1

Electrical

Energy

Engineering

Department

10/5/2018

Introduction: The transmission of electric power is done by 3-

phase, 3-wire overhead lines, a.c. transmission line

has resistance, inductance and capacitance

uniformly distributed along its length. The

performance of a transmission line depends on

parameters mentioned above . The efficiency and

voltage regulation of the line will be good or poor

depending to their parameters. Therefore, the

knowledge of these parameters is required and

necessary in order to make the electrical design of a

transmission line which was given in power course.

Also there are some parameters here must

considered such as thermal effect and corona. 2 Dr audih

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In order to make a design of OHL of TL firstly must collect

some parameters such as :

1-Temprature: maximum, minimum and average ambient

temperature which influences the conductor current rating

and sag .

The maximum operation temperature of ACSR conductor

should not exceed 75oC (to prevent annealing of aluminum).

2- Wind velocity: effected structure of towers and conductors.

3- Solar radiation :conductors and fittings such as insulation

material (ultraviolet and high thermal) .

4-Humidity: insulation materials and corona phenomena.

5- Rainfall (flooding) : tower lags and foundation structure also

corona discharge and insulation performances.

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6- Ice and snow : sag and tension of conductors.

7-Altidude : insulation design.

8-Polluation: insulation design.

9-Lightning : earthling wires screening armoring and

insulation levels .

10- Seismic factor: foundation and towers.

Technical & economic criteria for conductor are consider as :

1. Maximum power transfer capability of conductor .

2. Cross-section area of ( minimum in initial cost and power

losses).

3. Should be within standard sizes.

4. Suitable with environmental conditions.

5. Adequate with thermal capacity.

6. Recognized international standards for radio interference

and corona discharges.

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The conductors of OHL may be:

ACSR: Aluminum Conductor Steel Reinforced.

AAAC: All Aluminum Alloy Conductor.

ACAR: Aluminum Conductor Alloy Reinforced.

AACSR: All Aluminum Conductor Steel Reinforced.

AAC: All Aluminum Conductor.

Widely ACSR is used in TL since it’s mechanical strength and effectiveness cost. But in distribution widely uses is AAAC.

Aluminum provides the necessary conductivity while steel

provides the necessary mechanical strength. electrolytic action (corrosion) is reduce by adding a layer of grease

between aluminum and steel

(The steel strands are galvanized with zinc).

The insulation material used for conductor are polyvinylchloride

(PVC), linear polyethylene (PE) or cross-linked polyethylene

(XLPE).

The line conductors of TL types are based on animals names.

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Example Zebra ACSR

This become with 54 Al strands surrounding seven steel strands, all

strands of diameter d= 3.18 mm. is designated 54/7/3.18;

aluminium area = 428.9 mm2, steel area = 55.6 mm2, and described

as having a nominal aluminium area of 400 mm2

Diameter of each strand

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OVERHEAD POWER LINES conductors, network and environmental constraints - proprietary document

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1- Heat balance equation

The conductor thermal current rating in wind, ignoring any

voltage regulation considerations, is given by the following

simplified heat balance equation as valid for stranded

conductors:

Heat generated (I2 R conductor losses) = heat lost by

convection (watts/km) + heat lost by radiation (watts/km) -

heat gained by solar radiation (watts/km)

ΔP= I2R = HE + HR – HS

or general equation

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I2R20 {1 + α (t + θ)} = 387 (V. d)0.448 . θ + π.EC. s . d .[(t + θ +

273)4 - (t + 273)4] - αs. S . d (watts/km)

Where:

I = current rating, amps

R20 = resistance of conductor at 20°C

α = temperature coefficient of resistance per °C .

(for ACSR at 20°C, α = 0.00403)

t = ambient temperature, °C

θ = temperature rise, °C (t 1 = initial temperature and t

2 = final temperature).

αs = solar absorption coefficient - depends upon outward

condition of the conductor and varies between 0.6 for

new bright and shiny conductor to 0.9 for black

conditions or old conductor. Average value of 0.8, say,

S = intensity of solar radiation, watts/cm2

d = conductor diameter, cm

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V = wind velocity normal to conductor, cm/s

Ec = emissivity of conductor- differs with conductor surface

brightness. Typical values are 0.3 for new bright and

0.9 for black aluminum, ACSR or AAAC conductor.

Average value =0.6, say.

s = Stefan-Boltzmann's constant = 5.7 x 10-8 watts/m2

π = 3.41 592 654 For design purposes 0.5 or 0.6 m/s wind speeds are often

taken. Higher wind speeds would lead to higher ratings.

In practice, the heat balance is a highly complex process but

the above equation is adequate for calculation purposes.

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Power Carrying Capacity

Approximate economic power transfer capacity for different

line voltages are given in figures.

power transfer curve

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The table below shows the approximate Conductor Sizes (ACSR) for Power

Transfer Capabilities for transmission voltage up to 500 kV.

In practice, the capacity will be limited over long distances by the

conductor natural impedance (voltage regulation) as well as by conductor

thermal capacity.

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Depending upon the required electrical load transfer, the

number of overhead line conductors of a particular type (used

per phase) will vary. Conductor configurations are given in

figure.

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Therefore, under the following specific tropical conditions

(40OC ambient temperature, 0.894 m/s wind speed, 100

mW/cm2 solar radiation and 35OC temperature rise), the

calculated ratings for typical ACSR twin conductors at 230 kV

would be: -

A typical set of power transfer curves for the 2 x 400 mm2 conductor

case are given in figure (Power Transfer Curves slide 11).

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2- Corona discharge

High voltage gradients surrounding conductors (above about

18 kV /cm) will lead to a breakdown of the air around the

conductor surface known as corona discharge. The effect is

more pronounced at high altitudes. Generally, the breakdown

strength of air is approximately 31 kV peak/cm or 22 kV

rms/cm. This is a useful guide for the selection of a

conductor diameter or conductor bundle arrangement

equivalent diameter.

At higher voltage levels, 400kV and above, interferences

due to the corona effect can be determining the physical

size of the conductor rather than the thermal rating

characteristic.

Increasing the conductor diameter may be necessary in

order to reduce the surface to acceptable levels.

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The surface voltage gradient (corona phenomena) may be determined from Gauss's theorem for straight wire conductor : Where: Vg : is voltage surface gradient in (V/cm) Q: Surface charge per unit length in (C/m) ϵo: permittivity of free space =8.85x10-12 (F/m)

r: equivalent radius of smooth conductor in (cm)

2g

o

QV

r

In practical this may be expressed as :

, /  2

.2

ph

g

e

VV kV cm

d Dlog

d

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where

Vg = voltage surface gradient (kV/cm)

Vph = phase voltage (kV)

d = diameter of single conductor (cm)

D = distance between phases for single phase line or

equivalent spacing for three phase lines (cm)

•Note - For the three phase line configuration,

And diameter d=2r

312 23 31. .D D D D

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3

3

3

2 2

( )

( )

(D d )

10.940

c

GMD double circuit symmetrical

D d D e D f

D d D

a a a

b b b

c c

a

e D f

D e D f

D e ad de and so

m

3 . .ab bc ac

GMD single circuit unsymmetrical

D D D

3

23 (14) (28) 17.6388

. .

9m

ab bc acDGMD flat D D

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1 1 1 2 2 1 2 2

1 1 1 2 2 1 2 2

1 1 1 2 2 1 2 2

3

4

4

4

. . ;

. . .

. . .

. . .

AB BC AC

AB a b a b a b a b

BC b c b c b c b c

AC a c a c a c a c

GMD D D D where

D D D D D

D D D D D

D D D D D

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Example:

Consider a 132 kV single circuit Zebra ACSR line with

conductor diameter 28.62 mm and spacing as shown in Fig.

show if the corona phenomena is acceptable or no (voltage

surface gradient ).

4m

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Solution: 2 2 2

2 2 2

2 2 2

3

6 1.8 6.26

7 1.8 7.23

1 3.6 3.74

. . 5.53 553

ry

yb

br

ry yb br

D m

D m

D m

D D D D m cm

132 / 3 8.94 /  

2.86 2 553 .

2 2.86

g

e

V kV cm

log

8.94 is within the 18kV criteria and this is acceptable

Note : If the value result is high than 18kV we have two alternatives :

a)Increase the conductor diameter.

b)Increase the spacing distance

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3- Radio frequency interference (RFI)

The noise is measured in decibels(dB) . Acceptable noise levels depend upon the quality of service required and is described in terms of an acceptable signal-to-noise or signal plus noise-to-noise ratio. Some reception classifications are given in table :

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Thus if a signal has a field strength of, say, 60dB>1μv/m and

satisfactory reception is required then the noise from the

overhead line should not exceed 38dB>1μv/m. To satisfy

this condition above 1μv/m (dB>1μv/m) ,the noise can be

estimate from comparative equations of the form:

Where: Suffix '0' refers to the same quantities obtained from measurements RFI=calculated radio noise (dB>1μV/m. E mean=calculated mean voltage gradient (kV/cm). d = conductor diameter (cm). n : number of sub conductor per bundle. D: distance between phase and measurement antenna (m) f: frequency (Hz)

10

2

10 10 10 2

3.8 40 .

110 30 20

1

mean o meano

o

o o

o

dRFI RFI E E log

d

D fnlog log log

n D f

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Overhead line case steady example:

If we wish to transfer 40 MVA over a distance of 70 km then we

can calculate the conductor and tower horizontal size .Assume

Lynx ACSR overhead line under the following tropical

conditions operating at 132 kV:

Maximum operating temperature 75°C

Maximum ambient air temp. 40°C (temperature rise =35°C) Lynx conductor max. resistance 0.1441 Ω/km

Lynx conductor diameter 19.53 mm

Emissivity 0.6

Solar absorption coefficient 0.8

Solar radiation intensity 1000 W /m2

Wind velocity 0.447 m/s

(assuming normal atmospheric pressure)

The structure of conductors are shown in figure

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Cheek if the conductor propose and spacing are acceptable..

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Solution:

Load current at 132kV for 40MVA power transfer and unity

power factor is

The conductor thermal rating capability is first determined,

ignoring any voltage drop considerations, by comparing the

175 A load current requirement and the rating of the

conductor derived from the heat balance equation the

thermal capacity must be greater than load current to

accepted this design

2 4 0.448 4 4

2 1. 13.8 10 .( ).(v.d) . . . .( ) . . ,( )/C s Watts cI R E s d T T S d m

6

3

40 10175A

3. .cos 3 132 10 1L

L

PI

V

Note if the voltage level is 400kV and above starting with corona calculation

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2 1 1

2 4 0.448 4 4

2

2

2

1 2 1

:

. 13.8 10 .( ).( .d) . . . .( )

. . ,(

273 , 273

. ;

/ 760 . 293 /

/ )

( (27 ))3

t er

C

al

s

h m

where t t and T

I R t t v E s d

t T t

and I P I R then

v is effective wind velocity actual wind velocity

pressure

T T

S d Watts

t

cm

0.447 760 / 760 293 / 313 0.418 / s 41.8 / , then;scmm

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The conductor type is therefore is adequate on thermal

considerations for the load required.

3 454 A

and since I (454) (175)

206.107 10

thermal LoadI

The next check is then made for any corona discharge limitations

.  

2 .

2

ph

g

e

VV

d Dlog

d

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2 2 2

2 2 2

3

4.5 1 4.61

4.5 1 4.61

9

. . 5.76 576

ry

yb

br

ry yb br

D m

D m

D m

D D D D m cm

132 / 3 12.22 /  

1.953 2 576 .

2 1.953

g

e

V kV cm

log

Which is within the 18kV/cm criteria and Lynx conductor is

acceptable for this design

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If capacitive reactance is ignored the voltage drop, Vd, for a

line length, l, is calculated from the usual formula: -

If the load at the receiving end is given

in kVA, then for a three phase system

the load current as:

The main practical problem is now to obtain accurate values

for the line reactance.

1( ) ( ( )) I R j( L )L CV IZ I R jX I R j X X

C

4-Voltage drop calculation:

Z X

R

Φ

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It is useful to introduce the concept of kVA km for a given voltage drop

for a variety of overhead line configurations and different conductors.

For a 10% voltage drop the.

Some typical reactance values are given in Table

3 3LL

2 3

L

3 2 2

V kVA 3.kVA10%. = . cos sin .10 0.1×V = cos sin 10

3 3. 3.

0.1×V =kVA. cos sin .10

0.1 10 .V 100kVA= with the length/in km

Rcos +Xsin

L L

L

R X R XV V

or R X

Vor S

Z

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Skin Effect

When a conductor is carrying direct current (DC), this current is uniformly distributed over the whole cross-section of the conductor. But is case of (AC) the current flowing through the conductor is not distributed uniform through cross section , it is concentrate near the surface of the conductor as shown in Fig. This is known as skin effect.

Due to skin effect: the effective cross section area of the conductor through which current flows is reduced. Then the resistance of the conductor is slightly increased when carrying an alternating current.

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The skin effect depends upon the following factors : i. Nature of material ii. Diameter of wire−increases with the diameter of wire. iii. Frequency − increases with the increase in frequency. iv. Shape of wire − less for stranded conductor than the

solid conductor. It may be noted that skin effect is negligible when the supply

frequency is low (< 50 Hz) and conductor diameter is small

(< 1cm).

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Earth Wires

Where there is a risk of direct lightning strike to the phase

conductors, transmission lines are provided with overhead

earth (or ground) wires to shield them and also to provide a

low impedance earth return path.

Note that today’s earth wires on new circuits are equipped in

construction with an optical fiber in the center of the bundle.

This is known as optical fibre ground wire (OPGW) and is

used for data communications for protection relaying,

Supervisory Control and Data Acquisition (SCADA), and other

utility data transmission requirements such as power line

carrier (PLC).

The degree of shielding of the OHL phase conductors from

lightning strikes is determined by the shielding angle afforded

by the earth wire(s) running over the line.

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A single earth wire is considered to proffer a 30O shielding

angle as illustrated in figure .

.

Where lines are existing in

areas of high lightning activity

or with supporting structures

with wide horizontal spacing

configurations as 400 kV

towers, two earth wires are

often provided to permit a

lower shielding angle and,

therefore, better protection

shows in figure with 0Oangle

protection which employing

two earth wires