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Report on Calculations for Determination of Surface Electrical Field Strength and Critical Corona Voltage on Bundled Conductors.

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This report establishes that the maximum surface electrical field strength and critical corona voltage of the flexible conductor bundle for 400 kV switchyard is below the permissible values.

Page: 2 of 7

Contents

page

1. Introduction .....................................................................................................................3

2. System Data....................................................................................................................3

3. Conductor Data ...............................................................................................................3

4. Appendix .........................................................................................................................4

5. Conclusion ......................................................................................................................4

6. References......................................................................................................................4

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1 Introduction

The magnitude of minimum potential at the surface of the conductor at which the breakdown of the insulating properties of air occurs and corona starts is called disruptive critical voltage.

F. W. Peek has concluded from his limited experimental data that the disruptive critical voltage depends upon the atmospheric conditions, ambient air density, conditions of conductor surface, and mainly on the potential gradient at conductor surface. Surface voltage for a conductor in turn depends on the maximum line to ground voltage and the conductor configuration. Conductor configuration includes sub-conductor dimension, sub-conductor spacing and phase spacing of conductor bundles.

If the conductor attains a phase voltage of magnitude higher that the disruptive critical voltage for its configuration and ambient atmospheric conditions, ionisation of the air surrounding the conductor starts and corona is onset.

The objective of the present calculation is to determine the allowable value of disruptive critical voltage and check whether the maximum possible phase to ground voltage of the conductor bundle exceeds it or not.

2 System data

400kV AC Switchyard

Nominal System Voltage 400 kV

System Frequency 50 Hz

Altitude above sea level >1500 m

Barometric Pressure at design altitude 617 mm of Hg.

Design Ambient Temperature 35 0C

According to F. W. Peek, for air under conditions near sea level at 25 0C and at atmospheric

pressure of 760 mm of mercury, the maximum value of voltage gradient at which ionisation of

air starts is 30 kV/cm.

3 Conductor Data

The following type of flexible conductor bundle has been considered in the design:

i) Twin ACSR 954 MCM CARDINAL at the Jack Bus in Coupler bay

Sub-Conductor Diameter 30.42 mm

Sub-conductor spacing 200 mm

Conductor Spacing in 3φ configuration 6.5 m

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4 Appendix

Appendix-1: Check for Critical Surface Electric Field Strength of Overhead Bundle Conductor : A – Jack Bus at Coupler Bay

5 Conclusion

1. The maximum value of electric field strength at the twin bundled conductor is 13,5kV , which is less then permissible value of 18,78kV. This design is safe from electrical field effect.

2. The maximum value of line to ground (phase) voltage of the conductor bundle under consideration is 266.74 kV, whereas for its configuration in the switchyard the magnitude of Disruptive critical voltage necessary for corona onset is 660 kV. Thus surface potential gradient of the conductor bundle for the maximum conductor phase voltage is insufficient for corona initiation. Hence conductor design is safe from corona considerations.

6 References

1. Technical Data sheet for Overhead Conductor: Manufacturer – HASCELIK.

2. National Electrical Manufacturers Association (NEMA) CC 1-2005

3. F. W. Peek, Dielectric Phenomena in High Voltage Engineering, McGraw-Hill, New York, 1929.

4. E. Kuffel, W. S. Zaengl, J. Kuffel, High Voltage Engineering Fundamentals, Newnes, New York 2000.

5. M. V. Deshpande, Electrical Power System Design, Tata McGraw-Hill Publishing Co. Ltd.,

New Delhi, 4th Ed. 1992.

6. Rakosh Das Begamudre, Extra High Voltage Ac Transmission Engineering, New Age

International Publ. Ltd., New Delhi, (2nd Ed. 1990) Reprint 2004.

7. P. Sarma Maruvada, Corona Performance of High Voltage Transmission Lines, Research

Studies Press, Philadelphia, PA, 2000.

8. Turan Gönen, Electric Power Transmission Systems Engineering Analysis and Design,

John Wiley and Sons, New York, 1988.

9. H. M. Ryan, High Voltage Engineering & Testing, Institution of Electrical Engineers, London,

2nd Ed. 2001.

APPENDIX -1

Calculation

1.1 Calculations for bundle conductors:

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1.2.1 Calculation of maximum electric field strength on bundle conductor

Emax maximum electric field for twin – bundle conductors

dr

h4r

UE

2

0avg

⋅

⋅=

ln

)2

1(maxd

rBEE avg += )

21(

4 2

0

d

rB

dr

hlnr

U+

⋅

⋅=

Where;

U0: Nominal system voltage, phase to neutral in kVrms

kV2313

kV400

3

UU0 ===

Conductor type: 954 MCM ACSR

r: Radius of sub-conductor, r = 15.21 mm

d: Spacing between sub-conductors, d = 200 mm

B: 1 for twin bundled conductors

h: 1800cm at the max sag

maxE 50.1315.172.19

231)

20

521.121(

20521.1

18004521.1

3/4002

=⋅=⋅

+

⋅

⋅=

ln

kV/cm

Permissible surface electric field strength,

Epermissible = 30/√2 kV/cm x 0.89

R r r

d

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Epermissible = 21,2 kV/cm x 0.89 = 18.78 kV/cm

Result : Emax < Epermissible

1.2.2 Calculation of corona voltage

For 3-phases system, corona inception (onset) voltage (disruptive critical voltage), U0

⋅δ⋅⋅⋅⋅=

eqeq0

r

GMDlnrm2,213U

m: Surface factor, m = 0.87

δ: Relative air density, for 25oC air temperature and 760 mm Hg barometric pressure

t273

p3921,0

+⋅=δ

where p barometric pressure in mm Hg, t ambient temperature in Co

Temperature range: -10oC < t < 50oC

Average ambient temperature = 35oC

p = 617 mm Hg for 1500 m altitude

78547.035273

6173921.0

t273

p3921.0 =

+⋅=

+⋅=δ

Corona inception (onset) voltage (disruptive critical voltage):

kVU 66052.5

650ln*78547.0*52.5*87.0*2,21*30 =

=

Visual critical (corona) voltage:

δ⋅+⋅=

eq

0coronar

301.01UU = 756 kVrms

Nominal system voltage, Un (kVrms, phase to phase) = 400 kV

Permissible highest system voltage, Um (kVrms, phase to phase) = 420 kV

Considering 10% overvoltage in the system, Uover (kVrms, phase to phase) = 462 kV

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Maximum system voltage Uph,max (kVrms, phase to neutral) = 462 / √3 = 266,74 kV

Result: Ucorona > U0 > Uph,max