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
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)
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
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 =
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)
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
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