INTRODUCTION Sag tension calculation is carried out to estimate the sag in the conductor under v temperatures. The calculation is carried out for the conductor span lengths in use 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 conduct 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 θ2 - final Temperature D1- Sag at centre of insulator caten D2- Sag at centre of insulator caten w1- Equivalent weight of D3 - Conductor Sag below end of insu w2- Equivalent weight of Wwi- wind load D4 - total Sag insulator plus conduc 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 st Tension at any temperature θ2 f2 2 x [f2 - F] = G
Transcript
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
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
