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Following minimum clearances shall be maintained :System operating voltage 400 220 132 33
Lightning Impulse Withstand Level (LIWL) 1550 1050 650 170
Switching Impulse Withstand Level (SIWL) 1050
Power frequency voltage 630 460 275 80
Minimum phase to earth clearance mm 3500 2100 1300 320Minimum phase to phase clearance mm 4000 2100 1300 320Minimum sectional clearance mm 6500 5000 4000 3000Phase to phase distance between flexible conductor
Levels in the switchyard (Height from Plinth)System operating voltage 400 220 132 33
Plinth Level mFirst Level - Equipment Connection mSecond Level - Strung Bus - Busbar mThird Level - Strung Bus - Jack Bus mFourth Level - Shield wire m
CASE 1Voltage 420
Minimum Phase to phase clearance = m 4Centre-line distance between main conductor mid points m 7Span length m 100.00Height of conductor above ground m 15.3Conductor Type TARANTULLANo. of sub-conductor of a main conductor Nos. 2Current Carrying capacity A 2570Suitability to carry Short Circuit Current Suitable
m 0.45
m 6.00
kg 1000
No. of Disc Insulator Strings Nos. 4No. of disc in one string Nos. 30
kg 467.9
SAG
Annexure 1Sag-Tension Calculation, Sag Tension Chart and
Short Circuit Forces For Structure and Foundation Design
kVRMS
kVPEAK
kVPEAK
kVRMS
kVRMS
The above levels in switchyard will ensure adequate phase to phase, phase to earth clearances for maximum sag & swing, short circuit forces and wind forces.
kVRMS
Effective distance between Sub-conductor = Center line distance between Sub-conductor
Spacer Span = Centeline distance between connecting pieces or between one connecting piece and the adjacent support
Static Tensile force per (sub)conductor in flexible conductor per phase under minimum temperature and maximum wind condition
Static Tensile force PER CONDUCTOR in flexible conductor per phase under minimum temperature and NO wind condition (CIVIL INPUT)
Annexure 1Sag-Tension Calculation, Sag Tension Chart and
Short Circuit Forces For Structure and Foundation Design
Net Current Carrying Capacity of the BUNDLE = A 2570Suitability to carry Short Circuit Current Suitable
Annexure 1Sag-Tension Calculation, Sag Tension Chart and
Short Circuit Forces For Structure and Foundation Design
SAGTotal maximum sag = m 2.053Sag due to conductor m 1.296Sag due to Insulator m 0.757Height of jack bus/equipment below conductor m 8.3
m 0.947
SWINGTotal maximum swing of conductor = m 0.581Available margin = m 1.969Phase to phase spacing required = m 5.031SHORT CIRCUIT
kg 2000
kg 5514.9
Tensile force during short circuit kg 2772.2Tensile force caused by Pinch effect kg 5514.9Tensile force after short circuit (drop force) kg NAj 1.1
Therefore, available margin calculated between centre lines (excluding sub-conductor spacing, conductor width, equipment clamps etc) =
Static Tensile force in flexible conductor per phase under minimum temperature and maximum wind condition
Therefore design short circuit forceMaximum of following :
Annexure-1
Page 4 of 29
CALCULATION FOR FLEXIBLE CONDUCTORSSystem Parameters
Voltage = 420 kVCurrent Rating = 3000 A
= 40,000 ADuration of the first short circuit current flow = 1 Sec
System frequency = 50 Hz
Wind Parameters
Basic Wind Speed = = 47.00 m/s= 1.07
Terrain Category = 2
= 1.3750
Height of conductor above ground = 15.3000
Spacer, additional concentrated mass= 6.00 m
Spacer weight = 3 kgNo. of spacers in span = 14 nos.
= 0.00 kg
= 0 nos.
Conductor Parameters
Conductor Type = TARANTULLA
Type = AAC
Al Strands = 37
Steel Strands = 0
Al Strand Dia = 0.00523
St strand dia = 0
Cross sec. = 0.000794868 sq.m
Diameter = 0.0366 m
Weight = 2.91 kg/m
= 608200
Young's Modulus (N/sq.m) = 61997961264 N/sq.m.
Drag Coefficient = 1
DC Resistance = 0.0363 Ohm/km
= 3.1452 kg/m
Coefficient of Linear Expansion = 0.000023
= 0.00No. of Disc Insulator Strings = 4.00No. of disc in one string = 30.00
Weight of hardware = 60 kg
Length of Hardware before disc = 0.25 m
Disc Insulator Type = 120 kN
x = 0
Creepage = 440 mm.
Diameter of Disc = 0.28 m
Three phase Initial symmetrical short-circuit current (r.m.s)
Risk Coefficient as per Table 2 of IS: 802, Part 1, Sec 1For all Zones & for Reliability level 1(Voltage level upto 400kV)
Factor to convert 3 second peak gust speed into average speed of wind during 10 minutes period =
Spacer Span = Centeline distance between connecting pieces or between one connecting piece and the adjacent support
Additional concentrated mass (other than spacer) representing the connections of pentagraph isolator ( Mass of one connection)
Nos. of Trapzee Connection of pentagraph isolator in one span
Young's Mod. Kg./Cm2 Kg./Cm2106
Resulting Mass Per Unit length of one sub-conductor
/ oC
length of compensating spring in case of pentograph Isolator
Annexure-1
Page 5 of 29
Weight of Disc = 8.3 kg
Length of Disc = 0.145 m
= 4.600 m
1056.000
Layout Parameters
No. of sub-conductor of a main conductor = 2 nos.
1 T
= 2 T
Span length = 100.00 mBeam width 1.5 m
= 89.3 m
Maximum Ambient Temperature at site = 50.0000
Minimum Ambient Temperature at site = 0.0000
Rise in temperature = 35.0000
Final Temperature after Short Circuit = 200.0000
Radial Thickness of ICE over the conductor 0.0000 cm
Phase to phase spacing provided between phases = 7.0000 m= 0.45 m
Minimum Phase to phase clearance = 4 mHeight of jack bus/equipment below conductor 8.3 m
100000
Total consolidated length of disc Insulator & Hardware in one side of Span
Total consolidated weight of disc Insulator & Hardware in one side of Span
Static Tensile force PER CONDUCTOR in flexible conductor per phase under minimum temperature and maximum wind conditionStatic Tensile force in flexible conductor per phase under minimum temperature and maximum wind condition
Length of conductor carrying short circuit current (Chord length of main conductor in the span)
oC oC oC oC
Thice=
Effective distance between Sub-conductor = Center line distance between Sub-conductor
Resultant Spring constant of both support of one Span N/m
CASE – 1.CALCULATION FOR BUSBAR SIZING
Bundle Conductor Considered AAC TARANTULLA
No. of sub-conductor in a BUNDLE 2
1 Check for continuous thermal withstand capacity of the conductor
Required Current Carrying Capacity of the BUNDLED conductor 3000 Amps
Hence as given in Heat balance equation : (1)
where,(2)(3)
(4)(5)
where,I = the conductor current (A)
DC resistance of conductor at 20°C 0.0363
=γ the solar radiation absorption co-efficient Refer IEC 61597 0.50
Refer IEC 61597 900.00D = the conductor diameter (m) 0.0366 m
Refer IEC 61597 5.67E-08
the emmisivity co-efficient in respect to black body Refer IEC 61597 0.60Ambient Temperature in (C) 50 °CFinal Equilibrium Temperature (C) 85 °CAmbient Temperature in (K) 323 KFinal Equilibrium Temperature (K) 358 K
=λ the thermal conductivity of air film in contact with the conductor Refer IEC 61597 0.02585
Nu = Refer IEC 61597 25.7
Refer IEC 61597 1871.6v = wind speed in m/s Refer IEC 61597 1 m/s
System frequency 50 HzThermal Coefficient of Resistivity Refer IEC 61597 4.03E-03 /°Cpermeability (= 1, for non magmnatic material) 1
now,
where, DC resistance of the conductor at operating temperature 85 deg C
K Skin effect coefficientagain,
0.03630.058419
=> 0.073722Next for calculation of skin effect coefficient, a factor X [reference (2)]
=> X = 1.65603
K = 1.03512
=> 0.0763114.74E-05
16.47
21.68
73.12from heat balance equation - 2 we derive,
equation-3
From equation - 3, we obtain=> Current Carrying Capacity of the CONDUCTOR = 1285 Amps
Net Current Carrying Capacity of the BUNDLE = 2570 Amps
The current which a conductor can carry for a given temperature rise depends upon the rate at which the produced heat is dissipated. In case of an overhead conductor, the dissipation will be effected by radiation and by convection.
Pj + Psol = Prad + Pconv
Pj = RT I², Heat generated by Joule effectPsol = D Sγ i, Solar Heat Gain
Prad = s π D Ke (T24 – T1
4), Radiation Heat Loss
Pconv = λ Nu (T2 – T1) π, Convection Heat Loss
Rdc(20°C) Ω/kmRT= the electrical resistance of conductor at a temperature T (Ω/m)
Si = the intensity of solar radiation (W/m²), W/m2
s = the Stefan Boltzmann constant (5.67×10–8 W.m–2K–4) W.m–2K–4
Ke =
T1 =T2 =
W m–1K–1
the Nusselt number = 0.65 Re0.2 + 0.23Re
0.61
Re = the Reynolds number = 1.644×109v D[(T1 + 0.5(T2 – T1)]–1.78
f = =α
μ =
RT = Rdc x K
Rdc
Rdc(85°C) = Rdc(20°C) (1+ ×(Tα 2-20))Rdc(20degC) = Ω/km
Ω/milesRdc(85°C) Ω/miles
For this value of X, the skin effect coefficient K is obtained from Table 4.1.1 of "Power Engineers Handbook"
RT = Ω/milesΩ/m
Psol = D Sγ i
Prad = s π D Ke (T24 – T1
4)Pconv = λ Nu (T2 – T1) π
X=0 .063598×√ μ×fR
dc(850C )
T
solconvrad
R
PPPI
)(max
Check for Short Circuit Current carring capacity of the incoming line conductor
System short circuit current for System 40,000 At Duration of short circuit current 1 sec
Min. reqd. area of cross-section of conductor for short time rating
where,
Initial temp. of conductor before short ckt 85
Final temp of conductor after short ckt 200G Conductivity of conductor Reference: (2)-(c ) 40 %
Clause 5.2.2
0.878063
Minimum required cross-sectional area 566.49
Cross-section of each CONDUCTOR 794.87
Overall Cross-section of BUNDLE 1589.74
Suitability to carry Short Circuit Current Suitable
I"k3
Reference: (2)-(c)Clause 5.2.2 Eq (3)
in2
(Amin) =
Ti0C
Tf0C
in2
mm2
mm2
mm2
3
6
"
( 20 (15150 / ))0.144 10 log
( 20 (15150 / ))
k
f
i
I X t
T GX
T G
3
6
"
( 20 (15150 / ))0.144 10 log
( 20 (15150 / ))
k
f
i
I X t
T GX
T G
Annexure-1
Page 8 of 29
CASE – 3.
Short Circuit Force CalculationsCalculation are based on IEC 865-1 (1993)
FOR FLEXIBLE CONDUCTORS
= = 2 T
= 19620 N
= Three phase Initial symmetrical short-circuit (r.m.s) = 40000 A
= No. of sub-conductor of a main conductor = 2 nos.
= Sub–conductor mass per unit length = 2.91 kg/m
Diameter of flexible conductor = 3.660E-02 m
Cross Section of one sub-conductor = 7.949E-04
= = 6 m
= 0 kg
= 0 nos.
Spacer weight = 3 kg
No. of spacers in span = 14 nos.
Resulting Mass Per Unit length of one sub-conductor
= 3.145 kg/m
= Span length = 100 m
= 0
= = 4.6 m
= = 0.45 m
= Centre-line distance between main conductor mid points = 7 m
Beam Width 1.5 m
= = 89.3 m
S = = 100000 N/m
= Young's modulus = 6.2E+10 N/m2
= Duration of the first short circuit current flow = 1 Sec
= Gravitational Constant = 9.81
= Constant = 5.00E+07
f = System frequency = 50 Hz
Material Constant = 2.70E-19
Magnatic Constant, permeability of Vacuum = H/m
Static Tensile force in flexible conductor per phase under minimum temperature and maximum wind condition
=
= m2
Spacer Span = Centeline distance between connecting pieces or between one connecting piece and the adjacent supportAdditional Concerated mass (other than spacer) representing the connections of pentagraph isolator ( Mass of one connection)Nos. of Trapzee Connection of pentagraph isolator in one span
=
msc' =
length of compensating spring in case of pentograph of IsolatorTotal consolidated length of disk Insulator & Hardware in one side of Span
Effective distance between Sub-conductor = Center line distance between Sub-conductor
Length of conductor carrying short circuit current (Chord length of main conductor in the span)
Resultant Spring constant of both support of one Span N/m
m/s2
N/m2
Cth =
m4/(A2s)
µo= 4π×10–7
fin
l
dcl
lc
a
A s
ms'
d s
ms
ls
as
F st
E
I k 3 ¿¿¿n
T k 1
gn
msc '=m s '+ncmc
nlc+nsm s
nlc
nc=
mc=
ns=
lsp=
Annexure-1
Page 9 of 29
CASE – 3.
Short Circuit Force Calculations
= 30.62 N/m
= 0.4962
From eqn. 21, Angular direction of the force,
= 26.3888 Deg
From eqn. 22, Equivalent Static Conductor Sag at mid span,
= 3.9315 m
From eqn. 23, Period of Conductor oscillation,
= 3.5577 Sec.
= 3.4125 Sec.
From eqn. 25, The stiffness norm
= 1.18E-07
Where the actual Young's modulus is given by
= 3.50E+10
From eqn.19, Characteristic electromagnetic force per unit length on flexible main conductors,
From eqn. 20, the ratio of electromechanical force on a conductor under short circuit condition to gravity,
From eqn. 24, Resulting period of the conductor oscillation during the short circuit current flow,
N/m2
F '=μ0
2π×0 .75׿¿¿¿
r= F'
n×msc' ×gn
δ 1= tan−1r
bc=n×msc
' ×gn×l2
8 F st
T=2 π √0 . 8bc
gn
T res=T
4√1+r2 [1− π 2
64 [ δ1
900 ]2]
N=1Sl
+1
nEsA s
E s=E [0. 3+0 . 7×sin( F st
nAs σ fin
×900)] forF st
nA s
≤σ fin
E forF st
nA s
>σ fin
Annexure-1
Page 10 of 29
CASE – 3.
Short Circuit Force Calculations
From eqn.28,The stress factor of the main conductor is given by :
= 1.78E+00
From eqn. 29, Swing out angle at the end of the short-circuit current flow
= 33.4389 Deg
From eqn. 30, factor
= 0.7266
From eqn. 31, Maximun swing out angle
= 53.3986 Deg
From eqn. 32, Load Parameter
= 0.3490
From eqn. 33, The factor , can be calculated as a real solution of the equation,
0.00
= 0.7453
From eqn. 34, the tensile force is given by,
= 2772.1832 Kg
ζ=(ngnmsc
' l )2
24 Fst3 N
δ k=δ1 [1−cos(T k 1
T res
×3600)] for 0≤T k 1
T res
≤0 . 5
2δ1 forT k1
T res
>0 . 5
χ=1−rsin δk for 0≤ δ k≤90
1−r for δ k>90
δm=1.25 arccos χ for 0 .766≤ χ≤110+arccos χ for −0 . 985≤ χ<0 . 766
1800 for χ<−0. 985
ϕ= 3 (√1+r2−1) for T k1≥T res
4
3 (r sin δ k+cos δk−1) for T k 1<Tres
4
ψ
ϕ2ψ3+ϕ (2+ζ )ψ2+ (1+2 ζ )ψ−ζ (2+ϕ )=0 0≤ψ≤1
ψ
F t= F st (1+ϕψ ) for n=1 for Single conductor
1 . 1F st (1+ϕψ ) for n≥2 for bundle conductor
Annexure-1
Page 11 of 29
CASE – 3.
Short Circuit Force Calculations
From eqn. 35, the tensile force after short circuit caused by drop (drop force)
= NAKg
From Eqn. 36, The elastic expansion is given by,
= 8.9363E-04
From Eqn. 37, The thermal expansion is given by,
= ###
= ###
= 1.05
= 2.0531
= ###
Horizontal Span Displacement bh and Min. air clearance amin
From Eqn. 38, Factor CD is given by,
From Eqn. 39, Factor CF is given by,
From Eqn. 41, Maximum Horizontal Displacement within a span with strained conductors is given by,
From Eqn. 42, the distance between the mid points of the two main conductors during a line-to-line two-phase short circuit,
F f=1 . 2F st √1+8 ζδm
1800for r>0 .6 δm≥700
ε ela=N (F t−F st )
ε th=c th [ I k 3 over ital nA rSub size 8s right ] rSup size 82 T rSub size 8 ital res /4 matrix # ital for matrix # T rSub size 8k1 >= T rSub size 8 ital res /4 ## matrix ##c rSub size 8 ital th left [ I rSub size 8k3 rSup size 8
nA s]2
T k 1 for T k 1<T res /4 ¿
CD=√1+ 38 [ l
bc ]2
(εela+εth)
CF= 1 . 05 for r≤0 .80 . 97+0.1 r for 0 . 8<r<1 . 8
1. 15 for r≥1 .8
bh=CFCDbc sin δ1 for δm≥δ1
CFCDbc sin δm for δm<δ1
amin=a−2bh
Annexure-1
Page 12 of 29
CASE – 3.
Short Circuit Force Calculations
SUBCONDUCTORS ARE NOT EFFECTIVELY CLASHING
= 4.2760
= 12.2951
= 1.5721
=
0.2133
From eqn. 45, Short circuit current force
= 7862.0971Kg
From eqn. 47 & 48, Strain factor characterizing the contraction of bundle condoctor
= 0.7313
= 2.1267
= 1.1083
If j > 1 : The sub-conductor clash
If j < 1 : The sub-conductors reduce their distances but do not clash
Sub-conductor are considered to clash effectively if the clearence as between the mid -points of adjacent sub-conductors, as well as the distance ls between 2 adjacent spacers fulfil either equation (43) or (44)
From equation 46, the factor v1 is given by,
The factor as/ds is equal to
Factor V2 can be given by fig. 8 as function of V1
V2
Factor V3 can be given by
as /ds≤2 .0 and ls≥50as (43 )as /ds≤2. 5 and ls≥70as (44 )
v1=f1
sin1800
n √ (as−d s)msc'
μ0
2π¿¿
¿¿¿
ε pi=0 .375 nFv ls3 N
(as−d s)3 (sin
1800
n )3
ε st=1 . 5F st l s2
N
(as−d s)2 (sin
1800
n )2
j=√ ε pi
1+εst
Fv=(n−1 )μ0
2π¿¿
V 3=
ds
as
sin180n
× √(as
d s)−1
arctan √(as
ds)−1
Annexure-1
Page 13 of 29
CASE – 3.
Short Circuit Force Calculations
SUBCONDUCTORS ARE CLASHING
TENSILE FORCE IN CASE OF CLASHING SUB-CUNDUCTORSIf j ≥ 1, From eqn. 50, the tensile force is given by
= 5514.8618 Kg
From equation (51), ξ is given by the real solution of
0.00ξ . 1.0825801
From eqn. 52,
= 1.1872
From eqn. 53,= 1.13E+01
= 5514.8618 Kg
=
Therefore design force in kg (Maximum of Ft, Ff & Fpi)
v4=ηas−d s
as−η (as−ds)
F pi=Fst (1+ve
εstξ)
ξ3+εst ξ2−ε pi=0
ve=12+¿¿
v4=as−ds
d s
Annexure-2
Page 14 of 29
CASE – 1.
CALCULATIONS FOR SAG AND SWING OF STRUNG CONDUCTOR
System Voltage V = 420 kV
1 Basic Wind Speed = 47.00 m/sAs per IS 802: 1995, basic wind speed is based on gust velocity averaged over a short time interval of 3s.
Wind Zone as per IS: 802, Part 1, Sec 1 4
1.07
Terrain Category 2Terrain roughness coeficient (For different Terrain Category) = 1.0000
1.3750
34.1818 m/s36.5745 m/s
Height of conductor above ground 15.3000 metreGust Response Factor for conductor Gc = 1.9837
2 Pc = 81.8164
Weight of individual spacer = WSP = 3.0000 kgfSeparation between two spacers = SSP = 6.0000 metreWeight of sub-conductor per metre= W1 = 2.9100 kgf/mNo. of subconductors - single/twin/tri/quad = r = 2Diameter of sub-conductor = d = 3.6600 cmCross Sectional Area of sub-conductor = A = 7.9487Modulus of Elasticity of sub-conductor = ey = 608200.0000Coefficient of Linear Expansion = a = 2.3000E-05Maximum Ambient Temperature at site = t1 = 50.0000Minimum Ambient Temperature at site = t2 = 0.0000Rise in temperature = t3 = 35.0000Distance between centre line of beams (for conductor span) = la = 100.0000 mDIameter of disc = di = 0.2800Nos. of Insulator Strings in one side of conductor span (Single /Double) Ni = 4Weight of complete string insulator including hardware 1056.0000Weight of single string insulator including hardware Wi= 264.0000Length of insulator string = li = 4.6000 mWidth of beam on which conductor is strung = Bw = 1.5000 m
Ten1= 1000.0000 KgDrag Coefficient 1.0000
3 Effect of Ice formation
Radial Thickness of ICE over the conductor 0.0000 cmD1= 3.6600 cm
Increase in Conducter weight due to effect of Ice formation w3= 0.0000 kg/m
4 Total weight of sub-conductor per phase = Wc = W1+WSP/(r*SSP)+w3 = 3.1452 Kg/m
5 Wind Load on conductor as per IS 802 & IS 5613 = Pcc = 5.9401 Kg/m
Vb =
Risk Coefficient as per Table 2 of IS: 802, Part 1, Sec 1For all Zones & for Reliability level 1(Voltage level upto 400kV) = K1 =
K2 = Factor to convert 3 second peak gust speed into average speed of wind during 10 minutes period = K0 =
Meteorological reference wind speed = Vb/K0 VR = Design wind speed = VR x K1 x K2 Vd =
Design Wind Pressure =0.6 x Vd 2 /g kgf/m2
cm2
Kg/cm2
/ oCoC oC oC
WiT=
Tension per SUB-CONDUCTOR under max. wind and min. temp. conditions = Cdc =
Thice=Effective dia of the conductor considering ICE effect = d+2*Thice
Pc * (d/100) * Cdc * Gc =
Annexure-2
Page 15 of 29
CASE – 1.
6 Clear span of conductor = L = la-(2*li)-lt-Bw = 89.3000 m
7 2.1371Loading factor during no wind condition = Q2 = 1.0000
8 SAG CALCULATIONS DUE TO CONDUCTOR
8.1f1 = Ten1/A = 125.8071
0.3957
3.1640E+07
-10192.9819
To solve the following equation:The working stress F at tempature t1+t3, is given by the cubic equation
940491268.11
we get f2 = 304.3152
8.2 Tension in conductor at maximum temperature and no windcondition = Ten2 = f2*A = 2418.9041 Kg
Max sag due to conductor = Wc*L² / (8*Ten2) Sc= 1.2961
9 SAG DUE TO INSULATOR
From Fig 1, we get
Tension per insulator string = Ten2* r / Ni Teni1= 1209.4521
Weight of conductor per String Insulator = Wc*r/Ni Wci= 1.57264.6021 m
U2 = √((li/2)² + (di/2)²) = 2.3043 m
0.0304
0.0608
Taking moments at 'P'
Teni1 * U1 *Sin(φ + δ) = (Wci * L/2) * U1 * Cos(φ + δ) + Wi * U2 *Cos(φ + β)
Simplifying :
TP1 = (Wci*L/2) * U1 * Cos δ + Wi*U2*Cos β - Teni1*U1*Sin δ = 760.8692
TP2 = Teni1*U1*Cos δ + Wci*(L/2)*U1*Sin δ + Wi*U2*Sin β = 5610.2697
0.1348
Sag due to Insulator = Si = U1*Sin(φ + d) = 0.7569 m
Loading factor during max wind condition = Q1= √(1+(Pcc/Wc)2) =
Under minimum temperature and maximum wind condition condition, the sub-conductor experiences a stress of f1
Kg/cm2
Weight of sub conductor per m per cm2 = S = Wc/A =
GB = (S * L * Q2)2 * ey/24 =
F = f1 - GB * (Q1/(f1*Q2))2 - a * ey * (t1+t3-t2) =
f22 * (f2 - F) - GB =
Kg/cm2
U1 = √(li2 + (di/2)2) =
δ = Tan-1 [(di/2)/li] =
β = Tan-1 [di/li] =
φ = Tan-1(TP1/TP2) =
Annexure-2
Page 16 of 29
CASE – 1.
10 Total maximum sag of moose conductor = Sc+Si = Stot = 2.0530 m
11 Height of conductor above ground 15.3000 m
Height of jack bus/equipment below conductor 8.3000 mMinimum Phase to phase clearance = 4.0000 mTotal maximum sag of moose conductor = Sc+Si = Stot = 2.0530 m
0.9470 m
SWING CALCULATIONS
1 SAG DUE TO CONDUCTOR (under maximum temperature rise in temperature and maximum wind conditions):
1.4450E+08
-1.0193E+04
To solve the following equation:1.11E+10
we get f21 = 1002.7182
Tension in conductor at maximum temperature and maximum windcondition = Ten21 = f21*A= 7970.2854 Kg
0.3934 m
2 SAG DUE TO INSULATOR
From Fig 1, we get
Teni2 = Ten21*r/Ni 3985.1427
U1 = √(li2 + (di/2)2) = 4.6021 m
U2 = √((li/2)2 + (di/2)2) = 2.3043 m
0.0304
0.0608
Taking moments at 'P'
TenI2 * U1 * Sin(φ + δ) = (WcI*L/2) * U1 * Cos(φ+ δ) + Wi * U2 *Cos(φ+ β)
Simplifying :
TP1 = (WcI*L/2) * U1 * Cos δ + Wi*U2*Cos β - TenI2*U1*Sin δ = 372.2725
TP2 = TenI2*U1*Cos δ + Wc*(L/2)*U1*Sin δ + Wi*U2*Sin β = 18378.4466
0.0203
SAG due to Insulator = Si1 = U1*Sin(φ + δ) = 0.2331
Therefore, available margin excluding sub-conductor spacing =
SGB = (Q1 * S *L)2 * ey/24 =
SF = (f1-SGB/f12) - a*ey*(t1+t3-t2) =
f212 * (f21 - SF) - SGB =
Kg/cm2
SAG due to conductor = Sc1 = Wc*L2/(8*Ten21) =
δ = Tan-1 [(di/2)/li] =
β = Tan-1 [di/li] =
φ = Tan-1(TP1/TP2) =
Annexure-2
Page 17 of 29
CASE – 1.
3 SWING DUE TO CONDUCTOR (SWC)
Wind load acting on span = Pcc * L*r = 1060.9103 KgWeight of conductor = Wc * L *r= 561.7260 Kg
From Fig 3:Tan Y1 = (r*Pcc * L/r*Wc * L) = 1.8887
1.0838
SWC = Sc1* Sin Y1 = 0.3476 m
4 SWING DUE TO INSULATOR (SWI)
100.1105 kg
1.5708
SWI = Si1 * Sin Y2 = 0.2331 m
5 Total Swing = Swtot = SWC + SWI = 0.5808
6 Phase to phase spacing provided between phases = 7.0000 mSubconductor spacing = 0.4500 mMinimum Phase to phase clearance = 4.0000 mPhase to phase spacing required = 5.0308 mTherefore, available margin = 1.9692 m
Y1 = Tan-1 (Pcc/Wc) =
Wind load on insulator = Wpi = (Pc/2)*di*li *Gc*Cdc=
Y2 = Tan-1 (Ni*Wpi/Ni*Wi) =
CASE - 2 ANNEXURE - 2
Page 18 of 29
CASE 2.
SAG TENSION CHART
NAME OF PROJECT:
GENERAL DATA
CONDUCTOR TYPE: TARANTULLA
NAME OF BAY: 0.35
SPAN LENGTH (Centre Lime distance between beams): 100.00 m
MINIMUM STRINGING TEMPERATURE: 10.00 Deg C
TEMPERATURE RANGE FOR DRAWING STRINGING CHART:
MINIMUM: 0.00 °C MAXIMUM: 50.00 °C
WIND PRESSURE ON CONDUCTOR PER M RUN: 0.00 kg/m
CONDUCTOR DATA
OVERALL DIA OF THE CONDUCTOR: 3.660 cm
CROSS SECTIONAL AREA OF CONDUCTOR: 7.949 cm²
WEIGHT OF CONDUCTOR PER METER: 2.910 kgf/m
COEFFICIENT OF LINEAR EXPANSION: 0.00002300 per °C
NO. OF CONDUCTORS PER PHASE: 2
TENSION PER CONDUCTOR UNDER MIN TEMP & MAX WIND CONDITION: 1000.00 kg
MODULUS OF ELASTICITY: 608200.00 kg/cm2
INSULATOR AND TURNBUCKLE DATA
NUMBER OF INSULATOR STRING(S): 4.00
LENGTH OF INSULATOR: 4.600 m
DIAMETER OF INSULATOR: 0.280 m
WEIGHT OF INSULATOR: 264.000 kg
CASE - 2 ANNEXURE - 2
Page 19 of 29
RESULTS
MAXIMUM CLEAR SPAN OF CONDUCTOR: 89.30 m
S.NO. TEMPERATURE TOTAL SAG
1 42 587.17 3.8 1.68 5.48
2 12 624.61 3.57 1.59 5.163 14 621.89 3.59 1.6 5.194 16 619.21 3.6 1.61 5.215 18 616.56 3.62 1.61 5.236 20 613.94 3.63 1.62 5.257 22 611.36 3.65 1.62 5.278 24 608.81 3.66 1.63 5.299 26 606.28 3.68 1.64 5.31
10 28 603.79 3.69 1.64 5.3311 30 601.33 3.71 1.65 5.3612 32 598.9 3.72 1.65 5.3813 34 596.5 3.74 1.66 5.414 36 594.13 3.75 1.66 5.4215 38 591.78 3.77 1.67 5.4416 40 589.46 3.78 1.68 5.46
TENSION PER CONDUCTOR
CONDUCTOR SAG
INSLULATOR SAG
Type Al Strand Steel StrandsAl Strand DiaSt strand di Cross sec. Diameter Weight
sq.m m kg/kmBEAR ACSR 30 7 3.350E-03 3.350E-03 3.2612E-04 2.3450E-02 1.229 7.870E+05 8.02E+10 1 0.1093 0.00001843BEAVER ACSR 6 1 3.990E-03 3.990E-03 8.7525E-05 1.1970E-02 0.303 8.090E+05 8.25E+10 1 0.3825 0.00001931BUX ACSR 30 7 4.500E-03 4.500E-03 5.8846E-04 3.1500E-02 2.196 7.870E+05 8.02E+10 1 0.0569 0.00001843CAT ACSR 6 1 4.500E-03 4.500E-03 1.1133E-04 1.3500E-02 0.385 7.350E+05 7.49E+10 1 0.3007 0.00001931COYOTO ACSR 26 7 2.540E-03 1.900E-03 1.5159E-04 1.5860E-02 0.521 7.870E+05 8.02E+10 1 0.3035 0.00001954DEER ACSR 30 7 4.270E-03 4.270E-03 5.2984E-04 2.9890E-02 1.977 7.870E+05 8.02E+10 1 0.0673 0.00001843DOG ACSR 6 7 4.720E-03 1.570E-03 1.1854E-04 1.4150E-02 0.394 7.350E+05 7.49E+10 1 0.2733 0.00001992FERRET ACSR 6 1 3.000E-03 3.000E-03 4.9480E-05 9.0000E-03 0.171 8.090E+05 8.25E+10 1 0.6766 0.00001931FOX ACSR 6 1 2.790E-03 2.790E-03 4.2795E-05 8.3700E-03 0.1489 8.090E+05 8.25E+10 1 0.7822 0.00001931GOAT ACSR 30 7 3.710E-03 3.710E-03 3.9998E-04 2.5970E-02 1.492 7.870E+05 8.02E+10 1 0.0891 0.00001843GOPHER ACSR 6 1 2.360E-03 2.360E-03 3.0620E-05 7.0800E-03 0.106 8.090E+05 8.25E+10 1 1.0933 0.00001931GUINEA ACSR 12 7 2.920E-03 2.920E-03 1.2724E-04 1.4600E-02 0.59 1.055E+06 1.08E+11 1 0.2630 0.00001584LARK ACSR 30 7 2.920E-03 2.920E-03 2.4777E-04 2.0440E-02 0.922 7.870E+05 8.02E+10 1 0.1350 0.00001843LEOPARD ACSR 6 7 5.280E-03 1.760E-03 1.4840E-04 1.5840E-02 0.493 7.730E+05 7.88E+10 1 0.2184 0.00001954LION ACSR 30 7 3.180E-03 3.180E-03 2.9386E-04 2.2260E-02 1.097 7.870E+05 8.02E+10 1 0.1213 0.00001843LYNX ACSR 30 7 2.790E-03 2.790E-03 2.2620E-04 1.9530E-02 0.844 7.870E+05 8.02E+10 1 0.1576 0.00001843MINK ACSR 6 1 3.660E-03 3.660E-03 7.3646E-05 1.0980E-02 0.255 8.090E+05 8.25E+10 1 0.4546 0.00001931MOOSE ACSR 54 7 3.530E-03 3.530E-03 5.9699E-04 3.1770E-02 2.002 6.860E+05 6.99E+10 1 0.0547 0.00001991OTTER ACSR 6 1 4.220E-03 4.220E-03 9.7907E-05 1.2660E-02 0.339 8.090E+05 8.25E+10 1 0.3419 0.00001931PANTHER ACSR 30 7 3.000E-03 3.000E-03 2.6154E-04 2.1000E-02 0.976 7.870E+05 8.02E+10 1 0.1363 0.00001843RABBIT ACSR 6 1 3.350E-03 3.350E-03 6.1699E-05 1.0050E-02 0.214 8.090E+05 8.25E+10 1 0.5426 0.00001931RACCOON ACSR 6 1 4.090E-03 4.090E-03 9.1968E-05 1.2270E-02 0.318 8.090E+05 8.25E+10 1 0.3640 0.00001931SHEEP ACSR 30 7 3.990E-03 3.990E-03 4.6263E-04 2.7930E-02 1.726 7.870E+05 8.02E+10 1 0.0770 0.00001843SPARROW ACSR 6 1 2.670E-03 2.670E-03 3.9193E-05 8.0100E-03 0.135 8.090E+05 8.25E+10 1 0.8540 0.00001931SQUIRREL ACSR 6 1 2.110E-03 2.110E-03 2.4477E-05 6.3300E-03 0.085 8.090E+05 8.25E+10 1 1.3677 0.00001931TIGER ACSR 30 7 2.360E-03 2.360E-03 1.6185E-04 1.6520E-02 0.604 7.870E+05 8.02E+10 1 0.2202 0.00001843WEASSEL ACSR 6 1 2.590E-03 2.590E-03 3.6880E-05 7.7700E-03 0.128 8.090E+05 8.25E+10 1 0.9077 0.00001931WOLF ACSR 30 7 2.590E-03 2.590E-03 1.9494E-04 1.8130E-02 0.727 7.870E+05 8.02E+10 1 0.1828 0.00001843ZEBRA ACSR 54 7 3.180E-03 3.180E-03 4.8448E-04 2.8620E-02 1.623 6.860E+05 6.99E+10 1 0.0674 0.00001991ANT AAC 7 3.100E-03 5.2834E-05 9.3000E-03 0.144 6.187E+05 6.31E+10 1 0.5419 0.000023BLUE BOTTLE AAC 7 3.660E-03 7.3646E-05 1.0950E-02 0.201 6.187E+05 6.31E+10 1 0.3887 0.000023BUTTERFLY AAC 19 4.650E-03 3.2266E-04 2.3250E-02 0.886 6.082E+05 6.20E+10 1 0.0892 0.000023CATTER-PILLAR AAC 19 3.530E-03 1.8595E-04 1.0590E-02 0.511 6.187E+05 6.31E+10 1 0.1547 0.000023CHAFER AAC 19 3.780E-03 2.1322E-04 1.8900E-02 0.586 6.082E+05 6.20E+10 1 0.1349 0.000023CLEGG AAC 7 4.170E-03 9.5600E-05 1.2510E-02 0.261 6.187E+05 6.31E+10 1 0.2995 0.000023COCKROACH AAC 19 4.220E-03 2.6575E-04 2.1100E-02 0.73 6.082E+05 6.20E+10 1 0.1083 0.000023EARWIG AAC 7 3.780E-03 7.8555E-05 1.1340E-02 0.215 6.187E+05 6.31E+10 1 0.3644 0.000023FLY AAC 7 3.400E-03 6.3554E-05 1.0200E-02 0.174 6.187E+05 6.31E+10 1 0.4505 0.000023GRASS HOPPER AAC 7 3.910E-03 8.4051E-05 1.1730E-02 0.23 6.187E+05 6.31E+10 1 0.3406 0.000023IRIS AAC 7 2.480E-03 3.3814E-05 7.4400E-03 0.092 6.187E+05 6.31E+10 1 0.8467 0.000023LADY BIRD AAC 7 2.790E-03 4.2795E-05 8.3700E-03 0.117 6.187E+05 6.31E+10 1 0.669 0.000023LOCUST AAC 19 5.360E-03 4.2872E-04 2.6800E-02 1.176 6.082E+05 6.20E+10 1 0.0671 0.000023MAYBUG AAC 37 4.090E-03 4.8611E-04 2.8630E-02 1.343 5.976E+05 6.09E+10 1 0.0593 0.000023MOTH AAC 19 5.000E-03 3.7306E-04 2.5000E-02 1.025 6.082E+05 6.20E+10 1 0.0771 0.000023PANSY AAC 7 2.780E-03 4.2489E-05 8.3400E-03 0.116 6.187E+05 6.31E+10 1 0.6738 0.000023ROSE AAC 7 1.960E-03 2.1120E-05 5.8800E-03 0.058 6.187E+05 6.31E+10 1 1.3556 0.000023SCORPION AAC 37 4.270E-03 5.2984E-04 2.9890E-02 1.464 5.976E+05 6.09E+10 1 0.0544 0.000023SPIDER AAC 19 3.990E-03 2.3757E-04 1.9950E-02 0.652 6.082E+05 6.20E+10 1 0.1205 0.000023TARANTULLA AAC 37 5.230E-03 7.9487E-04 3.6600E-02 2.91 6.082E+05 6.20E+10 1 0.0363 0.000023WASP AAC 7 4.390E-03 1.0595E-04 1.3170E-02 0.29 6.187E+05 6.31E+10 1 0.2702 0.000023SHIELD WIRE 7/9 SW 7 3.660E-03 7.3646E-05 1.2180E-02 0.583 1933000 1.97E+11 1.2 0.000012SHIELD WIRE 7/8 SW 7 9.0500E-05 1.2180E-02 0.706 1933000 1.97E+11 1.2 0.000012
Young's Mod. Kg./Cm2
Young's Modulus (N/sq.m)
Drag Coefficien
t
DC Resistance
Coefficient of Linear Expansion
Kg./Cm2
BLANK SW
disc insulator x120 440 0.28 8.3 0.145xx
Creepage
Diameter of Disc
Weight of Disc
Length of Disc
SKIN EFFECT TABLE
Sl No. X K1 0.00 1.000002 0.10 1.000003 0.20 1.000014 0.30 1.000045 0.40 1.000136 0.50 1.000327 0.60 1.000678 0.70 1.001249 0.80 1.00212
10 0.90 1.0034011 1.00 1.0051912 1.10 1.0075813 1.20 1.0107114 1.30 1.0147015 1.40 1.0196916 1.50 1.0258217 1.60 1.0332318 1.70 1.0420519 1.80 1.0524020 1.90 1.0644021 2.00 1.0781622 2.10 1.0937523 2.20 1.1112624 2.30 1.1306925 2.40 1.1520726 2.50 1.1753827 2.60 1.2005628 2.70 1.2275329 2.80 1.2562030 2.90 1.2864431 3.00 1.3180932 3.10 1.3510233 3.20 1.3850434 3.30 1.4199935 3.40 1.4557036 3.50 1.4920237 3.60 1.5287938 3.70 1.5658739 3.80 1.6031440 3.90 1.64051
Source : Electrical Transmission & Distribution Reference book by Central Station Engineers of Westinghouse Electric CorporationSource : Bureau of Standards Bulletin No. 169 on pages 226-8Source : TNEB HANDBOOK
Source : Electrical Transmission & Distribution Reference book by Central Station Engineers of Westinghouse Electric Corporation
Doc. No. : YN1H300126-403, Rev. A
document.xls Page 24 of 29
n
f 50 Hz as
k 1.81 As per IEC-909 ds
k 1.81 as/ds
1/t 22.557720876 ds/as
t 0.0443307196
g 1.4990796579 Sqrt((as/ds)-1)
3.4103692621
21.417118966
2.2165359823 h
e st
e pi
4.276003
1.572075
A 0.0230400592sqrt[(1-2*ya/as)/2*ya/as]
B 0.6168024783
C 0.2851491873
D 0.3129163279
E 0.0409238672
F 0.2147150177
G 0
V2 1 - A + B - C*[( D + E)*F + G ]
1.5720982655
-0.00002
fTpi v3
2pfTpi
ft
v1 ya
v2 asv3
2*ya/as
asw
fh
Doc. No. : YN1H300126-403, Rev. A
document.xls Page 25 of 29
2
0.45
3.66E-02
12.295081967
0.0813333333
3.3608156699
0.2132866076
0.6291488471
7.31E-01
2.13E+00
9.50E-02
0.0959789734
0.4220219258
1.170275665
0.2878319318
0.3334549187
-6.49E-06
Annexure-2
Page 26 of 29
CASE –
CALCULATIONS FOR SAG AND SWING OF STRUNG CONDUCTOR
System Voltage V = 420 kV
1 Basic Wind Speed = 0.00 m/sAs per IS 802: 1995, basic wind speed is based on gust velocity averaged over a short time interval of 3s.
Wind Zone as per IS: 802, Part 1, Sec 1 1
1.07
Terrain Category 2Terrain roughness coeficient (For different Terrain Category) = 1.0000
1.3750
0.0000 m/s0.0000 m/s
Height of conductor above ground 15.3000 metreGust Response Factor for conductor Gc = 1.9837
2 Pc = 0.0000
Weight of individual spacer = WSP = 3.0000 kgfSeparation between two spacers = SSP = 6.0000 metreWeight of sub-conductor per metre= W1 = 2.9100 kgf/mNo. of subconductors - single/twin/tri/quad = r = 2Diameter of sub-conductor = d = 3.6600 cmCross Sectional Area of sub-conductor = A = 7.9487Modulus of Elasticity of sub-conductor = ey = 608200.0000Coefficient of Linear Expansion = a = 2.3000E-05Maximum Ambient Temperature at site = t1 = 40.0000Minimum Ambient Temperature at site = t2 = 0.0000Rise in temperature = t3 = 0.0000Distance between centre line of beams (for conductor span) = la = 100.0000 mDIameter of disc = di = 0.2800Nos. of Insulator Strings in one side of conductor span (Single /Double) Ni = 4Weight of complete string insulator including hardware 1056.0000Weight of single string insulator including hardware Wi= 264.0000Length of insulator string = li = 4.6000 mWidth of beam on which conductor is strung = Bw = 1.5000 m
Ten1= 1000.0000 KgDrag Coefficient 1.0000
3 Effect of Ice formation
Radial Thickness of ICE over the conductor 0.0000 cmD1= 3.6600 cm
Increase in Conducter weight due to effect of Ice formation w3= 0.0000 kg/m
4 Total weight of sub-conductor per phase = Wc = W1+WSP/(r*SSP)+w3 = 3.1452 Kg/m
5 Wind Load on conductor as per IS 802 & IS 5613 = Pcc = 0.0000 Kg/m
Vb =
Risk Coefficient as per Table 2 of IS: 802, Part 1, Sec 1For all Zones & for Reliability level 1(Voltage level upto 400kV) = K1 =
K2 = Factor to convert 3 second peak gust speed into average speed of wind during 10 minutes period = K0 =
Meteorological reference wind speed = Vb/K0 VR = Design wind speed = VR x K1 x K2 Vd =
Design Wind Pressure =0.6 x Vd 2 /g kgf/m2
cm2
Kg/cm2
/ oCoC oC oC
WiT=
Tension per SUB-CONDUCTOR under max. wind and min. temp. conditions = Cdc =
Thice=Effective dia of the conductor considering ICE effect = d+2*Thice
Pc * (d/100) * Cdc * Gc =
Annexure-2
Page 27 of 29
CASE –
6 Clear span of conductor = L = la-(2*li)-lt-Bw = 89.3000 m
7 1.0000Loading factor during no wind condition = Q2 = 1.0000
8 SAG CALCULATIONS DUE TO CONDUCTOR
8.1f1 = Ten1/A = 125.8071
0.3957
3.1640E+07
-2432.7896
To solve the following equation:The working stress F at tempature t1+t3, is given by the cubic equation
6319246.35
we get f2 = 121.8959
8.2 Tension in conductor at maximum temperature and no windcondition = Ten2 = f2*A = 968.9115 Kg
Max sag due to conductor = Wc*L² / (8*Ten2) Sc= 3.2357
9 SAG DUE TO INSULATOR
From Fig 1, we get
Tension per insulator string = Ten2* r / Ni Teni1= 484.4558
Weight of conductor per String Insulator = Wc*r/Ni Wci= 1.57264.6021 m
U2 = √((li/2)² + (di/2)²) = 2.3043 m
0.0304
0.0608
Taking moments at 'P'
Teni1 * U1 *Sin(φ + δ) = (Wci * L/2) * U1 * Cos(φ + δ) + Wi * U2 *Cos(φ + β)
Simplifying :
TP1 = (Wci*L/2) * U1 * Cos δ + Wi*U2*Cos β - Teni1*U1*Sin δ = 862.3686
TP2 = Teni1*U1*Cos δ + Wci*(L/2)*U1*Sin δ + Wi*U2*Sin β = 2275.2868
0.3623
Sag due to Insulator = Si = U1*Sin(φ + d) = 1.7612 m
10 Total maximum sag of moose conductor = Sc+Si = Stot = 4.9969 m
11 Height of conductor above ground 15.3000 m
Height of jack bus/equipment below conductor 8.3000 mMinimum Phase to phase clearance = 4.0000 mTotal maximum sag of moose conductor = Sc+Si = Stot = 4.9969 m
-1.9969 m
Loading factor during max wind condition = Q1= √(1+(Pcc/Wc)2) =
Under minimum temperature and maximum wind condition condition, the sub-conductor experiences a stress of f1
Kg/cm2
Weight of sub conductor per m per cm2 = S = Wc/A =
GB = (S * L * Q2)2 * ey/24 =
F = f1 - GB * (Q1/(f1*Q2))2 - a * ey * (t1+t3-t2) =
f22 * (f2 - F) - GB =
Kg/cm2
U1 = √(li2 + (di/2)2) =
δ = Tan-1 [(di/2)/li] =
β = Tan-1 [di/li] =
φ = Tan-1(TP1/TP2) =
Therefore, available margin excluding sub-conductor spacing =
Annexure-2
Page 28 of 29
CASE –
SWING CALCULATIONS
1 SAG DUE TO CONDUCTOR (under maximum temperature rise in temperature and maximum wind conditions):
3.1640E+07
###-2432.7896
To solve the following equation:93728283.38
we get f21 = 217.4941
Tension in conductor at maximum temperature and maximum windcondition = Ten21 = f21*A= 1728.7905 Kg
1.8135 m
2 SAG DUE TO INSULATOR
SGB = (Q1 * S *L)2 * ey/24 =
SF = (f1-SGB/f12) - a*ey*(t1+t3-t2) =
f212 * (f21 - SF) - SGB =
Kg/cm2
SAG due to conductor = Sc1 = Wc*L2/(8*Ten21) =
Annexure-2
Page 29 of 29
CASE – From Fig 1, we get
Teni2 = Ten21*r/Ni 864.3952
U1 = √(li2 + (di/2)2) = 4.6021 m
U2 = √((li/2)2 + (di/2)2) = 2.3043 m
0.0304
0.0608
Taking moments at 'P'
TenI2 * U1 * Sin(φ + δ) = (WcI*L/2) * U1 * Cos(φ+ δ) + Wi * U2 *Cos(φ+ β)
Simplifying :
TP1 = (WcI*L/2) * U1 * Cos δ + Wi*U2*Cos β - TenI2*U1*Sin δ = 809.1771
TP2 = TenI2*U1*Cos δ + Wc*(L/2)*U1*Sin δ + Wi*U2*Sin β = 4023.0083
0.1985
SAG due to Insulator = Si1 = U1*Sin(φ + δ) = 1.0443
3 SWING DUE TO CONDUCTOR (SWC)
Wind load acting on span = Pcc * L*r = 0.0000 KgWeight of conductor = Wc * L *r= 561.7260 Kg
From Fig 3:Tan Y1 = (r*Pcc * L/r*Wc * L) = 0.0000
0.0000
δ = Tan-1 [(di/2)/li] =
β = Tan-1 [di/li] =
φ = Tan-1(TP1/TP2) =
Y1 = Tan-1 (Pcc/Wc) =