The working
Data for the cable chosen for this example:
4-core, cross-sectional area 4mm
2
, distance
between conductors 3mm, length 30m.
Distance between conductors should be
obtained from the cable manufacturer.
To calculate X
cable
:
first determine cable inductance L in
Henries per metre (H/m) from:
L=10
-7
. 4 log
e
.
d
r
where d is the distance between the con-
ductors
and r is the radius of a conductor, from:
radius r =
√[(conductor cross-sectional area) ÷ π]
= 1.13mm
Dimensions must be in consistent units.
So, L = 10
-7
. 4 . log
e
3
H/m
1.13
=10
-7
. 3.905 H/m
To convert to Ω/m, multiply by 100π
∴ X
cable
= 100π (10
-7
. 3.905) Ω/m
= 1.23 . 10
-4
Ω/m
For a 30m cable,
X
cable
= 30 . 1.23 . 10
-4
Ω/m
= 0.0037 Ω
The calculated value of X
cable
is insignificant
in relation to the other values (in this example)
and could be ignored.
Calculation of motor %X
In the following expression:
%X =
[((X
2
. X
M
) / (X
2
+ X
M
)) + (X
1
+ X
cable
)]
x 100
V / (√3 . I)
Substitute the values for X
1
, X
2
, X
cable
,:
%X = 100 x
[(8.913 . 171.3) / (8.913 + 171.3)] + (8.161 + 0.0037)
415 / (√3 . 1.93)
= 13.4
Set Function 76 = 13.4
42
The data necessary for the calculations:
Motor rating plate data:
V = Rated voltage (Function 05) = 415V
I = Rated FLC of the motor = 1.93A
Manufacturer’s data for the equivalent cir-
cuit:
X
1
= Stator reactance = 8.161Ω
X
2
= Rotor reactance (referred to stator)
= 8.913Ω
X
M
= Magnetising reactance = 171.3Ω
NOTE It is essential to check that the data
provided by the manufacturer is for a star-
connected motor.
R
cable
R
1
X
1
X
2
X
M
X
cable
Motor Equivalent Circuit (one phase only)
R
1
= stator resistance, as used
to calculate %R, Function 75.
I
V
To calculate the value of
motor circuit reactance, %X
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