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Corona Losses Dependence from the Conductor Diameter

ISUF KRASNIQI,

VJOLLCA KOMONI

Faculty of Electrical and Computer Engineering

University of Prishtina,Bregu i diellit p.n. 10000 Prishtina

AVNI ALIDEMAJ

KEK- Kosovo Energy Corporation J.S.C.

GAZMEND KABASHI

KOSTT - Transmission System and Market Operator of Kosovo

KOSOVO

[email protected], [email protected], [email protected],

[email protected]

Abstract: - This paper presents possibility to decrease the corona power losses in overhead transmission lines.Corona power losses can be reduced by increasing the diameter of the conductor and used bundled conductorsper phase. The objectives were to determine the corona power losses depend on conductors diameters. Thesimulation is completed using the corona model for one 400 kV and 220 kV overhead transmission line isdeveloped in Matlab/Simulink. The objectives are to determine the corona effect in high voltage transmission

lines, and to identify factors of decreasing the corona losses, such as increasing the diameter of conductors, andthus have to increase the critical disruptive voltage. The paper describes the analytical approach, computational

tools and simulations models.

Key-Words: - Electric discharge, Electric field, Corona model, Critical disruptive voltage, Power losses,Transmission line.

1 Introduction

During the unusual situation in the overheadtransmission line when the intensity of the electricfield exceeds the dielectric strength of air, thenaround the conductor is electric drilling, whichcauses increasing losses and increasing the apparentconductivity. This phenomenon is called the corona.Therefore, corona, defined as a self-sustainedelectric discharge in which the field intensifiedionization is localized only over a portion of the

distance between the electrodes. When the voltagehigher than the critical voltage is applied between toparallel polished wires, the glow is quite even. Afteroperation for a short time, reddish beads or tuftsform along the wire, while around the surface of thewire there is a bluish white glow.

The a.c. corona viewed through a stroboscope

has the same apperance as direct current corona.

As corona phenomenon is initiated a hissing

noise is heard and ozone gas is formed which

can be detected by its chracteristic colour.

2 Corona in transmission line2.1 Critical disruptive voltage

If one-phase transmission line shown in Fig.1.Let r be the radius of each conductor and d the

distance between the conductors such that d>> r. Inthis single-phase transmission line, let q be the

charge per unit length on one of the conductors andhence q on the other. If the operating voltage is U,the potential of conductor A with respect to neutralplane N will be U/2 and that of conductor B will be- U/2.

Fig. 1 1-ph transmission line

- qq pr

x

d

N BA

Recent Researches in Power Systems and Systems Science

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The electric field intensity at P due to the bothline charge will be

+=

xdx

qEx

11

2 0(1)

The potential different between the conductors

r

rdqdxEU

r

rd

x

==

ln0

(2)

Since r is very small as compared to d,

drd = . Substituting for q from the aboveequation,

r

dUq

ln

0

= (3)

( )x

dxdx

dUEx

ln

'

= (4)

Where U is the line to neutral voltage of thesystems.

Critical disruptive voltage is defined as the

voltage at which complete disruption of dielectricoccurs. This voltage corresponds to the gradient atthe surface equal to the breakdown strength of air.This dielectric strength is denoted byg0 and is equal

to cmkV/30 peak at NPT i.e., 250C and 760 mm

of Hg.

At any other temperature and pressure

0'0 gg = (5)

Where is the air density correction factor and is

given by

t

b

+=

273

92.3 (6)

Therefore the critical disruptive voltage is given by

[ ]kVr

dgrU ln00 = (7)

For high voltage transmission line the ACSR

conductors are used. The cross-section of suchconductors a series of arcs of circles each of much

smaller diameter then the conductor as a whole. Thepotential gradient for such conductor will be greaterthan for the equivalent smooth conductor. Theirregularities on the surface are increased furtherbecause of the deposition of dust and dirt on its

surface and the breakdown voltage is furtherreduced. Average value for the ration of breakdownvoltage for such conductor and a smooth conductorlines between 0.85, and is denoted by m0.

The final expression for the critical disruptivevoltage after taking into account the surface of theconductor is given by:

[ ]kVr

dmgrU ln000 = (8)

2.2 Corona loss

In high voltage transmission line when theapplied voltage exceeds a critical disruptive value,

the thin layer of air around the transmission lineionizes. This ions result in space charges which

move round the conductor. To remain the charges inthe motion required the energy derived from thesupply system. To maintain the flow of energy overthe conductor it is necessary to supply thisadditional loss from the supply system. This

additional power is referred to as corona loss.

Peek study the effect of various parameters onthe corona loss and he deduced an empiricalrelation:

( ) ( ) kmkWUUd

rfP p /

2510241

20

5 +

=

(9)

Where f is the frequency supply (Hz), the airdensity correction factor, Up the operating voltage inkV, U0 the critical disruptive voltage (kV), rradiusof the conductors (m) and dspacing (or equivalency

spacing) between conductors (m).In overhead transmission line the following

factors affect corona los: (i) electrical factors, (ii)atmospheric factors and (iii) factors connected with

the conductors.Electrical factors, referring to the equation (9) it

is seen that the corona loss is a function offrequency. Thus higher the frequencies of supplyand the losses are higher due to corona. This meansthat d.c. corona loss is less as compared with a.c.corona loss. This is because during the coronaphenomenon of a.c. is always present thirdharmonics and hence frequency is not only 50 Hzbut it is contains also third harmonic component.


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Atmospheric Factors, consist in air density andweather condition. Air density affects the generationof corona sources as demonstrated by Peekempirical equation (9). From this equation the losses

are a function of air density correction factor. The

lower value of

causes the higher the loss, becauseappears directly in the denominator of the equationand indirectly in the value of critical disruptivevoltage.

[ ]kVr

drmU ln1.21 00 = (10)

For the lower value of losses will be higher,

because the lower value of, will be have the lower

value of0U and hence higher the value of

( )20UU , where Uis the operating voltage in kV.During the bad weather conditions such as rain,snow and hailstorm will diminish the criticaldisruptive voltage and hence increase the corona

loss. These is due to the fact that rain droplets on thetransmission line conductors can be viewed as sharpedges which enhances the electric field andtherefore reduces the corona disruptive voltage andhence increase the corona power loss. Coronageneration increases whenever moistureaccumulates on the conductor. Conductor current, if

it heats the conductor, discourages the formation ofwater drops during fog and during high humidity,but has little effect during heavy rain and snow.Corona loss observations in the operating linesduring the hoarfrost have shown that the highest

corona losses occur when hoarfrost accumulates ona cold conductor, during the nigh time hours, whenload currents are not sufficient to warm theconductors enough to melt the hoarfrost [3].

Wind speed has been found to have a very smalleffect on corona generation unless the wind isblowing particles onto conductors.

Factor connected with conductors consist inconductor surface conditions, conductor diameterand number of conductors.

The conductors are exposed to atmosphericconditions; the surface would have dirt etc.deposited on it which will lower the disruptivevoltage and increase corona loss. Audible noise isprimarily a foul-weather phenomenon thereforeconductor-surface conditions are important onlyinasmuch as they affect water drop formation.

From the equation (9) for corona loss shows thatthe conductor size appears at two places and the

other parts of equation are assumed constant, so:

( ) kmkWUUd

rkP p /

20= (11)

From this expression shows that the first lossesare proportional to the square root of the diameter of

the conductor, if the diameter of conductor arelarger, then the loss will be larger. Secondly, sinceU0 is approximately directly proportional to the

diameter of the conductor, hence larger the size ofthe conductor now the critical disruptive voltage hasto be large and hence smaller will be differencebetween the operate and critical disruptive voltage.Number of conductors is an input into thecalculation of the electric field at the surface ofconductors. For operating voltage 400 kV and aboveit, is found that one conductor per phase gives largecorona loss and hence large radio interference (RI)

level which interferes with the communication lineswhich are normally run parallel with the powerlines. Most research has shown that the RI does notincrease with the number of conductors for a fixedconductor diameter [3].

The higher the corona losses in the powertransmission lines with one conductor is solved withby using two or more than two conductors per phaseor as they are known as bundling of conductors. By

bundling the conductors the self geometric meandistance (GMD) of the conductors is increasedthereby; the critical disruptive voltage is increasedand hence corona loss is reduced.

To reducing corona loss can be used following

methods: (i) large diameter of conductors (ii)hallows conductors, (iii) bundled conductors.With the aim to reduce the corona power losses,have been made experiments and research howaffects have the larger diameter and bundledconductors.

If conductor radius is larger, surface field

intensity is less and hence corona losses are lower.For the same current carrying capacity, an ACSR

conductor has larger radius, therefore thetransmission lines with ACSR conductors havelower corona loss. Also, for bundled conductors

lines effective radius is larger and hence corona lossis less.

Corona losses do not generally play an importantrole in the overall design of transmission lines. Withmost computer programs that evaluate only the cost

of resistive losses in overhead transmission lines.But, there are conditions where corona losses may

influence the economic choice of conductors, andcompact lines may be one of those conditions. The

cost of transmission line conductors, usuallyexpressed in terms of an annualized cost, is made up


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of the annualized cost of capital investment and theannual cost of energy losses incurred during theoperation of the line. The capital cost is almostdirectly proportional to the conductor cross-section,or to d2, where d is the conductor diameter. In the

absence of corona on conductors, the energy lossesconsist mainly of the resistive orI2R losses, whereIis the load current flowing through the line, andR isresistance of the conductor. Insulator leakage lossesare generally negligible compared to the resistivelosses.

The economic choice of conductors, for a given

transmission voltage and load current, involvesminimizing the total annualized cost of conductorsover the expected life of the line. Since the capitalcost increases while the cost of resistive energylosses decreases with d, there is an optimum value

ofdfor which the total cost attains a minimum. InFigure 2, curve 1 shows the variation of the total

cost as a function of conductor diameter d.Minimum total cost is obtained for an optimumconductor diameter d1. For conductor sizes either

lower or higher than d1, the total cost will be higher.The increase in total cost may become important for

lower load currents and/or higher energy costs.

Fig. 2 Economic choice of conductors

In the presence of corona on conductors, themean annual corona losses should be added to theresistive losses to determine the annualized theenergy losses. As in the case of resistive losses,corona losses decrease as d increases. This isillustrated by curve 2 of Figure 2, which differs

from curve 1 at lower values of d and mergesasymptotically with curve 1 for the increased valueofd. The minimum total cost of curve 2 occurs at aslightly larger diameterd2.

With the increasing cost of energy, studiescarried out in several countries have shown that it isimportant to take into account the cost of coronalosses in the economic choice of conductors,

particularly for lightly loaded or compacttransmission lines in the range of 230400 kV, linesin traversing regions of high altitude or of extremepollution, and also for normally loaded lines atvoltages above 750 kV (3).

The mean annual corona losses of high-voltagetransmission lines are usually an order of magnitudelower than the resistive losses. However, themaximum corona losses can be of the same order ofmagnitude as the resistive losses.

3 Case studies

Matlab/Simulink has been used to develop

the corona model for analyzing the corona

losses in 400 kV overhead transmission line.

Figure 3 shows the block schematic of thepresented model in Matlab/Simulink for the

corona losses in 400kV transmission lines.

Figure 3. Simulation corona model for 400kV

transmission line

With simulation the corona model and applying

the Peek expression are calculate the corona loss.The effects of critical disruptive voltage in the

corona loss are shown in Figure 4.

Figure 4. Corona losses in 400kV transmission line

Humbjet nga efekti kuror

5

5.05

5.1

5.15

5.2

5.25

20

2.00

E+01

20.2

20.4

20.6

20.8 21

21.2

21.4

21.6

21.8 22

22.2

22.4

22.6

22.8 23

23.2

23.4

23.6

23.8 24

24.2

24.4

24.6

24.8 25

Tensioni (kV)

kw/km

196.13

s

7.82

rezistenca

241

konstanta1

50

frekuenca

400

Tensioni i linjes (kV)

Tensioni i kurores

Prodhimi

u2

sqrt

Math

Function

25

Konstanta

Humbjet

-K-

-K-

GainDot Product1

Divide1

Divide

1

Add1

Add


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In the case, where the critical disruptive voltageis less, the difference between the operating voltageUp and critical disruptive voltage U0 is the largest,hence the corona losses are larger. During the foulweather, especially when there is fog, the dielectric

strength is less hence the critical disruptive voltagesare less. In opposite, during the fair weather, thedielectric strength is larger hence the criticaldisruptive voltages are larger.

Similar calculations were made for 230 kVtransmission line, in this case corona loss are lowerthan the corona losses in the 400 kV transmission

lines.The effects of critical disruptive voltage in the

corona loss, in the 220 kV transmission lines, areshown in Figure 5.


While, lower corona losses in the 230kVtransmission lines than the corona losses in the400kV transmission lines, are presented in Figure 6.

Critical disruptive voltage is defined as the

voltage at which the gradient at the surface equal tothe breakdown strength of air equal to 30 kV/cm. So,if the operates voltage less than critical disruptivevoltage, then corona will not appear. However, if theoperates voltage is larger than the critical disruptivevoltage, then will corona appears. Corona discharge

is the greater if the difference between operatingvoltage and the critical disruptive voltage is larger.From the expression (8) of critical disruptive voltageis seen that to increasing the critical disruptivevoltage can be done by increasing the diameter ofthe conductor.

Also, to show the reduction of corona losses withincreasing diameter of conductor are usedMATLAB/ SIMULINK to develop the coronamodel for analyzing the corona losses in 400 kVoverhead transmission line depend of the diameterof conductors. Figure 6 shows the block schematicof the presented model in Matlab/Simulink for the

corona losses in 400kV transmission lines depend ofthe conductor diameter.

Figure 6. Simulation corona model for transmission

line depend of conductor diameter

The effects of increase the conductor diameter todecrease the corona loss, in the 400 kV transmission

lines, are shown in Figure 7.


depend of the conductor diameter

Similarly the effects of increase the conductordiameter to decrease the corona loss, in the 230 kV

transmission lines, are shown in Figure 8.


depend of the conductor diameter

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

13

.6

13

.7

13

.8

1

4

14

.2

14

.3

14

.5

14

.6

14

.8

1

5

15

.1

15

.3

15

.4

15

.6

15

.8

15

.9

16

.1

16

.2

16

.4

16

.6

16

.7

16

.9

1

7

17

.2

17

.4

17

.5

mm

kW/cm

Corona l osses depended from conductor c ross section

1.86

1.88

1.9

1.92

1.94

1.96

1.98

2

10.8

11.2

11.6

12.0

12.4

12.8

13.2

13.6

14.0

14.4

14.8

15.2

15.6

16.0

16.4

16.8

17.2

17.6

18.0

18.4

18.8

19.2

19.6

20.0

Uk (kV)

Pk[kW

/km]

rrezja

-K-

mp1-K-

mp

36.5

kons

400

Tensioni i linjes[kV]

196.13

S

Rrezja[mm]

Prodhimi

ln

Math

Function2

sqrt

Math

Function1

u2

Math

Function

Humbjet

-K-

Gain2

-K-

Gain

50

Frekuenca

Dot Product4

Dot Product3

Dot Product2

Dot Product1

Divide2

Divide1

Divide

15140

D[mm]

25

Constant3

1

241

Constant

Add1

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0

1

2

3

4

5

6

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3

15.

4

15.

5

15.

7

15.

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16.

2

16.

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16.

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16.

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17.

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18.

1

18.

3

18.

4

18.

6

18.

7

18.

9

19.

1

19.

2

mm

kW/cm


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4 Conclusion

In this paper has been presented the effects ofconductor diameter in critical disruptive voltage andin the corona losses. Matlab/Simulink model has

been used to analyzing the corona power lossesdepends of the critical disruptive voltage or for thediameter of conductors.

The results obtained from the simulation haveshown that corona losses are larger, where thecritical disruptive voltage is less; hence thedifference between the operating voltage Up andcritical disruptive voltage U0 is the largest. Duringthe foul weather, the critical disruptive voltages areless, and hence the corona power losses are larger.

On the other hand, a very efficient measure toreduce corona losses is to increase the diameter of

the conductor. By using the Peek empirical formulathe corona power loss is calculated. The resultsshow that corona losses are decrease if theconductors diameters are increased.

References:[1] Mayen Abdel-Salam, Essam Zaki Abdel-Aziz

Corona power loss determination on multi-

phase power trasmission lines, Electric powersystems research, volume 58, Issue 2, 2001,Pages 123-132.

[2] Enrique E. Mombello, Giuseppe Ratta, Heetar

D. Suarez and Federico O. Torres, Corona losscharacteristics of contaminated conductors infair weather.Electric power systems research,volume 59, Issue 2, 2001, Pages 21-29.X1.

[3] EPRI, Transmission Line Reference Book 115-230kV Compact Line Design, Electric PowerResearch Institute 2007.

[4] D. Das, Electrical Power Systems, New AgeInternational Publishers, New Delhi, 2006.

[5] F.W. Peek, Dielectric Phenomena in HighVoltage Engineering, McGraw-Hill, 1929

[6] A. Ersoy, A. Kuntman, An Experimental

Study on Corona Losses in Conductors,Journal on Electronics and ElectricalEngineering, Vol. 3, No. 1, Pages 352-354.

[7] Cem Eroncel, Suat Ilhan, Aydogan Ozdemir,Adnan Kaypmaz, Corona Onset Voltage andCorona Power Losses an in Indoor Corona

Cage, International Middle East PowerSystems Conference, Cairo University,

December 2010, pages 791-794.

[8]

Z. M. Al Hamouz, Corona Power Loss VersusOhmic power Loss in HVDC transmission lines,

[9] Prof. C. S. Indulkar, Sensitivity Analysis ofCorona and Radio Noise in EHV Transmission

Lines, IE (I) Journal EL, Vol 84, March 2004,Pages 197-200.

[10]Raymond Lings, Vermon . Chartier, SarmaMaruvada, Overview of Transmission LinesAbove 700 kV,IEEE PES 2005 Conference and

Exposition in Africa, Durban, South Africa, 11-15 July 2005, Pages 33-43.

[11] Mehmet Salih Mamis, State-Space Transient

Analysis of Single-Phase Transmission Lineswith Corona, International Conference onPower Systems Transients IPST 2003, NewOrleans, USA,


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