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Asymmetrical Starting Current
It is a commonly known fact that current lags voltage
by 90° when a voltage is applied to a purely inductive
load. As can be seen from Figure 1, if the AC voltage is
applied at a peak, the current will rise from 0 to its
peak, 90° later in time. It may also be seen that during
the time voltage completes a positive or negative half-
cycle, current has made the transition from one peak to
another.
Thus, as shown in Figure 2, if voltage is applied at a
zero crossing, current will make the transition from
minimum peak to maximum peak. Current of course,
cannot instantaneously be at its minimum value, it
must begin at zero.
Thus it rises from zero to a value that is equal to 2
times the peak value (2 × Imax).
Depending on when the voltage is applied, the RMS
current may vary by as much as 1.73 times.
=
+
2
2
I
DC
AC
RMSasymm
=
+
2
I
[( 2I
)
RMS asymm
RMS
=
+
2
2
I
(
2
I
)
I
RMS asymm
RMS
Figure 1
Figure 2
2
I
]
RMS
2
RMS
=
2
2
I
3
I
RMS asymm
RMS
= 3
I
I
RMS asymm
RMS
Where I rms is current when voltage is applied at a
maximum, or the symmetrical current.
A motor or a transformer is never a perfect inductor,
therefore, the value of 1.73 will never be reached. The
DC offset will die away as a function of the X/R ratio
(typically a few cycles). Figure 3 represents an exag-
geration of the three phase current of a motor starting.
When is this 'asymmetrical current' a concern?
When setting instantaneous relays, care must be taken
to ensure that the instantaneous element does not op-
erate during normal operating conditions such as a
motor start. Symptoms of an instantaneous element
that is set too sensitive are nuisance or intermittent
tripping of the relay during energizing of the system.
Furthermore, CTs do not react predictably when a DC
current is applied. The waveform that is shown in Fig-
ure 3 is not necessarily the waveform that each of three
phase CTs would output. If there is a residual connec-
tion for ground fault detection, that element could oper-
ate when asymmetrical currents are present.
APPENDIX E
Figure 3
E-1
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