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Professor Peter WolfsWestern Power Chair (Transmission and Distribution)

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Conductor material properties

Resistivity Wm units resistances between the faces of a cubewith one metre side length.

IACS

International Annealed Copper Standard 1.72*10-8 Wm at 20C

Small amounts of impurities increase resistance

Resistivity of Aluminium 2.82*10-8 Wm at 20C

Resistivity of Iron 10*10-8 Wm at 20C

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From Gonen pg 66-7

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Copper

97% IACS, 8890 kg/m3, , 405-460MPa

Stranded Aluminium

61% IACS, 2700 kg/m3, , 160-185MPa

Aluminium Alloy 1120

59% IACS, 2700 kg/m3,

, 230-250MPaGalvanised Steel

10% IACS, 7800 kg/m3, , 1310-1390MPa

Aluminium Clad Steel

20% IACS, 6590 kg/m3, , 1270-1340MPa

From Olex Aerial Conductor Catalogue

http://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.html

http://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.htmlhttp://www.olex.com.au/Miscellaneous/Catalogues-and-Brochures.html

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Copper1.72*10-8 Wm * 8890 kg/m3

= 152.9*10-6 W kg/m2

Aluminium

2.82*10-8 Wm * 2700 kg/m3

= 76.1*10-6 W kg/m2

For the same resistance aluminium conductors are49.7% the weight of copper

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From http://www.lme.com/home.asp

London Metal Exchange PrimaryAluminium(99.7% purity < 0.2 Fe < 0.1% Si)

$US/tonne

28th June 2011 $2,466

London Metal Exchange Grade ACopper conforming to BS EN1978:1998 (Cu-Cath-1)

$US/tonne

28th June 2011 $9,000

http://www.lme.com/home.asphttp://www.lme.com/home.asp

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For the same resistance aluminium conductors are49.7% the weight of copper

Aluminium is 27% the cost of copper

For the same resistance the metalin an aluminiumconductor is 13.6% of the cost ofthe metalacopper conductor (on 28th June 2011)

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Conductors cost more than the metal

Conductor prices can be given as aprocessing charge (set for each

conductor type) plus the metal cost For example $6/kg plus the LME metalprice on the delivery date

Contracts for construction can haverise and fall provisions

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ConductorCode Construction KilogramsperkilometreTensileStrength(kN)

ACResistanceW/km

Saturn 37/3.00 AAC21mm diameter 721 42.2 0.135

299Arms

Nitrogen 37/3.00 AAAC21mm diameter

721 62.2 0.139

295Arms

Lemon 30/3.007/3.00

ASCR/GZ21mm diameter

973 90.4 0.167

269Arms

Darts 30/3.007/3.00ASCR/AC

21mm diameter

913 91.6 0.155

280Arms

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Cost = Losses + Conductor Cost

Losses are proportional to R = HR

Sum of all conductor costs are (assumed) inverse to R = K/R

R

KHRC

02

R

KH

R

C

HKR

HKHKC

Cost is minimum when all conductor costs = cost of loss

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The Net present Value of n annual payments or incomeamounts

Where ris the real interest rate (interest inflation);nis the term in years

and q=1+r.

As an example for a 6% interest rate the capitalisation factor for20 annual income payments, say due to energy sales, is 11.5.

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100MW 132kV single circuit line continuous loading;

20 year time frame, 6% real interest rate, $60MWhr

Assume the total costs to purchase and suspend conductors is$20/kg (this includes the conductors plus the incrementalcosts in the towers)

Solution

The phase current is 437.4 Arms.

Use a one kilometre section to find H and K

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Finding Kwork on a one kilometre section

Start with a ACSR/AC conductor that is large enough to at leastcarry the phase current

Hurdles Rac=0.0675W/km and 1,880 kg/km

These phase conductors weigh 5640 kg and cost $112,800 toinstall

Installed conductor cost = K/Rac; K= 7614

Loss cost = HR.

Assume Rac=0.0675W the three phase loss would be 38.7kW;

The annual loss is 339 MWhr or $20,340Over 20 years the NPV will be $233,910

i.e. HR=233910; H=3.465*106

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K= 7614

H=3.465*106

Rac=0.0468 we dont have one conductor this big.

This needs two conductors try Golf Rac=0.0915W/km and1380 kg/km

New Conductor cost 6 *1380Kg * $20/kg = $165,600

New losses Rac = Rac=0.0457W/km = $158,539

New cost $165,600+$158,539 = $324,139 Old cost $112,800+$233910 = $346,710

H

KR

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Factors to Consider - Conductor span

Determined by the conductor strength relative toweight

Determined by the tower height and allowable

ground clearance Lines will expand if hot and sag this might reduce

clearance

The line must survive high winds and in the

Australian Alps ice loading Conductors should not clash horizontal

clearances

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Conductor stress

Where s = the stress in Pascals (Pa) or N/m2

T is the conductor tension in Newtons (N)

CSA is the cross sectional area of the conductor in m2

Conductor strain

Where eis the conductor elongation (dimensionless)

s = the stress in Pascals (Pa) or N/m2

Y is Youngs modulus or the Modulus of Elasticity in Pascals

CSA

Ts

Ye

s

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200m of Krypton AAAC conductor is tensioned to12kN. What is the stress and elongation?

Solution

CSA is 158mm2

Note AAAC has an ultimate tensile strength (UTS) of230-250MPA.

This conductor is stressed to 33% of UTS.

MPaN

CSA

T9.75

m10158000,12 26

s

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200m of Krypton AAAC conductor is tensioned to12kN. What is the stress and elongation?

Solution

Y is 65 GPA

The conductor will stretch 0.00117 times its lengthThe 200M section will stretch 0.234m

39

6

1017.1Pa1065Pa109.75

Ye

s

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Coefficient of Thermal Expansion

Where eis the thermal expansion (dimensionless)

DT is the change in temperature C

CTE is the Coefficient of thermal expansion

AAC - 23.010-6/C

AAAC - 23.010-6/C

Copper - 17.010-6/C

Galvanised steel 11.510-6/C Aluminium clad steel 12.910-6/C

ASCR/GZ and ASCR/AC Knee point stress transfers tosteel and aluminium wires bird cage

TCeTED

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200m of Krypton AAAC conductor is tensioned to12kN at 25C. How much will the conductor lengthchange for a 40C temperature rise due to loadcurrent if the tension remains the same.

Solution

The conductor will expand by 0.00092 times

(dimensionless).The 200m section will expand by 0.184m.

36100.92C40C/1023

D TCeTE

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From Gonen pg 627

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1

2

cosh

H

wL

w

Hd

Where

d - is the sag or deflection in metres

H - is the horizontal component of tension in

Newtons

L - is the span length in metersw - is the conductor weight in Newtons/m

The total conductor tension at the support is

Where V is the vertical tension equal to half the

span weight in Newtons

22VHT

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Find the sag for 200m span of Krypton, tensioned at

12kN. Krypton weighs 433kg/km

Solution w= 4.24N/m

m767.1

1N120002

m200m/24.4cosh

m/N24.4

N12000

12

cosh

N

H

wL

w

Hd

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HwL

wHl

2sinh2

Where

l - is the conductor length in metres

H - is the horizontal component of tension inNewtons

L - is the span length in meters

w - is the conductor weight in Newtons/m

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Find the length of conductor for 200m span of

Krypton, tensioned at 12kN.

m04.200

N120002m200N/m24.4sinh

N/m24.4N120002

2sinh

2

H

wL

w

Hl

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TwLd8

2

Where

d- is the conductor deflection or sag

T - is the conductor tension in NewtonsL - is the span length in meters

w - is the conductor weight in Newtons/m

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Find the sag for 200m span of Krypton, tensioned at

12kN. Krypton weighs 433kg/km

Solution

m767.1

N120008

m200N/m24.4

8

2

2

T

wLd