sag tension 765kv
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INTRODUCTION
Sag tension calculation is carried out to estimate the sag in the conductor under various
temperatures. The calculation is carried out for the conductor span lengths in use in 765kV
INPUT DATA
Input data required for carrying out the calculations are as follows;
Initial tension
c/c distance of tower
Expansion coefficient (α)
Elasticity modulas (E)
No. of strings
weight of string
No. of conductos (n)
String length (RS)
PARAMETERS USED
l - half span length of conductor
L - span length
f1 - Stress at Temprature θ1 below end of string
f2 - Stress at Temprature θ2
below support
conductor at Temprature θ1
conductor at Temprature θ2
X - Half inclined length of conductor span
M'- Equivalent conductor weight
BASIS OF CALCULATION
Tension at any temperature θ2 deg C
a)
the equation to be solved is as follows:
conductor diameter (dc)
conductor Area (Ac)
girder width (lg)
tower height (h1)
tower height (h2)
Wind Pressure on cond (Pwc) Diameter of string insulator (di)
Wind Pressure on insulator (Pwi)
string weight/ conductor (Wwi)
Conductor weight (Mc)
spacer weight (Ms) Conductor chord length (lc)
θ1 - Initial Temperature Wwi - Equivalent weight of insulator with wind
θ2 - final Temperature
D1- Sag at centre of insulator catenary'
D2- Sag at centre of insulator catenary'
w1- Equivalent weight of
D3 - Conductor Sag below end of insulator string
w2- Equivalent weight of Wwi- wind load
D4 - total Sag insulator plus conductor
T1 - Tension at Temprature θ1
T2 - Tension at Temprature θ2 X1 - Projected Length of SP
ns- No. of spacers X2- Projected length of SP+RS
X3- Projected length of insulator string
Tension at any temperature θ2
f22 x [f2 - F] = G
where F= f1- -(θ2 -θ1)αE
G =
f1=
b) Loading due to wind on conductor and insulator:
c) Loading due to self weight of the conductor and spacers:
weight of the spacers has been considered alongwith the weight of the conductor.
The equivalent weight of the conductor and spacers is given by:
where
M' = weight of the sub conductor
n = no. of sub conductor
Equivalent weight of the conductor in the loaded condition:
equivalent weight of conductor under full wind condition is given by
d) Maximum sag(D4)
Refer Fig 1
where
T: tension in kg/conductor
string length
X = (l-RS) X 1.0005(assumed)
w22l2E
6Ac2
T1/Ac
Wind loading Wwc = Pwc x dc for conductor
Wind loading Wwi = Pwi x di for insulator
M' = M'c + (ns.Ms)/(n.lc) ….. As per IEC - 865
ns = no. of spacers
Ms = weight of the spacer
lc = chord length of the conductor ( total span less the girder width and length of the insulator string)
w1 = [(M')2 + (Wwc)2]
a1= T/W1 for conductor catenary
a2= T/Wwi for insulator catenary
W1 : equivalent conductor weight
W1 = no of string x string weight
X1 = a 2 X
a1
2
22
16T
l1
w E
√
RSP = RS + SP
X3 = X2 - X1
X = 1/2 * 1-X3
a2
a2
a1
Sag D4 = D3 + D2 - D1
e) Point of Maximum sag from the Support towers
2 wl
2 wl
Reference: Text Book:"GENERATION, TRANSMISSION AND UTILIZATION OF ELECTRICAL POWER"-
A.T.STARR
SP = a2 sinh X1
a2
X2 = a2 sinh-1RSP
a2
D1 = a2( coshX1 - 1) Ref page 54 of Text book "Generation Transmissionand Utilization of Electrical Power" -A.T.STARR
D2 = a2( coshX2 - 1)
D3 = a1( coshX - 1)
XP1 =1 l + Th
XP2 =1 l + Th
SAMPLE CALCULATION
Circuit : 765kV Quad Moose 104 m span)
General DataInitial tension 2250 kg./condc/c of tower 104 mGirder width lg 2 mc/c tower - leg 104 mTower Height 39 m
139.74 Ref ANNEXURE-I
172.08 Ref ANNEXURE-I
Conductor DataNo. of conductors(n) 4
2.4 Kg/m3.83E-02 m
Conductor Area (Ac) 0.000865 sq.mExpansion Coefficient(a) 0.000023 degC as per IS 398 (P-III-1976)Elasticity Modulus(E) 4.71E+09 kg/sq.m as per IS 398 (P-III-1976)
Spacer DataSpacer span 7.5 m
11 Nos7 kg
Insulator & Hardware DataNo of strings 2 NosNo of Disc Insulators/string 47 NosDiameter of each disc(di) 0.255 mWeight of disc Disc 7.5 kgLength of each disc(li) 0.145 mWeight of Insulator Hardware 54.2 kgLength of insulator Harware including insulator(lh) 7.854 m
Preliminiary Claculation7.854 m
Conductor chord length(lc) 86.292 mTotal string weight 759.2 kgString weight/conductor(Wwi) 189.8 kgEquivalent conductor weight(M') 2.623 kg/m
MAIN CALCULATION
Wind pressure on conductor(Pwc) kg/m2
Wind pressure on Insulator(Pwi) kg/m2
Conductor weight(Mc)Conductor Diameter(dc)
No. of spacers(ns)Spacer weight (ms)
String Length(LS)
1 Load calculation for conductor= 0.03825x139.74= 5.35 kg
Eq.Wt. of conductor under still wind condition W1 = 2.6231 kg/m
Eq.Wt of conductor under full wind condition W2 == √(2.623^2+5.345^2 )= 5.9500 kg/m
2 Load calculation for string insulator wind load Wwi =
= 0.255 x 172.08 x 0.5 x 7.854= 172.32 kg
Equivalent weight of insulator with wind Wi == √((189.8)^2+(172.318)^2)= 256.3545 kg
3
f1 =
= 22500.000865
Hence f1 = 2600073.96
Half span length of conductor = (half span - insulator length) x 1.0005= ((104-2)/2-7.854)x1.0005= 43.17 m
G =
= 5.95^2x43.17^2x4709000000(6x0.00086536^2)
Wind Load Wwc = dc x Pwc
√(M')2 + (Wwc)2
d x Pwi x 0.5 x LS
√(string weight/cond)2+(Wwi)2
Calculation of tension at θ2 Deg C(5 Deg.C) and full wind condition - T2
Initial tension at 0 deg C and full wind condition (T1)Area (Ac)
kg/m2
LH
Substituting the value of W2 for full wind condition and other values, G can be calculated as
w22l2E
6 Ac2
Hence G = 6.9148E+19
F =
Putting all the values we get F = 2600073.958-5.95^2*43.17^2x4709000000/(6x0.00086536^2x
2600073.958^2)-(5-0)x4709000000x0.000023= -8.17E+06
E101^3-E91*E101^2-E82
2540857.511^3--8169925.317x2540857.511^2-6.91483522104351E+0190.00E+00
= 2540857.51
= 2540857.511 x 0.0008654Hence = 2198.76 kg
d) Sag under full wind conditions - Initial temperature 0 deg C
Sag point XP1 = 1/2 x (L) XP1 = 52 m
with reference to fig 1 and equations given under section 4.3
a1 = T1 = 2250 = 378.15w1 5.9500
a2 = T1 = 2250 = 68.93wi 256.355/7.854
X(ass) = ((l-2)/2-RS) x 1.0005 = ((104-2)/2-7.854)x1.0005= 43.17 m
X1 = (a2/a1) X
Substituting the value of W2 for full wind condition and other values with temprature diffrence of 5oC, F can be calculated as
f1 - w22l2E - (θ2-θ1)Ea
6Ac2f12
The stress f2 at 5 deg C could be found out by sloving the cubic equation "f23-Ff2
2-G=0" for f2
Now, f23-Ff2
2-G
we get f2 kg/m2
Hence the tension T2 under full wind condition at 5 deg C = f2 x Ac
f2
The tension(T2) values are calculated for full wind conditions up to 75 deg.C in steps of 5 deg.C
kg/m2
kg/m2
= (68.934/378.151)x43.168= 7.87
SP == 68.934xSINH(7.869/68.934)= 7.89
RSP == 7.886+7.854= 15.74
X2 == 68.934xASINH(15.74/68.934)= 15.61
X3 = X2 - X1= 15.607-7.869= 7.74
= XP1 - X3= 52 -7.737- 1= 43.26
D1 == 68.934x(COSH(7.869/68.934)-1)= 0.45
D2 == 68.934x(COSH(15.607/68.934)-1)= 1.77E+00
D3 == 378.151x(COSH(43.263/378.151)-1)= 2.47743675
Hence sag at full wind condition at 0 deg C is given by
D4 = D3 + D2 - D12.477+1.774-0.45
Hence D4 = 3.802 m
SUMMARY
a2sinh(X1f/a2)
SP+LS
a2sinh-1(RSP/a2)
X
a2(cosh (X1/a2) -1)
a2(cosh (X2/a2) -1)
a2(cosh (X3/a1) -1)
The Sag tension at various temperatures for both still wind & full wind condition for the following cases are carried out.
1) 765kV Quad Bull - 54 m Span with Tower Height of 27m2) 765kV Quad Bull - 104 m Span with Tower Height of 39m3) 765kV Quad Bull - 93 m Span with Tower Height of 39m
SAG TENSION CALCULATION-765 KVCIRCUIT:765 KV Quad Bull (54 M SPAN)
Initial tension 2250 kg/cond 11
c/c of tower 104 m 7.5 kgGirder width (lg) 2 m Eq Cond weight 2.639 kg/mSpan (c/c tower-lg) 102 m Cond dia 3.83E-02 mTower height(h1) : 39 m Cond area 8.65E-04 sq mTower height(h2) : 39 m Exp. Coefficient 2.30E-05 / deg cWind pr. on cond 139.74 Kg/sqm Elas Modulus 4.71E+09 kg/sqmWind pr on insulator: 172.08 Kg/sqm No of strings 2No of conductors: 4 Dia of string insul 0.255 mCond weight 2.4 Kg/m weight/string 379.6 kgspacer span 7.5 m String weight/cond. 189.8 kg
String length(RS) 7.854 mCond chord len (lc) 86.292 m
FULL WIND CONDITION STILL WIND CONDITION
Tension (kg) Sag (in meters)
0 2250.00 52.00 3.808 1069.69 52.00 3.825 2198.92 52.00 3.897 1040.43 52.00 3.922
10 2150.83 52.00 3.984 1013.32 52.00 4.02715 2105.48 52.00 4.069 988.12 52.00 4.12820 2062.64 52.00 4.154 964.63 52.00 4.22825 2022.10 52.00 4.237 942.66 52.00 4.32630 1983.67 52.00 4.319 922.06 52.00 4.42235 1947.20 52.00 4.399 902.71 52.00 4.51640 1912.53 52.00 4.479 884.48 52.00 4.60845 1879.52 52.00 4.557 867.28 52.00 4.69850 1848.06 52.00 4.635 851.01 52.00 4.78755 1818.03 52.00 4.711 835.59 52.00 4.87560 1789.33 52.00 4.786 820.96 52.00 4.96165 1761.88 52.00 4.861 807.05 52.00 5.04570 1735.58 52.00 4.934 793.80 52.00 5.12875 1710.37 52.00 5.007 781.17 52.00 5.210
l = 43.17 (half span length)Ww(ins) = 172.32 (weight of insulator in still wind)Wi = 256.35 (weight of insulator in full wind)
Temp T(still wind) f1 w1 G1 F1 f2 gs(f2) a1s a2s1.36E+19 -7.67E+06 0.00E+00
0 1069.69 1236127.01 2.64E+00 1.36E+19 -8.21E+06 1202313.34 0.00E+00 4.05E+02 44.26440225 1040.43 1202313.34 2.64E+00 1.36E+19 -8.75E+06 1170984.22 0.00E+00 3.94E+02 43.0535703
10 1013.32 1170984.22 2.64E+00 1.36E+19 -9.29E+06 1141862.27 0.00E+00 3.84E+02 41.931707615 988.12 1141862.27 2.64E+00 1.36E+19 -9.83E+06 1114710.02 0.00E+00 3.74E+02 40.888881420 964.63 1114710.02 2.64E+00 1.36E+19 -1.04E+07 1089323.05 0.00E+00 3.66E+02 39.916587825 942.66 1089323.05 2.64E+00 1.36E+19 -1.09E+07 1065524.52 0.00E+00 3.57E+02 39.007507230 922.06 1065524.52 2.64E+00 1.36E+19 -1.15E+07 1043160.72 0.00E+00 3.49E+02 38.155307235 902.71 1043160.72 2.64E+00 1.36E+19 -1.20E+07 1022097.38 0.00E+00 3.42E+02 37.35448340 884.48 1022097.38 2.64E+00 1.36E+19 -1.25E+07 1002216.74 0.00E+00 3.35E+02 36.60022745 867.28 1002216.74 2.64E+00 1.36E+19 -1.31E+07 983415.08 0.00E+00 3.29E+02 35.888322350 851.01 983415.08 2.64E+00 1.36E+19 -1.36E+07 965600.70 0.00E+00 3.22E+02 35.21505555 835.59 965600.70 2.64E+00 1.36E+19 -1.42E+07 948692.20 0.00E+00 3.17E+02 34.577140960 820.96 948692.20 2.64E+00 1.36E+19 -1.47E+07 932617.08 0.00E+00 3.11E+02 33.971665265 807.05 932617.08 2.64E+00 1.36E+19 -1.52E+07 917310.55 0.00E+00 3.06E+02 33.396032170 793.80 917310.55 2.64E+00 1.36E+19 -1.58E+07 902714.54 0.00E+00 3.01E+02 32.847921675 781.17 902714.54 2.96E+02 32.3252539
X(ass)f X1f SPf RSPf X2 X3 X(act)s D1s D2s D3s D4s43.17 4.71404824 4.7229642 12.576964 12.413606 7.69955771 43.30 0.25125451702551 1.7520875691 2.31E+00 3.82E+0043.17 4.71404824 4.72347306 12.577473 12.405114 7.69106532 43.31 0.25833468316295 1.799553827 2.38E+00 3.92E+0043.17 4.71404824 4.72398444 12.577984 12.396612 7.68256412 43.32 0.26526067042823 1.8458413805 2.45E+00 4.03E+0043.17 4.71404824 4.72449807 12.578498 12.388107 7.67405894 43.33 0.27204065134612 1.8910114908 2.51E+00 4.13E+0043.17 4.71404824 4.7250137 12.579014 12.379602 7.66555388 43.33 0.27868227093787 1.935121452 2.57E+00 4.23E+0043.17 4.71404824 4.72553114 12.579531 12.371101 7.65705242 43.34 0.28519266299386 1.9782247284 2.63E+00 4.33E+0043.17 4.71404824 4.72605021 12.58005 12.362606 7.64855755 43.35 0.2915784746241 2.0203711477 2.69E+00 4.42E+0043.17 4.71404824 4.72657075 12.580571 12.35412 7.64007184 43.36 0.29784589510881 2.0616071232 2.75E+00 4.52E+0043.17 4.71404824 4.72709262 12.581093 12.345646 7.63159749 43.37 0.30400068649182 2.1019758855 2.81E+00 4.61E+0043.17 4.71404824 4.72761572 12.581616 12.337185 7.62313641 43.38 0.31004821430209 2.1415177145 2.87E+00 4.70E+0043.17 4.71404824 4.72813993 12.58214 12.328738 7.61469025 43.39 0.31599347741357 2.180270163 2.92E+00 4.79E+0043.17 4.71404824 4.72866517 12.582665 12.320309 7.60626043 43.39 0.32184113646577 2.2182682691 2.98E+00 4.87E+00
No of spacers(ns)
spacer weight(Ms)
Temperature deg c
Sag point ( in
meters)
Sag (in
meters)
Tension (kg)
Sag point (in meters )
43.17 4.71404824 4.72919136 12.583191 12.311896 7.59784821 43.40 0.32759554053733 2.255544755 3.03E+00 4.96E+0043.17 4.71404824 4.72971841 12.583718 12.303503 7.58945468 43.41 0.33326075194017 2.2921302113 3.09E+00 5.05E+0043.17 4.71404824 4.73024627 12.584246 12.295129 7.58108076 43.42 0.33884056911259 2.3280532675 3.14E+00 5.13E+0043.17 4.71404824 4.73077488 12.584775 12.286776 7.57272729 43.43 0.34433854765933 2.3633407476 3.19E+00 5.21E+00
Temp T(full wind) f1 w1 G1 F1 f2 gs(f2) a1f a2f0 2250.00 2600073.96 5.96E+00 6.94E+19 -8.21E+06 2541041.14 0.00E+00 3.77E+02 6.89E+015 2198.92 2541041.14 5.96E+00 6.94E+19 -8.75E+06 2485471.65 0.00E+00 3.69E+02 6.74E+01
10 2150.83 2485471.65 5.96E+00 6.94E+19 -9.29E+06 2433066.88 0.00E+00 3.61E+02 6.59E+0115 2105.48 2433066.88 5.96E+00 6.94E+19 -9.83E+06 2383560.16 0.00E+00 3.53E+02 6.45E+0120 2062.64 2383560.16 5.96E+00 6.94E+19 -1.04E+07 2336712.95 0.00E+00 3.46E+02 6.32E+0125 2022.10 2336712.95 5.96E+00 6.94E+19 -1.09E+07 2292311.39 0.00E+00 3.39E+02 6.20E+0130 1983.67 2292311.39 5.96E+00 6.94E+19 -1.15E+07 2250163.41 0.00E+00 3.33E+02 6.08E+0135 1947.20 2250163.41 5.96E+00 6.94E+19 -1.20E+07 2210096.11 0.00E+00 3.27E+02 5.97E+0140 1912.53 2210096.11 5.96E+00 6.94E+19 -1.25E+07 2171953.58 0.00E+00 3.21E+02 5.86E+0145 1879.52 2171953.58 5.96E+00 6.94E+19 -1.31E+07 2135594.88 0.00E+00 3.15E+02 5.76E+0150 1848.06 2135594.88 5.96E+00 6.94E+19 -1.36E+07 2100892.39 0.00E+00 3.10E+02 5.66E+0155 1818.03 2100892.39 5.96E+00 6.94E+19 -1.42E+07 2067730.30 0.00E+00 3.05E+02 5.57E+0160 1789.33 2067730.30 5.96E+00 6.94E+19 -1.47E+07 2036003.30 0.00E+00 3.00E+02 5.48E+0165 1761.88 2036003.30 5.96E+00 6.94E+19 -1.52E+07 2005615.47 0.00E+00 2.96E+02 5.40E+0170 1735.58 2005615.47 5.96E+00 6.94E+19 -1.58E+07 1976479.26 0.00E+00 2.91E+02 5.32E+0175 1710.37 1976479.26 2.87E+02 5.24E+01
X(ass)f X1f SPf RSPf X2 X3 X(act)f D1f D2f D3f D4f43.17 7.88369155 7.90 1.58E+01 1.56E+01 7.74E+00 43.26 4.51E-01 1.78E+00 2.48E+00 3.80843.17 7.88369155 7.90 1.58E+01 1.56E+01 7.73E+00 43.27 4.62E-01 1.82E+00 2.54E+00 3.89743.17 7.88369155 7.90 1.58E+01 1.56E+01 7.73E+00 43.27 4.72E-01 1.86E+00 2.60E+00 3.98443.17 7.88369155 7.90 1.58E+01 1.56E+01 7.72E+00 43.28 4.82E-01 1.90E+00 2.65E+00 4.06943.17 7.88369155 7.90 1.58E+01 1.56E+01 7.72E+00 43.28 4.92E-01 1.94E+00 2.71E+00 4.15443.17 7.88369155 7.90 1.58E+01 1.56E+01 7.71E+00 43.29 5.02E-01 1.97E+00 2.77E+00 4.23743.17 7.88369155 7.91 1.58E+01 1.56E+01 7.70E+00 43.30 5.12E-01 2.01E+00 2.82E+00 4.31943.17 7.88369155 7.91 1.58E+01 1.56E+01 7.70E+00 43.30 5.22E-01 2.05E+00 2.87E+00 4.39943.17 7.88369155 7.91 1.58E+01 1.56E+01 7.69E+00 43.31 5.31E-01 2.08E+00 2.93E+00 4.47943.17 7.88369155 7.91 1.58E+01 1.56E+01 7.69E+00 43.31 5.41E-01 2.12E+00 2.98E+00 4.55743.17 7.88369155 7.91 1.58E+01 1.56E+01 7.68E+00 43.32 5.50E-01 2.15E+00 3.03E+00 4.63543.17 7.88369155 7.91 1.58E+01 1.56E+01 7.68E+00 43.32 5.59E-01 2.19E+00 3.08E+00 4.71143.17 7.88369155 7.91 1.58E+01 1.56E+01 7.67E+00 43.33 5.68E-01 2.22E+00 3.13E+00 4.78643.17 7.88369155 7.91 1.58E+01 1.55E+01 7.67E+00 43.33 5.77E-01 2.26E+00 3.18E+00 4.86143.17 7.88369155 7.91 1.58E+01 1.55E+01 7.66E+00 43.34 5.86E-01 2.29E+00 3.23E+00 4.93443.17 7.88369155 7.91 1.58E+01 1.55E+01 7.66E+00 43.34 5.94E-01 2.32E+00 3.28E+00 5.007
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160
500
1000
1500
2000
2500
0
1
2
3
4
5
6
Full Wind ConditionTemp Vs Tension & Sag
Tension
Sag
Temp Deg C
Ten
sio
n k
g
Sag
m
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160
200
400
600
800
1000
1200
0
1
2
3
4
5
6
Still Wind ConditionTemp Vs Tension & Sag
Tension
Sag
Temp Deg C
Ten
sio
n k
g
Sag
m
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160
200
400
600
800
1000
1200
0
1
2
3
4
5
6
Still Wind ConditionTemp Vs Tension & Sag
Tension
Sag
Temp Deg C
Ten
sio
n k
g
Sag
m
Annexure IPOWER GRID CORPORATION OF INDIA LIMITED
765/400kV RAIPUR NEW & 400kV RAIPUR EXTN. S/SWIND PRESSURE CALCULATION FOR CONDUCTOR & INSULATOR STRING
The wind pressure on tubular bus & Bpi is calculated based on IS :802 (Part 1) -1995
Basic wind speed (Vb)as per cl. 8.1 of IS :802 = 39 m/Sec
Maximum Level of Equipment bus above FGL = 39 m
Note : Max.Wind Pressure on various components will occur at 14m level.Hence the same is considered for calculations
At 14m level from FGL,summary of wind pressure are as below :
I Wind pressure on Flexible Conductor AAC Bull = 139.74
II Wind pressure on Insulator String = 172.08
Detail calculation for the above are as follows:
A Claculation for Design Wind Pressure
A.1 Design Wind Speed :(as per cl.5.3 IS:875) =WhereVb = Basic wind speed as per cl5.2 of IS :875 = 39 m/sec
= 1.375
(From Table -1 ,For Reliability level 2) = 1.1= 1
(From Table - 3 ,for Terrain category-2)
Hence, Design Wind Speed Vz = 31.2 m/sec
A.2 =
= 584.064
= 60
B Wind Load on AAC Bull
B.1 Wind Load on AAC Bull Fpc = Pd * Cdc * Ac * Gc
Drag Coeefficient Cdc = 1
Unit Crossectional Area of Conductor Ac = 1Gust Response Factor Gc = 2.329
Therefore, Fpc = 60 * 1.2 * 1 * 2.032
= 139.74
C Wind Load on Insulator String
C.1 Wind Load on Insulator String Fpi = Pd * Cdi * Ai * Gi
Drag Coeefficient Cdi = 1.2
Unit Crossectional Area of String Ai = 1Gust Response Factor Gi = 2.39
Therefore, Fpi = 60 * 1.2 * 1 * 2.032
Kg/m2
Kg/m2
Vd (Vb x K1x K2)/K0
K0 K1 = Risk Coefficient
K2 = Terrain height & Structure size factor
Design Wind Pressure: (as per cl.5.4 of IS :875) Pd 0.6 x Vd2
N/m2
Kg/m2
m2
kg/m2
m2
= 172.08 kg/m2
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