Sag Tension 765kV

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

conductor diameter (dc)

c/c distance of tower

conductor Area (Ac)

girder width (lg)

Expansion coefficient (α)

tower height (h1)

Elasticity modulas (E)

tower height (h2)

No. of strings

Wind Pressure on cond (Pwc)

Diameter of string insulator (di)

Wind Pressure on insulator (Pwi)

weight of string

No. of conductos (n)

string weight/ conductor (Wwi)

Conductor weight (Mc)

String length (RS)

spacer weight (Ms)

Conductor chord length (lc)

PARAMETERS USED θ1 - Initial Temperature

Wwi - Equivalent weight of insulator with wind

θ2 - final Temperature

l

L - span length

D1- Sag at centre of insulator catenary'

f1 - Stress at Temprature θ1 f2 - Stress at Temprature θ2

below end of string D2- Sag at centre of insulator catenary'

w1- Equivalent weight of

below support D3 - Conductor Sag below end of insulator string

conductor at Temprature θ1 w2- Equivalent weight of

Wwi- wind load D4 - total Sag insulator plus conductor

conductor at Temprature θ2 T1 - Tension at Temprature θ1

X - Half inclined length of conductor span

T2 - Tension at Temprature θ2

X1 - Projected Length of SP

ns- No. of spacers

X2- Projected length of SP+RS

M'- Equivalent conductor weight

X3- Projected length of insulator string

BASIS OF CALCULATION Tension at any temperature θ2 deg C a)

- half span length of conductor

Tension at any temperature θ2 the equation to be solved is as follows: f22 x [f2 - F] = G

w

2

1 6T

l2E 2

1

where

G=

F= f1-

w

2

1 6T

l2E 2

-(θ2 -θ1)αE

1

w22l2E 6Ac2 T1/Ac

f1= b)

Loading due to wind on conductor and insulator: Wind loading Wwc = Pwc x dc for conductor Wind loading Wwi = Pwi x di for 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: M' = M'c + (ns.Ms)/(n.lc) ….. As per IEC - 865 where M' = weight of the sub conductor ns = no. of spacers Ms = weight of the spacer n = no. of sub conductor lc = chord length of the conductor ( total span less the girder width and length of the insulator string) Equivalent weight of the conductor in the loaded condition: equivalent weight of conductor under full wind condition is given by [(M')2 + (Wwc)2]

w1 = d)

Maximum sag(D4) Refer Fig 1 a1= T/W1 for conductor catenary a2= T/Wwi for insulator catenary where T: tension in kg/conductor W1 : equivalent conductor weight W1 = no of string x string weight string length X = (l-RS) X 1.0005(assumed) X1 = a2 X a1 SP = a2 sinh X1 a2

RSP = RS + SP X2 = a2 sinh-1RSP a2 X3 = X2 - X1 X = 1/2 * 1-X3 D1 = a2( coshX1 - 1) a2

Ref page 54 of Text book "Generation Transmission and Utilization of Electrical Power" -A.T.STARR

D2 = a2( coshX2 - 1) a2

D3 = a1( coshX - 1) a1 Sag D4 = D3 + D2 - D1

e)

Point of Maximum sag from the Support towers XP1 =1 l + 2

XP2 =1 l + 2

Th wl

Th wl

Reference: Text Book:"GENERATION, TRANSMISSION AND UTILIZATION OF ELECTRICAL POWER"A.T.STARR

SAMPLE CALCULATION Circuit : 765kV Quad Moose 104 m span) General Data Initial tension c/c of tower Girder width lg c/c tower - leg Tower Height Wind pressure on conductor(Pwc)

2250 104 2 104 39 139.74

172.08 kg/m

Wind pressure on Insulator(Pwi) Conductor Data No. of conductors(n) Conductor weight(Mc) Conductor Diameter(dc) Conductor Area (Ac) Expansion Coefficient(a) Elasticity Modulus(E)

4 2.4 3.83E-02 0.000865 0.000023 4.71E+09

Spacer Data Spacer span No. of spacers(ns) Spacer weight (ms)

2 47 0.255 7.5 0.145 54.2 7.854

Preliminiary Claculation String Length(LS) Conductor chord length(lc) Total string weight String weight/conductor(Wwi) Equivalent conductor weight(M')

7.854 86.292 759.2 189.8 2.623

=

2

Ref ANNEXURE-I Ref ANNEXURE-I

Kg/m m sq.m degC as per IS 398 (P-III-1976) kg/sq.m as per IS 398 (P-III-1976)

7.5 m 11 Nos 7 kg

Insulator & Hardware Data No of strings No of Disc Insulators/string Diameter of each disc(di) Weight of disc Disc Length of each disc(li) Weight of Insulator Hardware Length of insulator Harware including insulator(lh)

MAIN CALCULATION 1 Load calculation for conductor Wind Load Wwc = dc x Pwc

kg./cond m m m m kg/m2

Nos Nos m kg m kg m

m m kg kg kg/m

0.03825x139.74

2

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

= = =

√(M') + (Wwc) √(2.623^2+5.345^2 ) 5.9500 kg/m

Wwi

= = =

d x Pwi x 0.5 x LS 0.255 x 172.08 x 0.5 x 7.854 172.32 kg

Wi

= = =

√(string weight/cond) +(Wwi) √((189.8)^2+(172.318)^2) 256.3545 kg

2

2

Load calculation for string insulator wind load

Equivalent weight of insulator with wind

3

=

2

2

Calculation of tension at θ2 Deg C(5 Deg.C) and full wind condition - T2 f1

=

Initial tension at 0 deg C and full wind condition (T1) Area (Ac)

=

2250 0.000865 kg/m2

Hence

f1

=

2600073.96

Half span length of conductor

LH

= = =

(half span - insulator length) x 1.0005 ((104-2)/2-7.854)x1.0005 43.17 m

Substituting the value of W2 for full wind condition and other values, G can be calculated as G

=

2 2

w2 l E 6 Ac2

=

Hence

G

=

5.95^2x43.17^2x4709000000 (6x0.00086536^2) 6.915E+19

Substituting the value of W2 for full wind condition and other values with temprature diffrence of 5oC, F can be calculated as

F

=

f1

2 2

-

2

6Ac f1

Putting all the values we get F

= =

- (θ2-θ1)Ea

w2 l E 2

2600073.958-5.95^2*43.17^2x4709000000/(6x0.00086536^2x 2600073.958^2)-(5-0)x4709000000x0.000023 -8.17E+06

The stress f2 at 5 deg C could be found out by sloving the cubic equation "f23-Ff22-G=0" for f2 Now, f23-Ff22-G

E101^3-E91*E101^2-E82 2540857.511^3--8169925.317x2540857.511^2-69148352210435100000 0.00E+00

we get f2

=

2 2540857.51 kg/m

Hence the tension T2 under full wind condition at 5 deg C = f2 x Ac = 2540857.511 x 0.0008654 Hence f2 = 2198.76 kg The tension(T2) values are calculated for full wind conditions up to 75 deg.C in steps of 5 deg.C 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 =

2 378.15 kg/m

2250 = 256.355/7.854

2 68.93 kg/m

a1

=

T1 w1

=

2250 5.9500

a2

=

T1 wi

=

X(ass)

= =

((l-2)/2-RS) x 1.0005 43.17 m

X1

= = =

(a2/a1) X (68.934/378.151)x43.168 7.87

SP

= = =

a2sinh(X1f/a2) 68.934xSINH(7.869/68.934) 7.89

=

((104-2)/2-7.854)x1.0005

RSP

= = =

SP+LS 7.886+7.854 15.74

X2

= = =

a2sinh-1(RSP/a2) 68.934xASINH(15.74/68.934) 15.61

X3

= = =

X2 - X1 15.607-7.869 7.74

X

= = =

XP1 - X3 52 -7.737- 1 43.26

D1

= = =

a2(cosh (X1/a2) -1) 68.934x(COSH(7.869/68.934)-1) 0.45

D2

= = =

a2(cosh (X2/a2) -1) 68.934x(COSH(15.607/68.934)-1) 1.77E+00

D3

= = =

a2(cosh (X3/a1) -1) 378.151x(COSH(43.263/378.151)-1) 2.4774367

D4

=

D4

=

D3 + D2 - D1 2.477+1.774-0.45 3.802 m

Hence sag at full wind condition at 0 deg C is given by

Hence SUMMARY

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 27m 2) 765kV Quad Bull - 104 m Span with Tower Height of 39m 3) 765kV Quad Bull - 93 m Span with Tower Height of 39m

SAG TENSION CALCULATION-765 KV CIRCUIT:765 KV Quad Bull (54 M SPAN) Initial tension

No of spacers(ns)

2250 kg/cond

c/c of tower Girder width (lg) Span (c/c tower-lg) Tower height(h1) : Tower height(h2) : Wind pr. on cond Wind pr on insulator: No of conductors: Cond weight spacer span

104 2 102 39 39 139.74 172.08 4 2.4 7.5

spacer weight(Ms) Eq Cond weight Cond dia Cond area Exp. Coefficient Elas Modulus No of strings Dia of string insul weight/string String weight/cond. String length(RS) Cond chord len (lc)

m m m m m Kg/sqm Kg/sqm Kg/m m

FULL WIND CONDITION

Temp

Temperature deg c

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Tension (kg)

Sag (in meters)

Tension (kg)

Sag point (in meters )

Sag (in meters)

2250.00 2198.92 2150.83 2105.48 2062.64 2022.10 1983.67 1947.20 1912.53 1879.52 1848.06 1818.03 1789.33 1761.88 1735.58 1710.37

52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00

3.808 3.897 3.984 4.069 4.154 4.237 4.319 4.399 4.479 4.557 4.635 4.711 4.786 4.861 4.934 5.007

1069.69 1040.43 1013.32 988.12 964.63 942.66 922.06 902.71 884.48 867.28 851.01 835.59 820.96 807.05 793.80 781.17

52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00 52.00

3.82 3.922 4.027 4.128 4.228 4.326 4.422 4.516 4.608 4.698 4.787 4.875 4.961 5.045 5.128 5.210

43.17 172.32 256.35

T(still wind)

f1

w1

m kg kg m m

(half span length) (weight of insulator in still wind) (weight of insulator in full wind)

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

1069.69 1040.43 1013.32 988.12 964.63 942.66 922.06 902.71 884.48 867.28 851.01 835.59 820.96 807.05 793.80 781.17

1236127.01 1202313.34 1170984.22 1141862.27 1114710.02 1089323.05 1065524.52 1043160.72 1022097.38 1002216.74 983415.08 965600.70 948692.20 932617.08 917310.55 902714.54

2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00 2.64E+00

G1 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19 1.36E+19

43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17

X1f 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482 4.7140482

SPf 4.7229642 4.72347306 4.72398444 4.72449807 4.7250137 4.72553114 4.72605021 4.72657075 4.72709262 4.72761572 4.72813993 4.72866517 4.72919136 4.72971841

RSPf 12.57696 12.57747 12.57798 12.5785 12.57901 12.57953 12.58005 12.58057 12.58109 12.58162 12.58214 12.58267 12.58319 12.58372

X2 12.413606 12.405114 12.396612 12.388107 12.379602 12.371101 12.362606 12.35412 12.345646 12.337185 12.328738 12.320309 12.311896 12.303503

X(ass)f

kg kg/m m sq m / deg c kg/sqm

STILL WIND CONDITION

Sag point ( in meters)

l = Ww(ins) = Wi =

11 7.5 2.639 3.83E-02 8.65E-04 2.30E-05 4.71E+09 2 0.255 379.6 189.8 7.854 86.292

F1 -7.67E+06 -8.21E+06 -8.75E+06 -9.29E+06 -9.83E+06 -1.04E+07 -1.09E+07 -1.15E+07 -1.20E+07 -1.25E+07 -1.31E+07 -1.36E+07 -1.42E+07 -1.47E+07 -1.52E+07 -1.58E+07

f2 1202313.34 1170984.22 1141862.27 1114710.02 1089323.05 1065524.52 1043160.72 1022097.38 1002216.74 983415.08 965600.70 948692.20 932617.08 917310.55 902714.54

gs(f2) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

X3 7.6995577 7.6910653 7.6825641 7.6740589 7.6655539 7.6570524 7.6485576 7.6400718 7.6315975 7.6231364 7.6146902 7.6062604 7.5978482 7.5894547

X(act)s 43.30 43.31 43.32 43.33 43.33 43.34 43.35 43.36 43.37 43.38 43.39 43.39 43.40 43.41

D1s 0.251254517 0.258334683 0.26526067 0.272040651 0.278682271 0.285192663 0.291578475 0.297845895 0.304000686 0.310048214 0.315993477 0.321841136 0.327595541 0.333260752

a1s

a2s

4.05E+02 3.94E+02 3.84E+02 3.74E+02 3.66E+02 3.57E+02 3.49E+02 3.42E+02 3.35E+02 3.29E+02 3.22E+02 3.17E+02 3.11E+02 3.06E+02 3.01E+02 2.96E+02

44.264402 43.05357 41.931708 40.888881 39.916588 39.007507 38.155307 37.354483 36.600227 35.888322 35.215055 34.577141 33.971665 33.396032 32.847922 32.325254

D2s 1.752087569 1.799553827 1.845841381 1.891011491 1.935121452 1.978224728 2.020371148 2.061607123 2.101975885 2.141517714 2.180270163 2.218268269 2.255544755 2.292130211

D3s 2.31E+00 2.38E+00 2.45E+00 2.51E+00 2.57E+00 2.63E+00 2.69E+00 2.75E+00 2.81E+00 2.87E+00 2.92E+00 2.98E+00 3.03E+00 3.09E+00

D4s 3.82E+00 3.92E+00 4.03E+00 4.13E+00 4.23E+00 4.33E+00 4.42E+00 4.52E+00 4.61E+00 4.70E+00 4.79E+00 4.87E+00 4.96E+00 5.05E+00

43.17 43.17 Temp

4.7140482 4.73024627 4.7140482 4.73077488

12.58425 12.295129 7.5810808 12.58477 12.286776 7.5727273

43.42 43.43

0.338840569 0.344338548

2.328053268 2.363340748

3.14E+00 3.19E+00

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

T(full wind) 2250.00 2198.92 2150.83 2105.48 2062.64 2022.10 1983.67 1947.20 1912.53 1879.52 1848.06 1818.03 1789.33 1761.88 1735.58 1710.37

f1 2600073.96 2541041.14 2485471.65 2433066.88 2383560.16 2336712.95 2292311.39 2250163.41 2210096.11 2171953.58 2135594.88 2100892.39 2067730.30 2036003.30 2005615.47 1976479.26

w1 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00 5.96E+00

G1 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19 6.94E+19

F1 -8.21E+06 -8.75E+06 -9.29E+06 -9.83E+06 -1.04E+07 -1.09E+07 -1.15E+07 -1.20E+07 -1.25E+07 -1.31E+07 -1.36E+07 -1.42E+07 -1.47E+07 -1.52E+07 -1.58E+07

f2 2541041.14 2485471.65 2433066.88 2383560.16 2336712.95 2292311.39 2250163.41 2210096.11 2171953.58 2135594.88 2100892.39 2067730.30 2036003.30 2005615.47 1976479.26

gs(f2) 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

a1f 3.77E+02 3.69E+02 3.61E+02 3.53E+02 3.46E+02 3.39E+02 3.33E+02 3.27E+02 3.21E+02 3.15E+02 3.10E+02 3.05E+02 3.00E+02 2.96E+02 2.91E+02 2.87E+02

a2f 6.89E+01 6.74E+01 6.59E+01 6.45E+01 6.32E+01 6.20E+01 6.08E+01 5.97E+01 5.86E+01 5.76E+01 5.66E+01 5.57E+01 5.48E+01 5.40E+01 5.32E+01 5.24E+01

X1f 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916 7.8836916

SPf

43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17 43.17

RSPf 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01 1.58E+01

X2 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.56E+01 1.55E+01 1.55E+01 1.55E+01

X3 7.74E+00 7.73E+00 7.73E+00 7.72E+00 7.72E+00 7.71E+00 7.70E+00 7.70E+00 7.69E+00 7.69E+00 7.68E+00 7.68E+00 7.67E+00 7.67E+00 7.66E+00 7.66E+00

X(act)f 43.26 43.27 43.27 43.28 43.28 43.29 43.30 43.30 43.31 43.31 43.32 43.32 43.33 43.33 43.34 43.34

D1f 4.51E-01 4.62E-01 4.72E-01 4.82E-01 4.92E-01 5.02E-01 5.12E-01 5.22E-01 5.31E-01 5.41E-01 5.50E-01 5.59E-01 5.68E-01 5.77E-01 5.86E-01 5.94E-01

D2f 1.78E+00 1.82E+00 1.86E+00 1.90E+00 1.94E+00 1.97E+00 2.01E+00 2.05E+00 2.08E+00 2.12E+00 2.15E+00 2.19E+00 2.22E+00 2.26E+00 2.29E+00 2.32E+00

D3f 2.48E+00 2.54E+00 2.60E+00 2.65E+00 2.71E+00 2.77E+00 2.82E+00 2.87E+00 2.93E+00 2.98E+00 3.03E+00 3.08E+00 3.13E+00 3.18E+00 3.23E+00 3.28E+00

X(ass)f

7.90 7.90 7.90 7.90 7.90 7.90 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91 7.91

2500

6

2000

5

3 1000

2

500

Sag m

4

1500

Tension

Sag m

Tension kg

Full Wind Condition Temp Vs Tension & Sag

Tension

Sag

1

0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Temp Deg C

Tension kg

Still Wind Condition Temp Vs Tension & Sag 1200

6

1000

5

800

4

600

3

400

2

200

1

0

0 1

2

3

4

5

6

7

8

9

Temp Deg C

10

11

12

13

14

15

16

Sag

5.13E+00 5.21E+00

D4f 3.808 3.897 3.984 4.069 4.154 4.237 4.319 4.399 4.479 4.557 4.635 4.711 4.786 4.861 4.934 5.007

Temp Deg C

Annexure I POWER GRID CORPORATION OF INDIA LIMITED 765/400kV RAIPUR NEW & 400kV RAIPUR EXTN. S/S WIND 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 II

Wind pressure on Flexible Conductor AAC Bull Wind pressure on Insulator String

2 139.74 Kg/m 2 172.08 Kg/m

= =

Detail calculation for the above are as follows: A

Claculation for Design Wind Pressure A.1

A.2

B

Design Wind Speed :(as per cl.5.3 IS:875) Where Vb = Basic wind speed as per cl5.2 of IS :875

=

(Vb x K1x K2)/K0

K0

= =

39 m/sec 1.375

K1 = Risk Coefficient (From Table -1 ,For Reliability level 2) K2 = Terrain height & Structure size factor (From Table - 3 ,for Terrain category-2)

= =

Hence, Design Wind Speed Vz

=

Design Wind Pressure: (as per cl.5.4 of IS :875) Pd

=

1.1 1

31.2 m/sec 0.6 x Vd2

= =

2 584.064 N/m 2 60 Kg/m

Fpc

=

Pd * Cdc * Ac * Gc

Cdc Ac Gc

= = =

Fpc

= =

60 * 1.2 * 1 * 2.032 2 139.74 kg/m

=

Pd * Cdi * Ai * Gi

Cdi Ai Gi

= = =

1.2 2 1 m 2.39

Fpi

= =

Wind Load on AAC Bull B.1

Wind Load on AAC Bull Drag Coeefficient Unit Crossectional Area of Conductor Gust Response Factor Therefore,

C

Vd

1 2 1 m 2.329

Wind Load on Insulator String C.1

Wind Load on Insulator String Drag Coeefficient Unit Crossectional Area of String Gust Response Factor Therefore,

Fpi

60 * 1.2 * 1 * 2.032 2 172.08 kg/m