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Inrush Current Control in Transformers
1
Inrush Current Control in Transformers
Seshanna Panthala
Faculty of Engineering, Assumption University
Bangkok, Thailand
Abstract
The paper deals with the problem of magnetizing inrush current phenomenon in
transformers and describes the design of a robust time delay relay which can be used to
control the inrush current into transformers. Test results are presented on the
performance of the time delay relay to demonstrate the effectiveness of the relay in
reducing the switch on inrush current into a small laboratory transformer.
Keywords: Inrush current, time delay relay, bridge rectifier, current source, thermistor.
Introduction
When a transformer is switched on to
line, at times the circuit breaker trips or their
fuse blows. This happens even if the
transformer is on no load with its secondary
open. This is due to the heavy magnetizing
current drawn by the transformer. This current
may reach a level exceeding the full load
current. However, this heavy inrush current
magnitude depends on the instant on the a.c
wave at which the transformer is switched on.
If the instant happens to be such that the a.c
voltage wave is going through its peak value,
then there will be no inrush current drawn by
the transformer. The magnitude of the current
in this case will be at normal no load value. If
the instant happens to be such that the a.c wave
is going through its zero value, then the current
drawn will be very high leading to breaker
tripping. Hence to avoid inrush current, the
transformer is to be connected to the line when
the voltage is going through its peak. This
requires a point on wave switch (Panthala
1999) which makes the switching equipment
costly and is not adopted in practice. A
mechanical or electro-mechanical contactor is
used to connect the transformer to the line in
practice and there is no control on the instant of
switching. Inrush current does occur
occasionally leading to nuisance tripping of the
breaker. One simple way to reduce inrush
current is to insert a resistor in series with the
transformer at the beginning of switching and
then cut this resistor out after a short time to
allow normal operation. Another way is to use
NTC thermistor (AMETHERM 2001) in series
with primary. This NTC thermistor will offer
high resistance at the beginning of switching
and limit the inrush current. After a short time
thermistor resistance decreases to a low value
due to self heating and does not affect normal
operation. The NTC thermistor solution is
practicable for small transformers. In this paper
a time delay relay solution is presented which
will physically insert a resistor in the primary
circuit and then cut this resistor completely out
of the circuit automatically after a
predetermined time delay. First a brief theory is
presented to explain the reason for the inrush
current in transformers and then the time delay
relay circuit is described. Finally some test
results are presented.
Refer to Fig.1, the switch SW is closed at
time t =0. Neglecting the resistance of the
primary winding the equation for the primary
loop will be v = Nd /dt where v = V
m
sin (wt
+ ), d /dt = (V
m
/N ) sin (wt + ). Integrating
this equation we get = - m
cos (wt + ) + k.
The value of k is evaluated by applying the
initial condition that at t =0, = 0. The final
equation for the flux in the core is given by
= m

{
cos - cos (wt + )
}
where m
= V
m
/wN. It should be noted that this is a simplified
analysis. In a real case when resistance is taken
into account m
cos term dies down 2
Switching Behavior of Transformer
Fig. 1. Excitation circuit of transformer with secondary open
exponentially leaving the sinusoidally varying
term. Two extreme cases of flux variation can
be seen from the above equation depending on
the instant of switching.
Case1:
= 0, this means that the switch SW is
closed when the a.c voltage wave is passing
through its zero value. The core flux reaches a
maximum value of 2 m
. Under normal
operating condition the core flux is m
and the
core of the transformer is operating at the knee
of the B-H curve. In order to produce 2 m
the
current required will be extremely high because
of the non linear nature of the B-H curve and
drives the core material into saturation. This
results in heavy inrush current into the
transformer (Fig. 5).
Case2:
= 90
o
, this means that the switch SW
is closed when the a.c voltage wave is going
through its peak value. The core flux reaches a
maximum value of m
which is its normal
value and the current drawn will be normal no
load value. So, in order to avoid inrush current
the switch is to be closed when the voltage
wave is going through its peak value for which
point on wave switching system is required as
mentioned earlier.
Since the actual instant of closing the
switch can be any instant, inrush current will
occur at times and circuit breaker may trip. To
make sure that the switching is safe and secure
a time delay circuit is used to limit the inrush
current. The details of the proposed TDR is
given in the latter section.
Time Delay Relay Circuit
Refer to Fig. 2 wherein the time delay
relay circuit and its connection to a load such
as a transformer is shown. As soon as the
transformer is switched on the TDR comes into
action. The series resistor R limits the initial
current drawn by the transformer. After a
predetermined time the relay cuts out the
resistor R by short circuiting it through its NO
contact - thus allowing the normal transformer
operation. The design and working of the TDR
is as described below:
The steady state d.c current requirement
of the relay coil will decide the design of the
other components of the circuit. The capacitor
C
2
is to be chosen such that the average value
of the rectified current I
av
is equal to the current
required by the relay coil and the resistance of
the coil should be small compared to the
capacitive reactance of the capacitor C
2
at line
frequency. Under these conditions the average
rectified current is approximately equal to I
av
=
(V. .C
2
)/1.11 where V = rms value of the line
voltage (220V), = 2 f, f = line frequency
(=50Hz ) and C
2
=required capacitor value.
Knowing the relay current, it is now possible to
select the required capacitor and the bridge
diodes. The capacitor C
1
is to be selected from
the delay time required. The voltage across C
1
rises exponentially with a time constant =
C
1
.R
L
as shown in Fig. 3. Knowing the relay
pick up voltage and its coil resistance it is now
possible to choose the required value for C
1
. As
far as the working of the circuit is concerned it 3
Fig. 2. Time delay relay and load circuit connection
is easy to see that when the main switch is closed
the load drawing inrush current and the time
delay relay circuit are energized simultaneously.
The capacitor/relay combination is driven by a
constant average current source and the d.c
voltage rises exponentially. When this voltage
reaches the pick up voltage of the relay, its
normally open contact connected across the
series resistor R closes and thus removing it from
the load circuit. When the main switch is opened
the voltage across the relay coil will fall again
exponentially. When this voltage reaches the
drop out voltage of the relay, the contact opens
and the resistor is again in series with the load
and ready for next switching operation. The pick
up voltage of the 12volt relay used in the testing
is about 6volts and the contact closure time is
found to be 330ms as marked in fig.3.The drop
out voltage of this relay is about 4.5 volts and the
contact opening time is about 500ms (Fig. 4).
The important design considerations are:
(a) the normal operating voltage of the relay
has to be small ( 10% ) as compared to the
amplitude of the a.c supply voltage, (b) the
average current through the relay coil is
decided by the capacitor C
2
(see the equation
in the text), and (c) the relay contact rating
must be sufficient to meet the full load
current requirement of the transformer. If
very high load current is to be carried then a
bigger contactor is to be used which can
easily be operated with a smaller relay as
used in the testing. The bridge rectifier
output is like a constant current source. In
case the relay coil gets open circuited, then
the out voltage will rise as the capacitor C
1
will be charged with this constant average
current I
av
. Hence a zener diode of adequate
rating to carry I
av
continuously is connected
across the capacitor-relay combination to
limit the voltage rise to say 15 volts in this
design. The 50 resistor is used to limit the
switch on surge current into the TDR circuit
itself. 4
Test Results
The test results are presented in two parts:
(a) The TDR is tested for its pick up and drop
out performance as shown in the recordings in
Figs. 3 and 4. It was found that the pick up
voltage is 6 V and took 330 ms to close the NO
contact. This is the time duration in which the
series resistor is in the circuit. The drop out
voltage was 4.5 V and took 500 ms to open the
contact to insert the resistance R in the circuit
again. (b) The rec