Understanding IEC60909
Terminology/definitions
Fig. 1
A fault current waveform illustrating AC as well as DC decay
Withstand current
= also referred to as making currents
Interrupting duties
= also referred to as breaking short-circuit duties.
AC Decrement
= a symmetrical short-circuit current that has a time-varying change from
peak to peak during the fault (i.e. the peak to peak distance varies with
time)
Near to generator
short-circuits
= fault currents which have an AC decrement
Far from generator
short-circuits
= fault currents exhibiting no AC decrement
I
= initial symmetrical short-circuit current at the fault location. If there was
k
no AC decay, then this current would be constant in that the peak-to-peak
values would not change with time. If there is only DC offset (or decay)
then the peak-to-peak distances remain the same but are not symmetrical
w.r.t. the horizontal axis. With only AC decay, the peak-to-peak distances
remain symmetrical w.r.t. the horizontal axis but they decrease with time to
a steady state value.
Ik
= steady state current. This is the conventional symmetrical fault current
when the AC and DC decrements have disappeared. For far from
generator faults, Ik = I k.
IDC
= DC Current. The exponentially decaying DC component of the fault
current waveform due to the inductance of the system. It is determined by
the point on the voltage waveform at which the fault occurs. Note this is
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not
a current that can be measured, rather it is calculated. It is a
mathematical
model of a decaying transient inherent in the fault current
waveform.
Ip
= Peak Current. This is the maximum peak of i(t) as illustrated in Fig. 1.
The theoretical maximum is 2 2 I k as already shown. It is the half-cycle
peak as expressed by equation 2.13.
Ib
= Breaking Current. A current duty intended for the rating of the current
interrupting device for when the contacts part. For far contributions,
breaking duty equals initial symmetrical current, I k. For near contributions
special multipliers need to be applied to account for the AC decrement. Ib
has no DC decrement but Ib(asym) considers both AC and DC decrement.
Ib is a symmetrical r.m.s. current 55ms (for example) down the line
from I k.
IDC
Ib2
Ib(asym)
2
(1)
2
Where IDC is the DC current calculated for the same t as Ib.
Summary
The short circuit current for an RL circuit in which the pre-load current can be ignored is :
i( t )
iac ( t )
2 V
sin(
Z
idc ( t )
t
t
) e T
) sin(
A.
(2)
Where,
2 V
sin(
Z
iac ( t )
Z
R
j
L
) A , idc ( t )
t
R2
X2
,
arctan
2 V
sin(
Z
L
R
arctan
) e
X
R
t
T
A,
and
= impedance angle
= initial phase displacement (or offset) angle of the source voltage, v(t)
The time constant, T, for the circuit is given by, T
L
R
X
R
2
X
s. For a threephase fault, L
f R
and R are the positive sequence inductance and resistance of the system. For an earthfault, L and R
are derived from ZTOT = RTOT + jXTOT = Z1 + Z2 + Z0 .
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The maximum possible offset occurs when
i( t )
2 V
sin(
Z
2 V
sin(
Z
= ±90°, i.e. i( t )
t 90 ) e
t
T
or
t
t
90 ) e T A.
The asymmetrical r.m.s. equivalent of the transient current, Ir.m.s., is given by
4
Ir.m.s. ( t )
I AC 1 2 e
X
f t
R
4
K t I AC A . Where K( t )
1 2 e
X
f t
R
. K is called the
asymmetry factor. The asymmetrical r.m.s. fault current varies from 3·IAC when t = 0 to IAC when t
is large where IAC = InitSymRMS. Note that the asymmetrical rms current does not form part of
IEC60909.
The peak current, Ip, as per IEC 60909 is given by Ip
both is when X/R approaches
giving ip(max)
2
2
Ik"
1.02 0.98 e
2 Ik " or ip(max)
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2
2 I AC .
3R
X
. The limit for