114118002-Sag-Tension-765kV

INTRODUCTION

Sag tension calculation is carried out to estimate the sag in the conductor under various temperatures. The calculation calculation is carried out for the conductor 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 girder width $lg&

conductor 4rea $4c&

tower height $h+&

"lasticity modulas $"&

tower height $h&

'o. of strings iameter of string insulator $di&

ind ressure on cond $wc& ind ressure on insulator $wi& 'o. of conductos $n& 8onductor weight $1c& spacer weight $1s&

"#pansion coefficient $%&

weight of string string weight! conductor $wi& String length $(S& 8onductor chord length $lc&

PARAMETERS USED

,+ ) Initial Temperature

wi ) "quivalent weight of insulator with wind

, ) final Temperature

l ) half span length of conductor +) Sag at centre of insulator catenary2

* ) span length f+ ) Stress at Temprature ,+ f ) Stress at Temprature , w+) "quivalent weight of conductor at Temprature ,+ w) "quivalent weight of conductor at Temprature , T+ ) Tension at Temprature ,+

-elow end of string ) Sag at centre of insulator catenary2 -elow support 9 ) 8onductor Sag -elow end of insulator string wi) wind load : ) total Sag insulator plus conductor

T ) Tension at Temprature ,

/ ) 0alf inclined inclined length of conductor span /+ ) ro;ected *ength of S

ns) 'o. of spacers

/) ro;ected length of S<(S

12) "quivalent conductor weight

/9) ro;ected length of insulator string

BASIS OF CALCULATION Tension at any temperature θ2 e! C

a& Tension at any temperature , the equation to -e solved is as follows3 f  # =f  ) >? @ A

w

2

1

6T

2

l E  2

1

where

A@

>@ f+)

)$, ),+&%"

wl" 64c

f+@ -&

T+!4c

*oading due to wind on conductor and insulator3 ind loading wc @ wc # dc for conductor ind loading wi @ wi # di for insulator

c&

*oadin *oading g due to self self weig weight ht of the the conduc conductor tor and and spacer spacers3 s3 weight of the spacers has -een considered alongwith the weight of the conductor. conductor. The equivalent weight of the conductor and spacers is given -y3 12 @ 12c < $ns.1s&!$n.lc& C.. 4s per I"8 ) D65 where 12 @ weight of the su- conductor ns @ no. of spacers spacers 1s @ weight of the spacer n @ no. of su- conductor lc @ chord length of the conductor $ total span less less the girder width and length of the insulator string& "quivalent weight of the conductor in the loaded condition3 equivalent weight of conductor under full wind condition is given -y w+ @

=$12& < $wc&?

d& 1a#i 1a#imu mum m sag sag$ $:& :& (efer >ig + a+@ T!+ for conductor catenary a@ T!wi for insulator catenary where T3 tension in kg!conductor + 3 equivalent conductor weight + @ no of string # string weight string length / @ $l)(S& / +.BBB5$assumed& /+ @ a / a+

S @ a sinh /+ a (S @ (S < S / @ a sinh)+(S a /9 @ / ) /+ / @ +! E +)/9 + @ a$ cosh/+ ) +& a

(ef page 5: of Te#t -ook GAeneration Transmission and JtiliLation of "lectrical owerG )4.T.ST4((

 @ a$ cosh/ ) +& a

9 @ a+$ cosh/ ) +& a+ Sag : @ 9 <  ) +

e& oint of 1a#imum sag from the Support towers /+ @+ l < Th 

wl

/ @+ l < Th 

wl

(eference3 Te#t Fook3GA"'"(4TIH' T(4'S1ISSIH' 4' JTI*IK4TIH' H> "*"8T(I84* H"(G) 4.T.ST4((

SAMPLE CALCULATION Cir"uit # $%&'( )ua Moose *+, m span.enera/ Data

Initial tension c!c of tower Airder width lg c!c tower ) leg Tower 0eight ind pressure on conductor$wc& ind pressure on Insulator$ wi&

5B kg.!cond +B: m m +B: m 9M m +9M.7: kg!m +7.BD kg!m

(ef 4''"/J(")I (ef 4''"/J(")I

Conu"tor Data

'o. of conductors$n& 8onductor weight$1c& 8onductor iameter$dc& 8onductor 4rea $4c& "#pansion 8oefficient$a& "lasticity 1odulus$"&

: .:Ng!m 9.D9")B m B.BBBD65 sq.m B.BBBB9 deg8 as per IS 9MD $)III)+M76& :.7+"
Spa"er Data

Spacer span 'o. of spacers$ns& Spacer weight $ms&

7.5 m ** Nos $ '!

Insu/ator 0 1arare Data

'o of strings 'o of isc Insulators!string iameter of each disc$di& eight of disc isc *ength of each disc$li& eight of Insulator 0ardware *ength of insulator 0arware including insulator$lh&

 'os :7 'os B.55 m $3& '!

B.+:5 m 5:. kg 7.D5: m

Pre/iminiary C/a"u/ation

String *ength$*S& 8onductor chord length$lc& Total string weight String weight!conductor$wi& "quivalent conductor weight$12&

7.D5: m D6.M m 75M. kg +DM.D kg .69 kg!m

MAIN CALCULATION

+



*oad calculation for conductor ind *oad wc @ dc # wc

@ @

"q.t. of conductor under still wind condition

+

@

.69+ kg!m

"q.t of conductor under full wind condition



@ @ @

 O$12& < $wc& O$.69P<5.9:5P & 5.M5BB kg!m

wi

@ @ @

d # wi # B.5 # *S B.55 # +7.BD # B.5 # 7.D5: +7.9 kg

i

@ @ @

O$string weight!cond&<$wi& O$$+DM.D&P<$+7.9+D&P& 56.95:5 kg

*oad calculation for string insulator wind load

"quivalent weight of insulator with wind

9

B.B9D5#+9M.7: 5.95 kg

8alculation of tension at θ eg 8$5 eg.8& and full wind condition ) T f+

@

@

 Initial tension at B deg 8 and full wind condition $T +& 4rea $4c& 5B B.BBBD65

0ence

f+

@

6BBB79.M6

kg!m

0alf span length of conductor

*0

@ @ @

$half span ) insulator length& # +.BBB5 $$+B:)&!)7.D5:&#+.BBB5 :9.+7 m

Su-stituting the value of   for full wind condition and other values A can -e calculated as A

wl"

@

6 4c

0ence

A

@

5.M5P#:9.+7P#:7BMBBBBBB $6#B.BBBD6596P&

@

6.M+5"
Su-stituting the value of   for full wind condition and other values with temprature diffrence of 5o8 > can -e calculat >

@

>

@

f+

)

wl" 64cf +

) $θ)θ+&"a

utting all the values we get

@

6BBB79.M5D)5.M5PE:9.+7P#:7BMBBBBBB!$6#B.B 6BBB79.M5DP&)$5)B&#:7BMBBBBBB#B.BBBB9 )D.+7"
The stress f  at 5 deg 8 could -e found out -y sloving the cu-ic equation Gf 9)>f )A@BG for f  'ow f 9)>f )A

"+B+P9)"M+E"+B+P)"D 5:BD57.5++P9))D+6MM5.9+7#5:BD57.5++P)6M+ B.BB"
we get f 

@

5:BD57.5+ kg!m

0ence the tension T under full wind condition at 5 deg 8 @ f  # 4c @ 5:BD57.5++ # B.BBBD65: 1en"e

7 2

4

2*563$% '!

T8e tension9T2- :a/ues are "a/"u/ate 7or 7u// in "onitions up to $& e!3C in steps o7 & e!3C

d&

Sag under full wind conditions ) Initial temperature B deg 8 Sag point /+ @ +! # $*&

/+

@

5

m

with reference to fig + and equations given under section :.9 a+

@

T+ w+

@

5B 5.M5BB

@

97D.+5

a

@

T+ wi

@

5B @ 56.955!7.D5:

6D.M9

/$ass&

@ @

$$l)&!)(S& # +.BBB5 :9.+7 m

/+

@ @ @

$a!a+& / $6D.M9:!97D.+5+&#:9.+6D 7.D7

S

@ @ @

asinh$/+f!a& 6D.M9:#SI'0$7.D6M!6D.M9:& 7.DM

(S

@ @ @

S<*S 7.DD6<7.D5: +5.7:

/

@

asinh)+$(S!a &

@

$$+B:)&!)7.D5:&#

@ @

6D.M9:#4SI'0$+5.7:!6D.M9:& +5.6+

/9

@ @ @

/ ) /+ +5.6B7)7.D6M 7.7:

/

@ @ @

/+ ) /9 5 )7.797) + :9.6

+

@ @ @

a$cosh $/+!a & )+& 6D.M9:#$8HS0$7.D6M!6D.M9:&)+& B.:5



@ @ @

a$cosh $/!a & )+& 6D.M9:#$8HS0$+5.6B7!6D.M9:&)+& +.77"
9

@ @ @

a$cosh $/9!a +& )+& 97D.+5+#$8HS0$:9.69!97D.+5+&)+& .:77:9675

:

@

9 <  ) + .:77<+.77:)B.:5

D,

4

0ence sag at full wind condition at B deg 8 is given -y

1en"e

;36+2 m

SJ114(Q The Sag tension at various temperatures for -oth still wind R full wind condition for the following cases are carried out +& 765kV uad Full ) 5: m Span with Tower 0eight of 7m & 765kV uad Full ) +B: m Span with Tower 0eight of 9Mm 9& 765kV uad Full ) M9 m Span with Tower 0eight of 9Mm

ed as

BD6596

:D95+

kg!m

kg!m .BBB5

.

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

2250 kg/cond

c/c of tower Girder width (lg) Span (c/c towerlg) !ower height(h1) " !ower height(h2) " %ind pr& on cond %ind pr on ins*lator" ,o of cond*ctors" -ond weight spacer span

104 m 2m 102 m #$ m #$ m 1#$&'4 g/sm 1'2&0+ g/sm 4 2&4 g/m '&5 m

ULL !IN" CON"ITION !emperat*re deg c

!ension (kg)

0 5 10 15 20 25 #0 #5 40 45 50 55 .0 .5 '0 '5

2250&00 21$+&$2 2150&+# 2105&4+ 20.2&.4 2022&10 1$+#&.' 1$4'&20 1$12&5# 1+'$&52 1+4+&0. 1+1+&0# 1'+$&## 1'.1&++ 1'#5&5+ 1'10&#'

l  % w(ins)  %i  !emp

!(still wind) 0 5 10 15 20 25

Sag point

10.$&.$ 1040&4# 101# $++&12 $.4&.# $42&..

( in meters)

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

4#&1' 1'2 25. f1 12#.12'&01 1202#1# 11'0$+4&22 1141+.2&2' 1114'10&02 10+$#2#&05

STILL !IN" CON"ITI   Sag (in meters)

#&+0+ #&+$' #&$+4 4&0.$ 4&154 4&2#' 4
$ 4&#$$ 4&4'$ 4&55' 4&.#5 4&'11 4&'+. 4&+.1 4&$#4 5&00'

!ension (kg)

10.$&.$ 1040&4# 101# $++&12 $.4&.# $42&.. $22&0. $02&'1 ++4&4+ +.'&2+ +51&01 +#5&5$ +20&$. +0'&05 '$#&+0 '+1&1'

Sag point (in meters )

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

(half span length) (weight of ins*lator in still wind) (weight of ins*lator in f*ll wind) w1 2&.400 2&.400 2&.400 2&.400 2&.400 2&.400

G1 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$

1 '&.'0. +&210. +&'50. $&2$0. $&+#0. 1&040' 1&0$0'

f2 1202#1# 11'0$+4&22 1141+.2&2' 1114'10&02 10+$#2#&05 10.5524&52

#0 #5 40 45 50 55 .0 .5 '0 '5 3(ass)f 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' !emp 0 5 10 15 20 25 #0 #5 40 45 50 55 .0 .5 '0 '5 3(ass)f

$22&0. $02&'1 ++4&4+ +.'&2+ +51&01 +#5&5$ +20&$. +0'&05 '$#&+0 '+1&1'

10.5524&52 104#1.0&'2 10220$'&#+ 100221.&'4 $+#415&0+ $.5.00&'0 $4+.$2&20 $#2.1'&0+ $1'#10&55 $02'14&54

31f Sf 4&'1404+24 4&'22$.41$' 4&'1404+24 4&'2#4'#05. 4&'1404+24 4&'2#$+44#+ 4&'1404+24 4&'244$+0.5 4&'1404+24 4&'2501#'01 4&'1404+24 4&'255#1141 4&'1404+24 4&'2.05020' 4&'1404+24 4&'2.5'0'45 4&'1404+24 4&'2'0$2.22 4&'1404+24 4&'2'.15'2 4&'1404+24 4&'2+1#$$#5 4&'1404+24 4&'2+..51'5 4&'1404+24 4&'2$1$1#5+ 4&'1404+24 4&'2$'1+412 4&'1404+24 4&'#024.2'# 4&'1404+24 4&'#0''4++2 !(f*ll wind) 2250&00 21$+&$2 2150&+# 2105&4+ 20.2&.4 2022&10 1$+#&.' 1$4'&20 1$12&5# 1+'$&52 1+4+&0. 1+1+&0# 1'+$&## 1'.1&++ 1'#5&5+ 1'10&#'

31f 4#&1' '&++#.$155 4#&1' '&++#.$155

f1 2.000'#&$. 2541041&14 24+54'1&.5 24##0..&++ 2#+#5.0&1. 2##.'12&$5 22$2#11&#$ 22501.#&41 22100$.&11 21'1$5#&5+ 21#55$4&++ 2100+$2&#$ 20.''#0� 20#.00#� 2005.15&4' 1$'.4'$&2. Sf '&$0 '&$0

2&.400 2&.400 2&.400 2&.400 2&.400 2&.400 2&.400 2&.400 2&.400

1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$ 1&#.1$

1&150' 1&200' 1&250' 1
0' 1&#.0' 1&420' 1&4'0' 1&520' 1&5+0'

104#1.0&'2 10220$'&#+ 100221.&'4 $+#415&0+ $.5.00&'0 $4+.$2&20 $#2.1'&0+ $1'#10&55 $02'14&54

Sf 32 12&5'.$.4 12&41#.05$ 12&5''4'# 12&40511#. 12&5''$+4 12&#$..124 12&5'+4$+ 12&#++10'2 12&5'$014 12&#'$.021 12&5'$5#1 12&#'1100' 12&5+005 12&#.2.05+ 12&5+05'1 12򄈑 12&5+10$# 12-.45' 12&5+1.1. 12&##'1+4' 12&5+214 12+'#+5 12&5+2..5 12#0+' 12&5+#1$1 12+$.5 12&5+#'1+ 12�#502$ 12&5+424. 12&2$512$ 12&5+4''5 12&2+.''55

3# '&.$$55''1 '&.$10.5#2 '&.+25.412 '&.'405+$4 '&..555#++ '&.5'05242 '&.4+55'55 '&.400'1+4 '&.#15$'4$ '&.2#1#.41 '&.14.$025 '&.0.2.04# '&5$'+4+21 '&5+$454.+ '&5+10+0'. '&5'2'2'2$

3(act)s 4#� 4#
4# 4#&## 4#&## 4# 4# 4#&#. 4#&#' 4#&#+ 4#&#$ 4#&#$ 4#&40 4#&41 4#&42 4#&4#

w1 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00 5&$.00

G1 .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$ .&$41$

1 +&210. +&'50. $&2$0. $&+#0. 1&040' 1&0$0' 1&150' 1&200' 1&250' 1
0' 1&#.0' 1&420' 1&4'0' 1&520' 1&5+0'

f2 2541041&14 24+54'1&.5 24##0..&++ 2#+#5.0&1. 2##.'12&$5 22$2#11&#$ 22501.#&41 22100$.&11 21'1$5#&5+ 21#55$4&++ 2100+$2&#$ 20.''#0� 20#.00#� 2005.15&4' 1$'.4'$&2.

Sf 1&5+01 1&5+01

32 1&5.01 1&5.01

3# '&'400 '&'#00

3(act)f   4#&2. 4#&2'

4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1' 4#&1'

'&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155 '&++#.$155

'&$0 '&$0 '&$0 '&$0 '&$1 '&$1 '&$1 '&$1 '&$1 '&$1 '&$1 '&$1 '&$1 '&$1

1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01 1&5+01

1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5.01 1&5501 1&5501 1&5501

'&'#00 '&'200 '&'200 '&'100 '&'000 '&'000 '&.$00 '&.$00 '&.+00 '&.+00 '&.'00 '&.'00 '&..00 '&..00

4#&2' 4#&2+ 4#&2+ 4#&2$ 4#� 4#� 4#
4#
4# 4# 4#&## 4#&## 4# 4#

ull !#$d C%$d#&#%$ T' V* T'$*#%$ + Sa, 2500 2000 T'$*#%$ , 1500 1000 500 0 1

2

#

4

5

.

'

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12

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,o of spacers(ns)

11

spacer weight(7s)

'&5 kg 2&.#$ kg/m #&+#02 m +&.504 s m 2�05 / deg c 4&'10$ kg/sm 2 0&255 m #'$&. kg 1+$&+ kg '&+54 m +.&2$2 m

 -ond weight -ond dia -ond area 6p& -oefficient las 7od*l*s ,o of strings 8ia of string ins*l weight/string String weight/cond& String length(S) -ond chord len (lc) N  Sag (in meters)

#&+2 #&$22 4&02' 4&12+ 4&22+ 4. 4&422 4&51. 4&.0+ 4&.$+ 4&'+' 4&+'5 4&$.1 5&045 5&12+ 5&210

gs(f2) 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000

a1s 4&0502 #&$402 #&+402 #&'402 #&..02 #&5'02

a2s 44&2.44022 4#&05#5'0# 41&$#1'0'. 40&+++++14 #$&$1.5+'+ #$&00'50'2

0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000

#&4$02 #&4202 #02 #&2$02 #&2202 #&1'02 #&1102 #&0.02 #&0102 2&$.02

#+&155#0'2 #'Ƞ+# #.&.0022' #5&+++#22# #5&215055 #4&5''140$ ##&$'1..52 ##&#$.0#21 #2&+4'$21. #2ঢ়#$

81s 0&25125451' 0&25+##4.+#2 0&2.52.0.'04 0&2'2040.51# 0&2'+.+22'0$ 0&2+51$2..# 0&2$15'+4'4. 0&2$'+45+$51 0ྠ.+.5 0Ϭ+214# 0$$#4''4 0+411#.5 0'5$55405 0&###2.0'51$ 0&##++405.$1 0,##+54''

82s 1&'520+'5.$1 1&'$$55#+2' 1&+45+41#+05 1&+$10114$0+ 1&$#5121452 1&$'+224'2+4 2&020#'114'' 2&0.1.0'12#2 2&101$'5++55 2&14151''145 2&1+02'01.# 2&21+2.+2.$1 2&255544'55 2&2$21#0211# 2+05#2.'5 2&#.##40'4'.

8#s 2
00 2&#+00 2&4500 2&5100 2&5'00 2&.#00 2&.$00 2&'500 2&+100 2&+'00 2&$200 2&$+00 #&0#00 #&0$00 #&1400 #&1$00

gs(f2) 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000 0&0000

a1f #&''02 #&.$02 #&.102 #&5#02 #&4.02 #&#$02 #&##02 #&2'02 #&2102 #&1502 #&1002 #&0502 #&0002 2&$.02 2&$102 2&+'02

a2f   .&+$01 .&'401 .&5$01 .&4501 .01 .&2001 .&0+01 5&$'01 5&+.01 5&'.01 5&..01 5&5'01 5&4+01 5&4001 501 5&2401

81f 4&5101 4&.201

82f 1&'+00 1&+200

8#f 2&4+00 2&5400

84s #&+200 #&$200 4&0#00 4&1#00 4&2#00 4&##00 4&4200 4&5200 4&.100 4&'000 4&'$00 4&+'00 4&$.00 5&0500 5&1#00 5&2100

84f   #&+0+ #&+$'

4&'201 4&+201 4&$201 5&0201 5&1201 5&2201 5
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1&+.00 1&$000 1&$400 1&$'00 2&0100 2&0500 2&0+00 2&1200 2&1500 2&1$00 2&2200 2&2.00 2&2$00 200

. 5 4 #

Sa, 

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2 1 0 15

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Sa, 

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#&$+4 4&0.$ 4&154 4&2#' 4
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@

9M m!Sec

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ind pressure on >le#i-le 8onductor 448 Full ind pressure on Insulator String

@ @

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1en"e@ Desi!n ?in Spee (

4

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C/a"u/ation 7or Desi!n ?in Pressure

4.+

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4.

4 B

B.6 # Vd 5D:.B6: %+

?in Loa on AAC Bu//

F.+

ind *oad on 448 Full rag 8oeefficient Jnit 8rossectional 4rea of 8onductor Aust (esponse >actor Therefore

>pc

@

8dc 4c Ac

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d E 8dc + + .9M %+  *32 *;53$,

C

?in Loa on Insu/ator Strin!

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ind *oad on Insulator String rag 8oeefficient Jnit 8rossectional 4rea of String Aust (esponse >actor Therefore

>pi

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8di 4i Ai

@ @ @

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Fpi

4

%+  *32

4

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m!sec

m!sec

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4i E Ai

m

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