Functions
and characteristics
Calculation of DC distributionsystem characteristics
Short-circuit currents
L/R time constant
DB105060
Short-circuit currents
Calculation of the short-circuit current across the terminals of
a battery
During a short-circuit, the battery discharges a current equal to
b Vb = maximum discharge voltage (battery 100 % charged)
b Ri = internal resistance equivalent to all cells (a function of the capacity in amperehours).
Example
b consider a set of four 500 Ah batteries connected in parallel
b discharge voltage of one battery: 240 V (110 cells 2.2 V each)
b discharge current of one battery: 300 A with a run-time of 30 minutes
b discharge current of all four batteries: 1200 A with a run-time of 30 minutes
b internal resistance 0.5 mW per cell, i.e. for one battery:
Ri = 110 x 0.5 x 10-3 = 55 x 10-3 W
b short-circuit current of one battery: Isc = 240 V / 55 x 10-3 W = 4.37 kA
b neglecting the resistance of the connections, for all four batteries discharging the
short-circuit current in parallel, the total short-circuit current is four times that of one
battery, i.e. Isc = 4 x 4.37 kA = 17.5 kA.
Note: if the internal resistance is not known, it is possible to use the following rough
approximation: Isc = kc where c is the capacity of the battery in ampere-hours and k is a
coefficient close to 10 and always less than 20.
Other typical examples
b PABXs: Isc from 5 to 25 kA at 240 V DC with L/R = 5 ms
b submarine: Isc from 40 to 60 kA at 400 V DC with L/R = 5 ms.
DB105056
DB105059
L/R time constant
When a short-circuit occurs across the terminals of a DC circuit, the current rises
from the load current (y In) to the short-circuit current Isc over a period of time that
depends on the value of the resistance R and inductance L of the short-circuited
loop.
The equation determining the current in the loop is:
u = Ri + L di/dt
The curve of I versus time is defined (neglecting In) by the equation:
i = Isc (1 - exp(t/t))
where t = L/R is the time constant for the rise to Isc.
Practically speaking, after a time t = 3t, the short-circuit is considered to be
established, because the value of exp(-3) = 0.05 is neglig ble compared to 1 (see the
curve opposite).
The lower the time constant (e.g. battery circuit), the shorter the time required for the
current to rise to Isc.
To express breaking capacity, the interrupted short-circuit current with the following
time constants is used:
b L/R = 5 ms, fast short-circuit
b L/R = 15 ms, standardised value used in standard IEC 60947-2
b L/R = 30 ms, slow short-circuit.
In general, the value of the system time constant is calculated under worst-case
conditions, across the terminals of the generator.
Breaking-capacity values for:
b Compact NS (table page A-17) are the same for 5 ms and 15 ms
b Masterpact NW (table page A-19) are indicated for 3 values, 5 ms, 15 ms and 30 ms.
A-7