townsend’s Breakdown Criterion and can be written as

1)1( de Normally, de is very large, and hence the above equation reduces to 1de …………………………………….….11 For a given gap spacing and at a given pressure the value of voltage V which gives the values of and satisfying the breakdown criterion is called the spark breakdown voltage V, and the corresponding distance d is called the sparking distance. Townsend Mechanism explains the phenomena of breakdown only at low pressures, corresponding to dp values of 1000 torr-cm and below. For the high pressure breakdown Streamer Theory is to be used. 1.1.2 Streamer Theory of Breakdown in Gases

The theory predicts the development of a spark discharge directly from a single avalanche in which the space charge develop by the avalanche itself is said to transform the avalanche into a plasma steamer. In fig 1, a single electron starting at the cathode by ionization builds up an avalanche that crosses the gap. The electrons in the avalanche move very fast compared with the positive ions. By the time the electrons reach the anode the positive ions are in their original positions and form a positive space charge at the anode. This enhances the field, and the secondary avalanches are formed from a few electrons produced due to the photo-

6

ionization in the space charge region. This occurs first near the anode where the space charge is maximum and a further increase in the space charge. This process is very fast and the positive space charge extends to the cathode very rapidly resulting in the formation of a streamer.

Fig. 1

Ionization proces Comparatively narrow luminous tracks occurring at breakdown at pressures are called streamers. As soon as the streamer tip approaches the cathode, a cathode spot is formed and a stream of electrons rush from the cathode to neutralize the positive space charge in the streamer; the result is a spark and the spark breakdown occurs. A simple quantitative criterion to estimate the electric field rE which is produced by the space charge, at the radius r and that transforms an avalanche into streamer

is given by cmV

pxeE

x

r

71027.5 …………………………..12

where is the Townsend’s first ionization coefficient, p is the gas pressure in torr and x is the distance to which the streamer extends in the gap. When EEr and

dx the equation above simplifies into; p

dp

Epd ln5.0ln5.14ln . ……………..13

This equation is solved for pEandp

at a given p and d that satisfy the equation.

The breakdown voltage is given by the corresponding product Ed . It is generally assumed that for pd values below 1000 torr-cm and gas pressures varying from 0.01 to 300 torr, The Townsend mechanism operates, while at higher pressures and pd values the streamer mechanism plays the dominant role in explaining the breakdown phenomena.

7

1.2 Paschen’s Law The breakdown criterion 0)1(1 de ……………………….14 where and are functions of p

E , i.e.

p

Efp 1

and

p

Ef 2 . Also dVE Substituting for E in the expressions

and and rewriting equation 14 we have

11)(

21

pd

Vfpdepd

Vf …………………..15

This equation shows a relationship between V and pd, and implies that the breakdown voltage varies as the product pd varies. Knowing the nature of functions 21 fandf we can write the equation pdfV known as Paschen’s law and has been experimentally established for many gases. 1.3 Paschen’s curve Fig. 2 is shows the “Paschen Curve” for air, between two flat parallel copper electrodes, separated by 1 inch, for pressures between 3x10-2 torr and 760 torr.

Fig. 2

Paschen’s curve

8

2 Experimental Technique

2.1 Circuit Diagram

The test circuit is shown in Fig. 3. It consists of AC voltage source 220 V, Auto Transformer (0-220 V), 220V/300 kV transformer, water resistor (RW)=560 kΩ.

Fig. 3

Circuit diagram

2.2 Test Procedures

In the Fig 3 adjust the gap distance to an initial value from 5mm to 80mm.220V Power Frequency is applied to the Low Voltage side by a Auto Transformer. Slowly raise the voltage till faint hissing audible sound is heard. This is the beginning of corona. Hence the Corona Inception Voltage. Raise the Voltage further till such time there is a faint visible glow at the high voltage electrode. This is the Visible Corona Inception level. Then slowly reduce voltage further till such time the hissing sound subside i.e., dies down or becomes extinct. This voltage is called Corona Extinction Voltage. Once again raises the voltage till such time there is a Break Down. This voltage is called Breakdown Voltage. Then the measured

9

voltage has been corrected by the Air density correction factor and Humidity Correction factor. Reduce the voltage completely and open the circuit breaker. Then further breakdown has been obtained for different gap distances. 2.3 Air Density Correction factor The air density correction factor, kd is given by:

…………………16 Where, p = atmospheric pressure under test t = temperature (in 0C) under test conditions 2.4 Humidity Correction Factors: The humidity correction factor, kh is given by:

…………………………………17 The constant k is given in Fig 3 as a function of absolute humidity, curve a or b being applicable according to the type of voltage. The exponents m, n, and w depend on the type and polarity of the voltage and on the flashover distance d as given in Table 1 and Fig 5. Lacking more precise information, m and n are assumed to be equal.

2.5 Standard Reference Atmosphere: The standard reference atmosphere is : Temperature to = 20°C Pressure po = 101.3 kPa(760 mmHg) Humidity ho.= 11 g water vapor per cubic meter 2.6 According to IEC 60052 (2002) The breakdown voltage values v (kV) measured under actual conditions with the temperature t(oC), the pressure p (mmHg) and the absolute humidity k (g/m3) are reported to standard reference atmosphere as defined by Eq. V0 =

ܐܓ×

………………….18

10

Fig 4 Humidity Correction Factor k as a Function of Absolute Humidity

Fig 5

Values of the Exponents m and n for Air Density Correction and w for Humidity Corrections, as a Function of Spark over Distance, in Meters.

11

Table 1

Fig 6

Absolute Humidity of Air as a Function of Dry and Wet-Bulb Thermometer Readings

12

3 WORKDONE SO FAR

3.1 Calculation Wet condition temperature, Tw= 26 oC Dry condition temperature, Td= 27 oC Atmospheric Pressure, p = 76.45 Cm of Hg. Standard Temperature, to = 20°C Pressure , po = 101.3 kPa(760 mmHg) Measured Voltage=V in kV Humidity , ho= 11 g water vapor per cubic meter. We are using m=n=w Air density correction factor, kd = ( ୮

ܗܘ) × (ૠାܗܜ

ૠାܜ)

kd = (.ସହ

ૠ ) × (ૠା

ૠାૠ)

kd=0.9824 Humidity Correction factor, kh =(k)w = k, where w=1 From the Fig 2 and Fig 4, we get Absolute Humidity, k= 0.865. Therefore, kh = 0.865 Therefore, kd× kh=0.9824×0.865=0.8497 So the actual Breakdown voltage, Vo=

୩× ୩୦

13

3.2RESULTS

3.2.1 Breakdown voltage in respect to gap distances of SPHERE-SPHERE

The gap configuration of Sphere to Sphere is shown in the fig 7. The electrodes are used of two spheres. One sphere put into HV arm and another is grounded. Now the gap distance vary from 5mm-80 mm and obtained the characteristics of corona inception voltage, visible corona, corona extinction voltage and Breakdown Voltage.

Fig 7

gap distances are vary from 5mm-80mm of SPHERE-SPHERE

In table 2 shows the measured values of Sphere to Sphere are obtained and corrected by Air density correction factor as well as Humidity Correction factor w.r.t standard temperature and pressure.

Table 2 of sphere-sphere

Measured and Corrected value with respect to gap distances

14

Curve of Sphere to Sphere is shown in the fig 8. The corrected values are put in the graph w.r.t Gap distance.

Fig 8

Curve fitting of SHPERE-SPHERE

The curve equation has been obtained by Matlab. This curve of Sphere to Sphere is fitted with 5th degree of polynomial equation. The solution of this equation is followed by f(x) = p1*x^5 + p2*x^4 + p3*x^3 + p4*x^2 + p5*x + p6 Coefficients (with 95% confidence bounds): p1 = -6.222e-008 (-1.331e-007, 8.673e-009) p2 = 1.413e-005 (-1.265e-007, 2.838e-005) p3 = -0.001267 (-0.002289, -0.0002442) p4 = 0.04431 (0.0131, 0.07553) p5 = 1.382 (1.009, 1.754) p6 = 0.1895 (-1.139, 1.518) Goodness of fit: 4.492

3.2.2 Breakdown voltage in respect to gap distances of SPHERE-POINT

The gap configuration of Sphere to Point is shown in the fig 9. The electrodes are used of one spheres and one point. The Sphere put into HV arm and the point is grounded. Now the gap distance vary from 5mm-80 mm and obtained the characteristics of corona inception voltage, visible corona, corona extinction voltage and Breakdown Voltage.

15

Fig 9

gap distances are vary from 5mm-80mm of SPHERE-POINT

In table 3 shows the measured values of Sphere to Point are obtained and corrected by Air density correction factor as well as Humidity Correction factor w.r.t standard temperature and pressure.

Table 3 of SPHERE- POINT

Measured and Corrected value with respect to gap distances

16

Curve of Sphere to Point is shown in the fig 10. The corrected values of Sphere to Point are put in the graph w.r.t Gap distance.

Fig 10

Curve fitting of SHPERE-POINT

The curve equation of Sphere to Point has been obtained by Matlab. This curve is fitted with 5th degree of polynomial equation. The solution of this equation is followed by f(x) = p1*x^5 + p2*x^4 + p3*x^3 + p4*x^2 + p5*x + p6 Coefficients (with 95% confidence bounds): p1 = -1.147e-007 (-1.949e-007, -3.451e-008) p2 = 2.628e-005 (1.015e-005, 4.241e-005) p3 = -0.002038 (-0.003195, -0.0008812) p4 = 0.05771 (0.02238, 0.09303) p5 = 0.3095 (-0.1123, 0.7313) p6 = 0.5417 (-0.9621, 2.045) Goodness of fit: 5.752 3.2.3 Breakdown voltage in respect to gap distances of POINT- SPHERE

The gap configuration of Point to Sphere is shown in the fig 11. The electrodes are used of one spheres and one point. The Poin is put into HV arm and the Sphere is grounded. Now the gap distance vary from 5mm-80 mm and obtained the

17

characteristics of corona inception voltage, visible corona, corona extinction voltage and Breakdown Voltage

Fig 11

gap distances are vary from 5mm-80mm of POINT-SPHERE

In table 4 shows the measured values of Point to Sphere are obtained and corrected by Air density correction factor as well as Humidity Correction factor w.r.t standard temperature and pressure.

Table 4 of POINT-SPHERE

Measured and Corrected value with respect to gap distances

18

Curve of Point to Sphere is shown in the fig 12. The corrected values are put in the graph w.r.t Gap distance

Fig 12

Curve fitting of POINT-SPHERE

The curve equation of Point to Sphere has been obtained by Matlab. This curve is fitted with 5th degree of polynomial equation. The solution of this equation is followed by f(x) = p1*x^5 + p2*x^4 + p3*x^3 + p4*x^2 + p5*x + p6 Coefficients (with 95% confidence bounds): p1 = -1.607e-008 (-2.587e-007, 2.265e-007) p2 = 1.59e-007 (-4.861e-005, 4.893e-005) p3 = 0.0002603 (-0.003239, 0.003759) p4 = -0.01329 (-0.1201, 0.09353) p5 = 0.9657 (-0.31, 2.241) p6 =-0.6048 (-5.153, 3.943) Goodness of fit:52.61 3.2.4 Breakdown voltage in respect to gap distances of ROD(SQUARE)- SPHERE

The gap configuration of Rod(square) to Sphere is shown in the fig 13. The electrodes are used of one Rod of square cross section and another is Sphere. The Rod is put into HV arm and the Sphere is grounded. Now the gap distance vary from 5mm-80 mm and obtained the characteristics of corona inception voltage, visible corona, corona extinction voltage and Breakdown Voltage

19

Fig 13

gap distances are vary from 5mm-80mm of ROD(SQUARE)-SPHERE

In table 5 shows the measured values of Rod (square) to Sphere are obtained and corrected by Air density correction factor as well as Humidity Correction factor w.r.t standard temperature and pressure.

Table 5 of ROD(SQUARE)-SPHERE

Measured and Corrected value with respect to gap distances Curve is shown in the fig 14. The corrected values of Rod(square) to Sphere are put in the graph w.r.t Gap distance 3.2.4.2 Curve fitting of rod(square)- sphere

Fig 14 Curve fitting of ROD(SQUARE)-SPHERE

20

The curve equation of Rod(Square)-Sphere has been obtained by Matlab. This curve is fitted with 5th degree of polynomial equation. The solution of this equation is followed by f(x) = p1*x^5 + p2*x^4 + p3*x^3 + p4*x^2 + p5*x + p6 Coefficients (with 95% confidence bounds): p1 = 7.955e-008 (-2.334e-007, 3.925e-007) p2 = -1.491e-005 (-7.43e-005, 4.447e-005) p3 = 0.0009651 (-0.002919, 0.004849) p4 = -0.02699 (-0.1293, 0.07535) p5 = 1.021 (0.06245, 1.979) p6 = 0.03645 (-2.406, 2.479) Goodness of fit: 0.03829 3.3 Conclusion

In the experiment the Corona Extinction voltage is less than the Corona Inception voltage. Among four set-up, point-to-sphere, sphere-to-point, sphere-to-sphere, rod(square)-to-sphere the low breakdown voltage occurred in the set-up of sphere-to-point. If the air gap is present between the high voltage electrodes is very small, the Corona Inception, Visible Corona and Corona Extinction voltage measuring is not possible in physically.

21

4 Future Work

4.1FutureWork • To find out the breakdown Voltages with respect to following types of electrodes as Point-Point, Point-Rod(square), Rod(Square)-Rod(Square), Rod(circular)-Rod(circular), Rod(circular)-Point. • To find out the common Model Equation of Breakdown Voltages with respect to various gap distances.

22

References

1. IIEE Paper “High Frequency Breakdown Voltage”; by Thanh Duy Chu; March 1992.

2. IEEE paper “Influence of corona discharges on the breakdown voltage of airgaps”; K. Feser, Dr.-lng; Reprinted from PROC. IEE, Vol. 118, No. 9, SEPT. 1971.

3. IEEE Paper “Evaluation of Humidity Correction Factor of Disruptive Discharge Voltage of Standard Sphere Air Gaps”;by Osamu Fujii, TakahiroHayakawa, YukioMizuno, KatsuhikoNaito; EEJTrans 2008; 3:100–105.

4. IEEE Paper “Tests on the breakdown of air at elevated temperatures in non-uniform electric fields” by N.L.Allen, D.S.K.Lam and D.A.Greaves,in 2nd February 2000.

5. IEEE Paper “Effect Of Humidity On DC Breakdown Voltages In Ambient Air At High Altitude”by P A Calva Chavarria and A Robledo-Martinez;in San Franicisco, October 20-23, 1996.

6. IEEE Paper “Corona Inception and Breakdown in No uniform Field with Insulating Support in Air”;by V. Navinchandra Maller and Krishan D. Srivastava; in January 16, 1987.

7. IEEE Paper “Dielectric Breakdown in Nonuniform Field Air Gaps”;by N. L. Allen and M. Boutlendj, H. A. Lightfoot; in 1993.

8. IEEE Transactions on “Power Apparatus and Systems”, Vol. PAS-97, No. 6, Nov/Dec 1978.

9. “IEEE Standard Techniques for High-Voltage Testing”;6th edition; by Approved April 26,1982.

10. Book “High Voltage engineering”;M.S Naidu and V.Kamaraju,4th edition, Tata McGraw Hill Education Private Limited.

11. Html link http://www.sayedsaad.com/High_voltge/insulating_gases/insulating_gases.htm