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Dimensions
Section 12
Circuit breakers for direct
current applications (cont.)
24 V - 48 V direct current applications
Technical advice
Time constant L/R
When a short-circuit occurs across the terminals of a direct current circuit, the
current increases from the operating current (< In) to the short-circuit current Isc
during a time depending on the resistance
R
and the inductance
L
of the short-
circuited loop.
The equation that governs the current in this loop is:
U = Ri + Ldi/dt
.
A short-circuit current is established (neglecting In with respect to Isc)
by the equation:
i = Isc (1 - exp(-t/
τ
))
,
where
τ
= L/R
is the time constant used to establish the short-circuit.
In practice, after a time
t = 3
τ
the short-circuit is considered to be established,
because the value of exp(-3) = 0.05 is negligible compared to 1.
The lower the corresponding time constant (e.g. battery circuit), the faster a
short-circuit is established.
L/R Description
DC applications
2 ms
Very fast short-circuit
b
b
Photovoltaic applications
5 ms
Fast short-circuit established b
b
Resistive or slightly inductive circuits:
v
v
indicator light
v
v
trip units (MN, MX)
v
v
motor armatures
v
v
battery charger/uninterruptible power supply
(UPS)
b
b
Capacitive circuits: electronic controller
15 ms
Standardised value used in
standard IEC 60947-2
b
b
Inductive circuits:
v
v
electromagnetic coil
v
v
contactor coil
v
v
motor inductor
30 ms
Slower short-circuit
established
b
b
Highly inductive circuits:
v
v
electromagnetic coil
v
v
contactor coil
v
v
motor inductor
In general, the system time constant is calculated under worst case conditions,
across the terminals of the generator.
DB124245
DB124246
R L
Isc
95
63
40
τ
t
2
τ
3
τ
4
τ
% Isc
Isc