Cable ampacity calculations iec

F:Elementscable programscable ampacity calculation IEC.docx Page 1
1 SCOPE AND DEFINITIONS
The scope of the attached calculations is to determine the required cables sizes based on the
project standards and design criteria.
Design Criteria.
Following design criteria is used for the settings sheet.
Maximum Operating Conductor temperatures with Insulation:
1.1 Thermoplastic (PVC) = 75°C
1.2 Thermoset (XLPE or EPR) = 90°C
1.3 Cable Voltage Rating = 1 kV (Um = 1.2 kV)

2 CABLE AMPACITY
2.1 Conductor Ampacity Selection
The cable ampacities are based as follows;
PVC insulation, copper conductors –Conductor temperature: 70 °C, reference ambient
temperature: 30 °C
Current-carrying capacities in amperes
for installation methods–XLPE or EPR insulation, copper conductors –Conductor
temperature: 90 °C, reference ambient temperature: 30 °C
MM2
AIR
PVC
XLPE-)
3-1/C
(1.5-16MM2)
&
(25-400MM2)]
1-3/C
3-1/C
(1.5-16MM2)
&
(25-400MM2)]
1-3/C
2.5 25 25 32 32
4 34 34 42 42
6 43 43 54 54
10 60 60 75 75
16 80 80 100 100
25 110 101 135 127
35 137 126 169 158
50 167 153 207 192
70 216 196 268 246
95 264 238 328 298
120 308 276 383 346
150 356 319 444 399
185 409 364 510 456
240 485 430 607 538
300 561 497 703 621
400 600 600 823 823

Current-carrying capacities in amperes for methods of installation
PVC insulation, three loaded conductors/copper or aluminium –Conductor temperature: 70 °C, ambient
temperature: 30 °C in air, 20 °C in ground.
Current-carrying capacities in amperes for methods of installation
XLPE or EPR insulation, three loaded conductors/copper or aluminium – Conductor temperature: 90 °C,
ambient temperature: 30 °C in air, 20 °C in ground
MM2
DB
PVC- XLPE-
1-3/C-DB-COND
1-3/C -DB-
CABLE
1-3/C-DB-
COND
1-3/C -DB-
CABLE
2.5 24 24 28 30
4 30 33 36 39
6 38 41 44 49
10 50 54 58 65
16 64 70 75 84
25 82 92 96 107
35 98 110 115 129
50 116 130 135 153
70 143 162 167 188
95 169 193 197 226
120 192 220 223 257
150 217 246 251 287
185 243 278 281 324
240 280 320 324 375
300 316 359 365 419
400 400 400 400 500

2.2 Conductor Ampacity and Temperature de-rating factor (TDF)
Correction factor for ambient air temperatures other than 30 °C to be applied to the current-
carrying capacities for cables in the air.
AIR AMB TEMP
PVC-AIR-AMB-deg-C-10 1.22
PVC-AIR-AMB-deg-C-30 1
XLPE-AIR-AMB-deg-C-10 1.15
XLPE-AIR-AMB-deg-C-30 1

Correction factors for ambient ground temperatures other than 20 °C to be applied to the current-
carrying capacities for cables in ducts in the ground.
GR AMB TEMP
PVC-GR-AMB-deg-C-10 1.1
PVC-GR-AMB-deg-C-20 1
XLPE-GR-AMB-deg-C-10 1.07
XLPE-GR-AMB-deg-C-20 1

Correction factors for cables buried direct in the ground or in buried ducts for soil thermal
resistivities other than 2,5 K·m/W to be applied to the current-carrying capacities
soil thermal resistivity
Thermal Resistivity-K*m/W-1(DB) 1.5
Thermal Resistivity-K*m/W-1.5(DB) 1.25
Thermal Resistivity-K*m/W-2.5(DB) 1
Thermal Resistivity-K*m/W-1(DUCT) 1.18
Thermal Resistivity-K*m/W-1.5(DUCT) 1.1
Thermal Resistivity-K*m/W-2.5(DUCT) 1

Reduction factors for more than one circuit, cables laid directly in the ground –
Installation method – Single-core or multi-core cables.
DB-1/C OR 3/C
DB-Touching-Circuit-1 1
DB-Touching-Circuit-2 0.75
DB-One Dia apart-Circuit-1 1
DB-One Dia apart-Circuit-2 0.8
DB-0.125-m - apart-Circuit-1 1
DB-0.125-m - apart-Circuit-2 0.85

Reduction factors for group of more than one multi-core cable to be applied to reference current-
carrying capacities for multi-core cables in free air –
Reduction factors for group of more than one
multi-core cable
to be applied to reference current-carrying
capacities for multi-core cables in free air –
Ladder Tary-multi-layer-Circuit-1 1
Ladder Tary-multi-layer-Circuit-2 0.8
Ladder Tary-Single-layer-Circuit-1 1
Ladder Tary-Single-layer-Circuit-2 0.87

3 CABLE IMPEDANCE CALCULATIONS
3.1 Conductor Resistivity
The Resistivity is defined as the electrical resistance of a body of unit length, and
unit cross-sectional area or unit weight.
Volume Resistivity is commonly expressed in ohms for a theoretical conductor of
unit length and cross-sectional area, in inch-pound units in Ω ·cmil / ft and in
acceptable metric units in Ω·mm2/m. It may be calculated by the following equation:
 Where: = ρ = Volume resistivity, Ω·cmil / ft,
 A = cross-sectional area, cmil,
 L = gauge length, used to determine R, ft
 R = measured resistance.
 In Accordance with ASTM- B-193, Table 2
 Volume resistivity for Copper, Ω·cmil/ft or Ω·mm2/m = 10.371

A
L




R

3.2 Temperature Correction
The measurement is made at any other than a reference temperature; the
resistance may be corrected for moderate temperature differences to what it would
be at the reference temperature, as follows:
Where:
 Rt = resistance at reference temperature T2,
 R = resistance as measured at temperature T1,
 Alpha T = known or given temperature coefficient of
resistance
 of the specimen being measured at reference temperature T,
 T2 = reference temperature, and
 T1 = temperature at which measurement is made.
NOTE 1—The parameter AlphaT, in the above equation, varies with
conductivity and temperature. For copper of 100 % conductivity and a reference
temperature of 20°C, its value is 0.00393.
Rt R 1  T2 T1 

3.3 Resistance of stranded conductors Correction.
3.3.1 DC RESISTANCE @ 70 DEG C OR 90 DEG C
CALCULATE
CALCULATE
STRANDING
FACTOR
CALCULATE CALCULATE
Nominal
Cross
Section
Area
Nominal
CONDUCTOR
Diameter
Minimum
Number
of
Wires in
Conductor
Nominal
Stranded
CONDUCTOR
Diameter
Maximum
Resistance of
Conductor at
20 deg C
Annealed
Copper
Conductor Plain
Wires
Ώ / km
Resistance
at= t Deg C
temperature
IEC-60228-
Annex B
mm2
d=(4/pi*A)^.5
= mm
Circular
Cu
d x str-factor =
Mm
Rdc-t=
[1+0.00393
(t-20)]*
Rdc-20
Ώ/1000
meter =90
0.5 0.798 7 1.134 0.905 36 45.904
0.75 0.977 7 1.134 1.108 24.5 31.240
1 1.128 7 1.134 1.279 18.1 23.079
1.5 1.382 7 1.134 1.567 12.1 15.429
2.5 1.784 7 1.134 2.023 7.41 9.448
4 2.257 7 1.134 2.559 4.61 5.878
6 2.764 7 1.134 3.134 3.08 3.927
10 3.568 7 1.134 4.046 1.83 2.333
16 4.513 7 1.134 5.118 1.15 1.466
25 5.642 7 1.134 6.397 0.727 0.927
35 6.675 7 1.134 7.569 0.524 0.668
50 7.978 19 1.147 9.152 0.387 0.493
70 9.440 19 1.147 10.829 0.268 0.342
95 10.997 19 1.147 12.615 0.193 0.246
120 12.360 37 1.151 14.224 0.153 0.195
150 13.819 37 1.151 15.903 0.124 0.158
185 15.347 37 1.151 17.661 0.0991 0.126
240 17.480 37 1.151 20.115 0.0754 0.096
300 19.543 61 1.152 22.520 0.0601 0.077
400 22.566 61 1.152 26.004 0.047 0.060
500 25.230 61 1.152 29.073 0.0366 0.047
630 28.320 91 1.153 32.656 0.0283 0.036
800 31.913 91 1.153 36.800 0.0221 0.028
1000 35.680 91 1.153 41.143 0.0176 0.022

3.3.2 CALCULATE CABLE SPACING BASED ON INSULATION THICKNESS “PVC,
XLPE, EPR”.
Nominal
Cross
Section
Area
Nominal
Thickness
of PVC
Insulation
Nominal
Thickness
of XLPE
Insulation
Nominal
Thickness
of EPR
Insulation
fictitious
diameter
Dc of
single
core
PVC
cable
fictitious
diameter
Dc of
single
core
XLPE
cable
fictitious
diameter
Dc of
single
core
EPR
cable
Diameter
overlaid up
cores
Reduced
Neutral
Size
mm2
0.6/1
(1.2)
kV
mm
0.6/1
(1.2)
kV
mm
0.6/1
(1.2)
kV
mm
Dc=
dL+2 * ti
=mm
Dc=
dL+2 *
ti=mm
Dc=
dL+2 *
ti=mm Df=kDc=mm mm 2
0.5 0.6 0.7 1 2.105 2.305 2.905 1 0.5
0.75 0.6 0.7 1 2.308 2.508 3.108 1 0.75
1 0.6 0.7 1 2.479 2.679 3.279 1 1
1.5 0.6 0.7 1 2.767 2.967 3.567 1 1.5
2.5 0.6 0.7 1 3.223 3.423 4.023 1 2.5
4 1 0.7 1 4.559 3.959 4.559 1 4
6 1 0.7 1 5.134 4.534 5.134 1 6
10 1 0.7 1 6.046 5.446 6.046 1 10
16 1 0.7 1 7.118 6.518 7.118 1 16
25 1.2 0.9 1.2 8.797 8.197 8.797 1 16
35 1.2 0.9 1.2 9.969 9.369 9.969 1 16
50 1.4 1 1.4 11.952 11.152 11.952 1 25
70 1.4 1.1 1.4 13.629 13.029 13.629 1 35
95 1.6 1.1 1.6 15.815 14.815 15.815 1 50
120 1.6 1.2 1.6 17.424 16.624 17.424 1 70
150 1.8 1.4 1.8 19.503 18.703 19.503 1 95
185 2 1.6 2 21.661 20.861 21.661 1 95
240 2.2 1.7 2.2 24.515 23.515 24.515 1 120
300 2.4 1.8 2.4 27.320 26.120 27.320 1 150
400 2.6 2 2.6 31.204 30.004 31.204 1 240

XLPE, EPR”.
CALCULATE CALCULATE CALCULATE CALCULATE
Nominal
Cross
Section
Area
3-cond,
k=2.16
PVC
Reduced
Neutral Size
PVC
3-1/2-cond,
PVC
4-cond,
k=2.42
PVC
Df=kDc
Dc=
dL+2 * ti
Df=2.42 (3
Dc1+Dc2)/4 Df=kDc
mm2 3-cond-PVC mm-PVC
3-1/2-cond-
PVC 4-cond-PVC
0.5 4.55 1.00 4.42 5.58
0.75 4.99 1.00 4.79 6.07
1 5.36 1.00 5.11 6.48
1.5 5.98 1.00 5.63 7.18
2.5 6.96 1.00 6.45 8.28
4 9.85 1.00 8.88 9.58
6 11.09 1.00 9.92 10.97
10 13.06 1.00 11.58 13.18
16 15.37 1.00 13.52 15.77
25 19.00 1.00 16.57 19.84
35 21.53 1.00 18.70 22.67
50 25.82 1.20 22.42 26.99
70 29.44 1.20 25.46 31.53
95 34.16 1.40 29.55 35.85
120 37.64 1.40 32.47 40.23
150 42.13 1.60 36.37 45.26
185 46.79 1.60 40.28 50.48
240 52.95 1.60 45.46 56.91
300 59.01 1.80 50.67 63.21
400 67.40 2.20 57.97 72.61

XLPE, EPR”.
Nominal
Cross
Section
Area
3-cond,
k=2.16
XLPE
Reduced
Neutral Size
XLPE
3-1/2-cond,
XLPE
4-cond,
k=2.42
XLPE
Df=kDc
Dc=
dL+2 * ti
Df=2.42 (3
Dc1+Dc2)/4 Df=kDc
mm2
3-cond-
XLPE mm XLPE
3-1/2-cond-
XLPE
4-cond-
XLPE
0.5 4.98 2.10 5.46 5.58
0.75 5.42 2.31 5.95 6.07
1 5.79 2.48 6.36 6.48
1.5 6.41 2.77 7.06 7.18
2.5 7.39 3.22 8.16 8.28
4 8.55 4.56 9.94 9.58
6 9.79 5.13 11.33 10.97
10 11.76 6.05 13.54 13.18
16 14.08 7.12 16.14 15.77
25 17.71 7.12 19.18 19.84
35 20.24 7.12 21.31 22.67
50 24.09 8.80 25.56 26.99
70 28.14 9.97 29.68 31.53
95 32.00 11.95 34.12 35.85
120 35.91 13.63 38.42 40.23
150 40.40 15.81 43.51 45.26
185 45.06 15.81 47.43 50.48
240 50.79 17.42 53.22 56.91
300 56.42 19.50 59.21 63.21
400 64.81 24.52 69.29 72.61

XLPE, EPR”.
Nominal
Cross
Section
Area
3-cond,
k=2.16
EPR
Reduced
Neutral Size
EPR
3-1/2-cond,
EPR
4-cond, k=2.42
EPR
Df=kDc
Dc=
dL+2 * ti
Df=2.42 (3
Dc1+Dc2)/4 Df=kDc
mm2 3-cond-EPR mm EPR
3-1/2-cond-
EPR 4-cond-EPR
0.5 6.27 2.305 6.67 7.029
0.75 6.71 2.508 7.16 7.521
1 7.08 2.679 7.57 7.936
1.5 7.70 2.967 8.27 8.632
2.5 8.69 3.423 9.37 9.735
4 9.85 3.959 10.67 11.032
6 11.09 4.534 12.06 12.424
10 13.06 5.446 14.27 14.631
16 15.37 6.518 16.86 17.224
25 19.00 6.518 19.91 21.288
35 21.53 6.518 22.04 24.125
50 25.82 8.197 26.65 28.923
70 29.44 9.369 30.40 32.981
95 34.16 11.152 35.45 38.272
120 37.64 13.029 39.51 42.166
150 42.13 14.815 44.36 47.196
185 46.79 14.815 48.28 52.419
240 52.95 16.624 54.55 59.327
300 59.01 18.703 60.90 66.114
400 67.40 23.515 70.86 75.513

AC-RESISTANCE OF CONDUCTOR
Nominal
Cross
Section
Area R=R' (1+ys+yp)
ys=xs^4 / (192+0.8 . xs^4)
xs^2= 8.pi.f.(10^-7) ks /R'
ks=1
yp=xp^4*(dc/s)^2 0. 2.9/(192+xp^4)
xp^2=8.pi*f.10^-7 .lp /R'
kp=1
mm2 xs^2=
ys=xs^4 /
(192+0.8 .
xs^4)
xp^2=
yp=xp^4*(dc/s)^2.0.
2.9
/(192+xp^4)
R=R'
(1+ys+yp)
0.5 2.738E-06 6.510E-03 2.738E-06 2.091E-14 4.620E+01
0.75 4.023E-06 6.510E-03 4.023E-06 5.632E-14 3.144E+01
1 5.445E-06 6.510E-03 5.445E-06 1.192E-13 2.323E+01
1.5 8.145E-06 6.510E-03 8.145E-06 3.213E-13 1.553E+01
2.5 1.330E-05 6.510E-03 1.330E-05 1.053E-12 9.510E+00
4 2.138E-05 6.510E-03 2.138E-05 2.175E-12 5.916E+00
6 3.200E-05 6.510E-03 3.200E-05 5.762E-12 3.953E+00
10 5.385E-05 6.510E-03 5.385E-05 1.962E-11 2.349E+00
16 8.570E-05 6.510E-03 8.570E-05 5.734E-11 1.476E+00
25 1.356E-04 6.510E-03 1.356E-04 1.468E-10 9.330E-01
35 1.881E-04 6.510E-03 1.881E-04 3.080E-10 6.725E-01
50 2.547E-04 6.510E-03 2.547E-04 5.743E-10 4.967E-01
70 3.677E-04 6.510E-03 3.677E-04 1.289E-09 3.440E-01
95 5.106E-04 6.510E-03 5.106E-04 2.506E-09 2.477E-01
120 6.441E-04 6.510E-03 6.441E-04 4.176E-09 1.964E-01
150 7.948E-04 6.510E-03 7.948E-04 6.344E-09 1.591E-01
185 9.945E-04 6.510E-03 9.945E-04 9.930E-09 1.272E-01
240 1.307E-03 6.510E-03 1.307E-03 1.737E-08 9.677E-02
300 1.640E-03 6.510E-03 1.640E-03 2.760E-08 7.713E-02
400 2.097E-03 6.510E-03 2.097E-03 4.612E-08 6.032E-02

Inductance Inductance - Inductance -
Nominal
Cross
Section
Area
PVC
Insulated
L=K+0.2
Log e (2S
/d)
mH/km
PVC
Insulated
X=2pif*L
Ώ/km
XLPE
Insulated
L=K+0.2
Log e (2S
/d)
mH/km
XLPE
Insulated
X=2pif*L
Ώ/km
EPR
Insulated
L=K+0.2
Log e (2S /d)
mH/km
EPR
Insulated
X=2pif*L
Ώ/km
Typical Values for
Constant (K) for
different Stranded
Conductors (50 Hz)
n=3, K=0.0778
n=7, K=0.0642
n=19, K=0.0554
n=37, K=0.0528
n=61, K=0.0514
Typical Values for
Constant (K) for
different Stranded
Conductors (50 Hz)
n=3, K=0.0778
n=7, K=0.0642
n=19, K=0.0554
n=37, K=0.0528
n=61, K=0.0514
Typical Values for Constant
(K) for
different Stranded
Conductors (50 Hz)
n=3, K=0.0778
n=7, K=0.0642
n=19, K=0.0554
n=37, K=0.0528
n=61, K=0.0514mm2
0.5 0.2330703 0.0732212 0.2512262 0.078925 0.297502883 0.093463287
0.75 0.2109673 0.0662773 0.2275884 0.071499 0.270487529 0.084976163
1 0.1965267 0.0617407 0.2120421 0.066615 0.252455876 0.079311353
1.5 0.177925 0.0558968 0.1918829 0.0602818 0.228718644 0.071854081
2.5 0.1573508 0.0494332 0.1693922 0.0532161 0.201695389 0.063364475
4 0.1797057 0.0564562 0.1514817 0.0475894 0.179705662 0.056456199
6 0.1629193 0.0511826 0.1380623 0.0433736 0.162919334 0.051182618
10 0.1445377 0.0454079 0.1236337 0.0388407 0.144537705 0.045407859
16 0.1301779 0.0408966 0.1125648 0.0353633 0.130177935 0.040896604
25 0.1279172 0.0401864 0.1137885 0.0357477 0.12791723 0.040186383
35 0.1192845 0.0374743 0.1068696 0.0335741 0.119284456 0.037474317
50 0.1175864 0.0369409 0.1037302 0.0325878 0.108786415 0.03417626
70 0.1101962 0.0346192 0.1011915 0.0317902 0.10139625 0.031854571
95 0.109415 0.0343737 0.0963511 0.0302696 0.100614953 0.03160912
120 0.1047842 0.0329189 0.0953838 0.0299657 0.093384173 0.029337503
150 0.1050129 0.0329908 0.0966359 0.0303591 0.1050129 0.032990776
185 0.1050314 0.0329966 0.0975049 0.0306321 0.105031372 0.032996579
240 0.1037631 0.0325981 0.0954339 0.0299814 0.103763075 0.032598131
300 0.1028433 0.0323092 0.0938597 0.0294869 0.10284331 0.032309179
400 0.1006596 0.0316232 0.0928164 0.0291591 0.100659619 0.031623152

3.4 Conductor Reactance
D= Spacing between conductors
D= diameter of wire (2 x radius) + 2 x insulation thickness
r = Radius of conductors.
, the insulation thickness for multiconductor cables with outer coverings is as
follows,
XL 2  f L
L

8 
1 4 ln
D
r







 4  10
7

H
m


Nominal
Cross
Section
Area
Nominal
Thickness
of PVC
Insulation
Nominal
Thickness
of XLPE
Insulation
Nominal
Thickness
of EPR
Insulation
fictitious
diameter
Dc of
single
core
PVC
cable
fictitious
diameter
Dc of
single
core
XLPE
cable
fictitious
diameter
Dc of
single
core
EPR
cable
Dc=
dL+2 * ti
Dc=
dL+2 * ti
Dc=
dL+2 * ti
mm2
0.6/1
(1.2)
kV
mm
0.6/1
(1.2)
kV
mm
0.6/1
(1.2)
kV
mm mm mm mm
0.5 0.8 0.7 1 2.505 2.305 2.905
0.75 0.8 0.7 1 2.708 2.508 3.108
1 0.8 0.7 1 2.879 2.679 3.279
1.5 0.8 0.7 1 3.167 2.967 3.567
2.5 0.8 0.7 1 3.623 3.423 4.023
4 1 0.7 1 4.559 3.959 4.559
6 1 0.7 1 5.134 4.534 5.134
10 1 0.7 1 6.046 5.446 6.046
16 1 0.7 1 7.118 6.518 7.118
25 1.2 0.9 1.2 8.797 8.197 8.797
35 1.2 0.9 1.2 9.969 9.369 9.969
50 1.4 1 1.4 11.952 11.152 11.952
70 1.4 1.1 1.4 13.629 13.029 13.629
95 1.6 1.1 1.6 15.815 14.815 15.815
120 1.6 1.2 1.6 17.424 16.624 17.424
150 1.8 1.4 1.8 19.503 18.703 19.503
185 2 1.6 2 21.661 20.861 21.661
240 2.2 1.7 2.2 24.515 23.515 24.515
300 2.4 1.8 2.4 27.320 26.120 27.320
400 2.6 2 2.6 31.204 30.004 31.204
500 2.8 2.2 2.8 34.673 33.473 34.673
630 2.8 2.4 2.8 38.256 37.456 38.256
800 2.8 2.6 2.8 42.400 42.000 42.400
1000 3 2.8 3 47.143 46.743 47.143

4 CABLE VOLTAGE DROP CALCULATIONS.
Permissible Voltage Drop, with respect to Load Power Factor.
Volt drop can be defined as the difference in magnitude of the voltage at the supply
compared to the voltage at the load. This voltage drop is based on the loads power
factor, the cable's internal resistance and reactance, and the cable length.
The three phase voltage drop permitted on the circuit run is calculated using the
following equation.
Vd.3 I L R cos ( ) X sin ( )( 3
Where:
Vd3p = three phase voltage drop, volts (V)
ө = Power factor Angle
I = current flowing in cable, amperes (A)
L = route length of circuit, meters (m)
R = AC resistance of cable, ohm/kilometer (W/km)
X = reactance of cable, ohm/kilometer (W/km)

5 CABLE SIZING & CURRENT-CARRYING CAPACITY
CALCULATION STEPS
To calculate the current-carrying capacity requirements of a circuit:
STEP-1 Determine the current requirements, based on 1.25 times the FLA
continuous current, of the Loads.
STEP-2 Select the Cable Size based on the De-Rated Ampacity of the
Cable.
STEP-3 Calculate Length x Amp factor for each size of the cable based on
% voltage drop and the circuit power factor, as per the following formula.
STEP-4 Calculate the length of the selected cable based on the FLA of the
circuit.
STEP-4 If the calculated length L is < than the circuit length D, then
calculate Length x Amp FLA x D of the circuit.
STEP-5 Select the cable FLA x D with the matching Length x Amp L X I
factor.
STEP-6 Calculate Length x Amp factor for each size of the cable based on
% voltage drop and the circuit power factor, as per the above formula.
STEP-7 Calculate the Circuit Voltage drop for the length of the circuit.
STEP-8 if the voltage drop exceeds the design criteria then increases the
Cable size to meet the voltage drop.
STEP-9 SELECTS THE CALCULATED CABLE SIZE.
IL 
Vd3
R cos ( ) X sin ( )(
L
Vd3
R cos ( ) X sin ( )( )( I


Cable ampacity calculations iec

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Cable ampacity calculations iec