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8/6/2019 Week 2 20110627
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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.html8/6/2019 Week 2 20110627
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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.asp8/6/2019 Week 2 20110627
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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