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Sensitivity Analysis of Corona and Radio Noisein EHV Transmission Lines

Prof C S Indulkar,Fellow

In this paper, a sensitivity analysis of corona and radio noise in EHV transmission lines has been carried out withrespect to the various parameters and atmospheric conditions near the transmission lines.

Keywords: Corona loss; Radio interference; TV interference; EHV transmission; Sensitivity analysis

Prof C S Indulkar resides at B3, Gokel Society, Vasra Road, Baroda390 015, Gujarat.

This paper was received on June 24, 2002. Written discussion on this paper willbe entertained till May 31, 2004.

Vol 84, March 2004 197

INTRODUCTION

Corona on transmission lines causes power loss, radio andtelevision interference, and audible noise near the transmission

line. At extra-high-voltage (EHV) levels (at 345 kV and higher),the conductor itself is the major source of audio noise, radiointerference (RI), television interference (TVI), and coronaloss. RI is a noise type that occurs in the AM radio reception,including the standard broadcast band from 0.5 MHz to 1.6MHz. It does not take place in the FM band. Radio noise (RI

or TVI) is usually expressed in mV/m or in dB above 1 V/m.The effects of corona in EHV transmission lines depend on anumber of parameters that may not remain constant over aperiod, and the contributions of each add to the effects in acomplex manner. The determination of the disruptive criticalvoltage requires the assignment of average values for the

conductor irregularity factor that may vary considerably withthe weathering effects on the conductor. In the Peterson1

expression for the fair weather corona loss, the corona factorthat is a function of the ratio of the operating voltage to thedisruptive critical voltage may also vary depending upon theoperating voltage. Similarly, the radio and televisioninterference levels depend upon the variations in radialdistance from the conductor to the antenna and the lineheight. Some parameters are known with good accuracy andmay be taken as constant, whereas there are others which areaffected by errors of evaluation and may vary with time. Theusual interest consists in evaluating the disruptive criticalvoltage and the radio noise due to corona with respect to thesevariable parameters. Many approaches are available forconsidering these parameter changes including worst-caseanalysis, sensitivity analysis, and Monte Carlo simulation. Inthis paper, sensitivity analysis of the disruptive criticalvoltage, visual critical voltage, corona loss, and radio noise (RIand TVI) is performed.

SENSITIVITY ANALYSIS

A sensitivity analysis for the disruptive critical voltage, visual

critical voltage, corona loss, RI and TVI is carried out. Thenormalized sensitivities with respect to the parameters onwhich these quantities depend are evaluated. The normalized

sensitivity of a quantity with respect to a particular parameteron which it depends gives the change percentage in theparticular quantity for one percent change in the parameterbeing considered. Table 1 gives the nominal values of theparameters used in this paper for sensitivity analysis.

Disruptive Critical Voltage

A transmission line should operate just below the disruptivecritical voltage in fair weather, so that, corona only takes placeduring adverse atmospheric conditions. Therefore, thecalculated disruptive critical voltage is an indicator of thecorona performance of the line. However, a high value of the

disruptive critical voltage is not the only criterion of satis-factory corona performance. The sensitivity of the conductorto foul weather and the fact that corona increases more slowlyon stranded conductors than on smooth conductors shouldalso be considered. According to Peek conductors, aftermaking allowance for surface condition of the conductor byusing the irregularity factor, the expression for the disruptive

critical voltage (V0) is

V m r D r 0 0211= . ln( / ) kV (1)

where V0 is the disruptive rms critical voltage to neutral, kVs

r, radius of conductor in centimeters;D, spacing between twoconductors, cm; m0 , irregularity factor ( )0 10< m (1 for

smooth, polished solid, cylindrical conductors; 0.930.98 for

weathered, solid, cylindrical conductors; 0.870.90 forweathered conductor with more than seven strands; and 0.80

0.87 for weathered conductor with up to seven strands and is the air-density factor.

The air-density factor is:

= +3 9211 273. / ( )p t (2)

where p is the barometric pressure in centimeters of mercuryand tis the ambient temperature, C .

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Visual Critical Voltage

The expression for the visual critical voltage, Vv , given by

Peek2 is:

V m rr

D rv v= +L

NMM

O

QPP

211 10 3

..

ln( / )b g

kV (3)

where Vv is the visual critical voltage in kilovolts, rms; mv ,irregularity factor for visual corona ( )0 1< mv (1 for

smooth, polished, solid, cylindrical conductors; 0.930.98 forlocal and general visual corona on weathered, solid,cylindrical conductors; 0.700.75 for local visual coronaweathered stranded conductors; and 0.800.85 for general

visual corona on weathered stranded conductors.

It may be noted that the voltage equations (1) and (3) are forfair weather. For wet weather voltage values, the resulting fairweather voltage values should be multiplied by 0.80. For a

three-phase horizontal conductor configuration, the factors0.96 and 1.06 should be multiplied with the calculated

disruptive critical voltage for the middle conductor and for the

two outer conductors, respectively. The normalizedsensitivities of the disruptive critical voltage, V0 and visualcritical voltage, Vv are given in Table 2.

The normalized sensitivities of both V0 and Vv with respectto the pressure, irregularity factor, and conductor radius,

respectively are high and those with respect to the spacing and

temperature are low. The values ofV0 and Vv increase withan increase in the value of all parameters except the

temperature. These values decrease with an increase in thevalue of the temperature. The smoother the surface of a givenconductor, the higher is the disruptive voltage. For the same

diameter, a stranded conductor is usually satisfactory forabout 80%-85% of a smooth conductor. The air density factor,and hence V0 and Vv depend on the barometric pressure. The

barometric pressure in turn is a function of the altitude. Table 3

gives the standard barometric pressure3 as a function ofaltitude.

The values of V0 and Vv increase with a decrease in the

altitude. However, the increase in Vv is about 10% less thanthat in V0 .

Corona Loss

According to Peterson1, the expression for the fair weathercorona loss per phase or conductor, Pc is:

Pf V F

D d

c = 1 11066 10

2

4 2.

ln ( / )(4)

where d is the conductor diameter, cm; f, frequency, Hz; V,

line-to-neutral operating voltage in kVs; and F is the coronafactor determined by test and is a function of ratio ofVto V0 .

Typically, for fair weather corona, Table 4 gives the relationship3

between the corona factor, F and the ratio of the operating

voltage to the disruptive critical voltage, V/V0 .

For wet weather corona, the factor F has to be determined

using V/0.80 V0 . Table 5 gives the sensitivity values of corona

loss.

Table 1 Nominal values of system parameters

Irregularity Pressure, Irregularity Conductor Spacing, Temperature, Operating Supply

Factor, mV p, (cm, Hg) Factor, m0 Radius, r, cm D, cm t, C Voltage, V Frequency,f

(Line kV) (Hz)

0.9 74 0.9 1.5 550 10 345 60

Table 2 Sensitivity values of disruptive critical voltage and visual

critical voltage

Irregu- Pressure, Irregu- Conduc- Spacing, Tempe-

larity p larity tor D rature,

Factor, Factor, Radius, t

mV m0 r

Disruptive 1 1 0.830 0.169 0.035

Critical

Voltage, V0[Nominal

Value =

298.7 kV (line)]

Visual 1 0.902 .732 .169 .032

Critical

Voltage, VV[Nominal

Value =

370.9 kV (line)]

Table 3 Standard barometric pressures as function of altitude

Altitude, m Pressure, cm Hg Altitude, m Pressure, cm Hg

304.8 78.79 1524.0 63.22

152.4 77.40 1828.8 60.91

0 76.00 2133.6 58.67

304.8 73.30 2438.4 56.44

609.6 70.66 3048.0 52.27

914.4 68.10 4572.0 42.88

1219.2 65.54 6096.0 34.93

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The sensitivity values of the corona loss are calculated using avalue ofF = .07 from Table 4 for V/V0 = 1.155. The

sensitivity values with respect to the operating voltage andsupply frequency are quite high and with respect to theconductor, radius and spacing are low. Furthermore, thesensitivity with respect to the spacing is negative. As thespacing increases, the corona loss decreases. The corona loss isproportional to the frequency of the supply voltage.Therefore, the higher the frequency, the higher is the coronaloss. Thus, the corona loss at 60 Hz is greater than the one at 50Hz. Of course, the corona loss at zero frequency, that is, thedirect current, is far less than the one for alternating current.

Radio Interference

The radio interference is a noise type that occurs in the AMradio reception, including the standard broadcast band from0.5 MHz to 1.6 MHz. It does not take place in the FM band.Radio noise (radio or TV interference) is usually expressed in

millivolts per meter or in decibels above 1 V/m. Asconductors age, radio noise levels tend to decrease.

The RN is measured adjacent to a transmission line by anantenna equipped with a radio noise meter. The standard noisemeter operates at 1 MHz (in the standard AM broadcast band)with a bandwidth of 5 kHz. For measurements in the RIrange, a rod antenna usually determines the electric field, Eand a loop antenna usually determines the magnetic fieldcomponentH.

The approximate value of the RI can be determined from thefollowing empirical formula3:

RI = + +50 16 95 17 3686 3 93K E dm( . ) . ln( / . )

+ + +F Fn FW138949. (5)

where RI is the radio noise in decibels above 1 V/m at 1MHz;K, 3 for 750-kV class, 3.5 for others, gradient limits 15kV/cm-19 kV/cm; Em , maximum electric field at conductor

in kV (rms)/cm;D, (sub) conductor diameter, cm; Fn = 4dB

for single conductor (4.3422 ln (n/4) for n > 1; n, number ofconductors in bundle, D, radial distance from conductor to

antenna, m ( ) /h R2 2 1 2+ ; h, line height, m;R, lateral distance

from antenna to nearest phase, m; and FFW, 17 for foul

weather; and 0 for fair weather.

Table 6 gives the sensitivity values of RI.

RI is more sensitive to the maximum electric fieldEm, but lessso to the line height and the lateral distance from the antenna.

Although the RI is least sensitive to the parameter R, thelateral distance from the antenna, this parameter is the onethat can be adjusted to keep the RI within the specified limits.Table 7 gives the RI limits set by various countries4 in theworld.

Table 4 Corona factor as function ofV/V0

(V/V0) 0.600 0.800 1.00 1.20 1.4 1.6 1.8 2.0 2.2

F 0.012 0.018 0.05 0.08 0.3 1.0 3.5 6.0 8.0

Table 5 Sensitivity values of corona loss

Operating Supply Conductor Spacing,

Voltage, V Frequency,f Radius, r D

Corona loss,Pc, 2.01 1 .338 0.284

(Nominal

Value =

1.478 kW/km-

3 phase)

Table 6 Sensitivity values of RI

Maximum Conductor Line Lateral

Electric Radius, Height, Distance

Field,Em r h from

Antenna, R

RL 1.101 0.286 0.147 0.083

(Nominal

Value =

60.36 dB

above 1 V / m)

Table 7 RI limits in various countries in the world4

Country Distance from Line RI Limit Frequency Remarks

Switzerland 30 m from outermost 46 dB 500 kHz Dry

phase above Weather

1 V / m 10 C

(= 200

V / m)

Poland 20 m from outermost 57.5 dB 500 kHz Air

phase above 10 Humidity

1 V / m kHz < 80%

(= 750 Tempe-

V / m) rature

5 C

Czechoslovakia Voltage, Distance

kV from line

centre

220 50 m400 55 m 40 dB 500 kHz Air

above Humidity

750 70 m 1 V / m = 70%

Dry

Weather

Former USSR 100 m from 40 dB 500 kHz For 80%

outermost phase above of the

1 V / m year

limit

should

not be

exceeded

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Television Interference

In general, power line RN sources disturbing televisionreception are due to non-corona sources. Such power line

interference in the VHF (30 MHz-300 MHz) and UHF (300MHz-3000 MHz) bands is usually caused by sparking. Since,the sparks usually short out during rain, sparking is a fairweather problem rather than a foul weather one. Theexpression for the foul weather TVI in terms of the RI of atransmission line5 is:

TVI RI= +

+

L

N

MMMM

O

Q

PPPP

+201

1 15

3 210

21

2

21

2

log/

/

.f R h

h

b ge j

b ge j(6)

where TVI is the television interference, in decibels (quasi-peak) above 1 V/m at a frequency f, MHz; RI, radiointerference, in decibels (quasi-peak) above 1 V/m at 1 MHzand at standard reference location of 15 m laterally fromoutermost phase;f, frequency, MHz; h, is the height of closestphase, m.

Table 8 gives the sensitivity values of TVI.

The sensitivity study of TVI is carried out for an antennalocation at 15 m from the three-phase 345 kV line and for a TVchannel signal where the carrier frequency is 83.25 MHz. It isobserved that the sensitivity value of TVI with respect to the

electric field is very high and that with respect to the conduc-tor radius is moderately high. As conductors age, radio noise(RI or TVI) levels tend to decrease. Since, corona is mainly afunction of the potential gradients of the conductors and theRN is associated with the corona, the RN as well as coronawill increase with higher voltage, other things being equal.

CONCLUSIONS

Although the theoretical expressions for the corona effects,namely, corona loss and radio noise and the parameters onwhich they depend have been known in the literatureextensively for the past many years, this is the first time that asensitivity study on corona quantities has been carried out. It

has therefore been possible to determine how sensitive are thecorona quantities with respect to the parameters on whichthey depend. Further, work is in progress on the statisticalevaluation and Monte Carlo analysis of corona loss and radionoise.

REFERENCES

1. W S Peterson. AIEE Discussion. Transactions Am Inst Electrical

Engineering, vol 52, no 3, 1933, p 62.

2. F W Peek, (Jr). Dielectric Phenomena In High Voltage Engineering.

McGraw-Hill, New York, 1929.

3. T Gonen. Electric Power Transmission Engineering: Analysis and Design.Wiley Interscience, New York, 1988, p 538.

4. R D Begamudre. Extra High Voltage AC Transmission Engineering. Wiley

Eastern Limited, New Delhi, 1986, p 153.

5. Electric Power Research Institute. Transmission Line Reference Book: 345

kV and Abpve. 2nd edition,EPRI, Palo Alto, California, 1982.

Table 8 Sensitivity values of TVI

Maximum Conductor Line Frequency, Lateral

Electric Radius, Height, f Distance

Field, r h from

Em Antenna, R

TVI

(Nominal

Value =

25.15 dB

above

1V m/ )

2.643379 0.687 0.35299 0.34355 0.32358