52
3
Selection and application
3-4 Wiring protection
Fig. 3-11 Temperature rise in PVC insulated conductors due to let-through I
2
t
1000
500
400
300
200
100
50
60
80
40
30
20
10
600
800
0.01
0.05 0.1
0.5
1
5
10
50
1
100
500 1000
5000 10000
100000
Let-through I
2
t (×10
6
A
2
s)
T
emper
ature r
ise (K)
Wire sizes (mm
2
)
1.5
2.5
4
6
10
16
25
35
50
70
95
120
150
185
240
300
400
500
630
3-4 Wiring protection
3-4-1 Description
Wiring must be protected against the heat generated by
overcurrents. When a circuit fault occurs, the overload or short-
circuit current flowing into the fault point generates heat in the
wire to raise the wire temperature. While the wire temperature
is below the allowable temperature of the wire, the protective
device must interrupt the overcurrent to protect the wire.
The allowable temperature of the wire depends on the material
of the wire insulation. The highest temperature that the
insulation can tolerate is designated the allowable temperature
of the wire.
Since the temperature rise in the wire associated with
heat can be translated into a current-time characteristic, a
comparison of this characteristic with the current interrupting
characteristic of circuit breakers will help determine the
amount of protection.
Protection in the overload region can be generally discussed
with reference to a current-time characteristic diagram (see
Fig. 3-3); protection in the short-circuit region is discussed
in numeric terms with no allowance made for heat radiation.
Either way, the basic idea is to interrupt the overcurrent before
the wire is heated above its allowable temperature.
3-4-2 Thermal characteristics of wire
The temperature rise of wires due to overcurrent depends on
the let-through current and the continuous current carrying
time. The relationship between the temperature rise and the
allowable current is classified in three modes: continuous,
short-time, and short-circuit.
The allowable temperature limits of PVC insulated wires
typically used in low-voltage circuits are prescribed to be 70°C
(continuous), 100°C (short-time), and 160°C (short-circuit),
respectively.
Since heat radiation is negligible at the time of a short circuit,
the short-circuit protection of the wiring can be determined by
comparing the maximum breaking I
2
t value of the protective
device and the allowable I
2
t value of the wire.
R
0
(1+
DT
) i
2
dt=JMCd
T
transforms as
S
2
k
2
i
2
dt=
×
1
D
1
+
T
d
T
, where
D
p
JC
G
k
2
=
and
S
2
k
2
i
2
t=∫i
2
dt=
∫
1
D
1
+
T
d
T
=
T
0
S
2
k
2
log
e
1
D
+
T
0
1
D
+
T
234+
T
234+
T
0
i
2
t=5.05 log
e
×10
4
×S
2
i
2
t≈1.4×10
4
S
2
Conductor temperature following a short circuit
k
2
S
2
T
1
=
1
D
1
D
+
T
0 e
i
2
t
−
The following equation holds based solely on temperature rise.
k
2
S
2
T
1
= 1
D
+
T
0
e
i
2
t
−1
where
R
0
: Conductor resistance (
:
/cm)
D
:
Temperature coefficient of the conductor resistor,
4.27
u
10
−3
(1/°C)
T
:
Conductor temperature due to short circuit, 160 (°C)
T
0
: Conductor temperature before short circuit, 70 (°C)
T
1
: Rise in conductor temperature (K)
J:
Mechanical equivalent of heat, 4.19 (J/cal)
M: Conductor mass, 8.93 (g/cm
3
)
C:
Specific heat of the conductor, 0.092 (J/cm
3
°C)
G
:
Specific gravity of the conductor, 8.93 (g/cm
3
)
p:
Specific resistance of the conductor, 1.6
u
10
−6
(
:
/cm)
S:
Conductor cross section (mm
2
)
I
2
t: Current squared time (A
2
s)
The equation above suggests that temperature rise in the
conductor (wire) is determined by the let-through I
2
t.
Fig. 3-11 shows this relationship, while Table 3-9 (a) shows
allowable I
2
t when there is a short circuit.