IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
943
A Sequential Phase Energization Technique
for Transformer Inrush Current Reduction—
Part I: Simulation and Experimental Results
Yu Cui, Sami G. Abdulsalam, Student Member, IEEE, Shiuming Chen, Senior Member, IEEE, and
Wilsun Xu, Senior Member, IEEE
Abstract—This paper presents a new, simple and low cost
method to reduce inrush currents caused by transformer energization. The method uses a grounding resistor connected
at a transformer neutral point. By energizing each phase of
the transformer in sequence, the neutral resistor behaves as a
series-inserted resistor and thereby significantly reduces the energization inrush currents. The proposed method has been tested
by computer simulation and laboratory experiments. Both results
show that the method has a performance similar to that of the
resistor pre-insertion scheme. The proposed method is much less
expensive, however, since there is only one resistor involved and
the resistor carries only a small neutral current in steady-state.
Index Terms—Inrush current, power quality, transformer.
I. INTRODUCTION
I
NRUSH currents from transformer and reactor energization
have always been a concern in power industry. Over the past
several decades, a few methods have been proposed to limit the
inrush currents. Representative examples are the synchronous
closing of circuit breakers and the pre-insertion of series resistors [1]–[4].
Two recent developments in power industry have re-ignited
interests in finding better methods for controlling inrush currents. One of them is the deregulation of electricity market.
More and more independent power producers and co-generators are taking advantage of the situation. Their proposed generators often need to have the generator transformers energized
from the system side due to cost considerations. This results
in the problem of large inrush currents being injected into the
supply system. Another development is the increased awareness
on power quality. The power quality consequences of inrush
currents can be quite detrimental. Examples are motor tripping,
relay misoperation and so on. There is still a need to find simpler
and low cost schemes to limit the inrush currents. Independent
power producers are especially interested in such techniques.
The idea presented in this paper was conceived when we were
solving inrush current problems encountered by two co-generator plants in Canada. In view of the fact that the inrush currents are always unbalanced among three phases, a neutral re-
Manuscript received May 20, 2003; revised October 18, 2003. This work was
supported by the Alberta Energy Research Institute. Paper no. TPWRD-002402003.
The authors are with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail:
wxu@ece.ualberta.ca).
Digital Object Identifier 10.1109/TPWRD.2004.843467
Fig. 1. Proposed scheme: sequential phase energization aided with a
grounding resistor.
sistor could provide some damping to the currents. This is the
basis of the proposed idea. The idea is further improved by introducing delayed energization of each phase of the transformer.
This improvement has made the proposed scheme almost as effective as the pre-insertion resistor scheme. The performance
and characteristics of the proposed method have been investigated using simulations and experiments. Very encouraging results have been observed. This paper explains the proposed idea
and presents its performance characteristics. The results are obtained from simulation and experimental studies.
II. PROPOSED SCHEME
The basic mechanism of inrush current generation from transformer energization has been well documented in [5]. It is well
known that the inrush currents are highly unbalanced among
three phases. If a transformer is Y grounded at the energization side, its neutral current will also contain the inrush current.
One may, therefore, speculate that if a resistor is inserted into
the transformer neutral, it may reduce the magnitude of the inrush current in a way similar to that of the series-inserted resistor. This consideration formed the basic idea of the proposed
scheme, which is shown in Fig. 1. The bypass breaker may not
be needed or can have a low rating as the neutral current is close
to zero in normal system operation.
Unfortunately, a simple implementation of the above scheme,
simultaneous closing of all three-phase breakers, did not produce sufficient reductions on the inrush currents. This agrees
with the conclusion drawn in [6], [7]. We reasoned, however,
that if one closes each phase of the breaker in sequence with
some delays between them, the neutral resistance could behave
as a series resistor and improve the results. This simple improvement has proven to be very effective. In fact, the idea of
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
sequential energization of three-phase equipment can lead to a
new class of techniques to reduce switching transients. In the
subsequent sections, simulation and experimental study results
are presented to demonstrate the characteristics of the proposed
method. Main studies were conducted on a 30 kVA, 120/208 V,
three-phase three-limb laboratory transformer with grounded Y
primary and delta secondary.
III. SIMULATION RESULTS
The proposed scheme was first investigated using computer
simulations. Initially, we used PSCAD/EMTDC to evaluate the
proposed scheme. Unfortunately, the program produced erroneous results. Some of the simulation results presented in [8]
are therefore not quite correct. Further investigations revealed
that the program could not simulate transformers with neutral
impedances correctly, though it has that feature. Such transformer configuration is known to cause simulation difficulties
for the EMTP programs [9]. As a result, we had to develop a
dedicated simulation program for this project. The transformer
model adopted in this study was published in [10]. It is an equivalent electric and magnetic circuit model. The program was further enhanced with the capability of scanning through all possible voltage phase angles and outputting the maximum inrush
current. Details about the simulation model and model parameters are shown in the Appendix.
A. Sample Simulation Results
Three sets of simulations were conducted. The first set involves the closing of the first phase. The second set simulates
the closing of the 2nd phase after the first phase has reached
steady state. The third set is the energization of the 3rd phase
after the second phase switching has reached steady state. Typical inrush current waveforms are shown in Fig. 2 for the case
of
while different phase is energized. Examination
of extensive simulation results revealed the following.
• The inrush current occurs in all phases that are electrically
energized. For example, all three phases experience inrush
currents when the 3rd phase is switched in. The highest
inrush current does not necessarily occur in the switched
phase.
• It takes about 5 to 10 cycles for the inrush current to reach
steady state. As a result, there is no need to wait for a long
time to energize the next phase. In other words, the proposed scheme can be implemented by closing each phase
with 5 to 10 cycle delays.
• The instants of energization have an impact on the magnitude of the inrush current. However, the inrush currents
are small when the neutral resistance is in certain range
(see next section). There is no need to control the instant
of switching closing.
B. Impact of Neutral Resistance on Current Magnitude
The most important parameter for the proposed scheme is
the value of the neutral resistor. For this purpose, the maximum
inrush current as a function of the neutral resistance is investigated. In this study, the voltage phase angles at the breaker
Fig. 2. Typical inrush current waveforms for the case of R
different phase is energized.
= 2 5 when
:
closing instants are scanned through all possible values to obtain the maximum inrush current. The results for the three sequential switching scenarios are shown in Fig. 3.
It can be seen that a large resistance value yields more reduction on the inrush current for the first phase switching. This is
understandable since the resistor serves as a series resistor in
the energization circuit. For the second phase switching, a large
neutral resistance will cause more second phase inrush current
to flow through the first phase. As a result, less inrush current
flows into the neutral resistor, leading to reduced mitigation impact of the resistor. This phenomenon is shown in Fig. 4. In the
, the scheme is equivalent to enerextreme case of
gizing two series-connected transformer cores with a line-toline voltage. A large inrush current is expected. This explains the
checkmark-shaped characteristics of the second curve. For the
third phase switching, the inrush current increases with the neutral resistor. So it is not desirable to have the resistor in the circuit when the 3rd phase is energized. Further analysis of the phenomenon reveals that once the 3rd phase is energized, the neutral
current reduces to zero almost instantaneously. Therefore, the
resistor has no direct impact on reducing the inrush current. This
CUI et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION—PART I
Fig. 5.
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Flux pattern for the case of 3rd phase energization (R = 0).
Fig. 6. Comparison of the neutral resistor scheme with the series resistor.
Fig. 3.
Magnitude of inrush current as affected by the neutral resistor.
Fig. 4. Current flow pattern for the case of second phase energization.
explains why the scheme of simultaneous breaker closing does
not work. However, the size of the neutral resistor can change
the steady-state voltage that crosses the third breaker before it is
closed. When the neutral resistance is zero, the breaker voltage
is zero. This can be understood from Fig. 5. In this figure, phases
A and B have been energized, so the flux in the phase C core is
The voltage induced on the phase C winding becomes
3rd energization curve with the higher one of the 1st and the
2nd energization curves. For the results shown in Fig. 3, the optimal value is found to be about 3 . With this resistance value,
the reduction of inrush current is about 89% for the first phase
energization, 91% for the 2nd phase energization and 93% for
the 3rd phase energization respectively, in comparison with the
cases of zero neutral resistance. This is a significant reduction
on the inrush current. Fig. 6 shows the effectiveness of the proposed scheme in comparison with the series resistor insertion
scheme. For the case of a 3- resistor, the proposed scheme is
essentially as effective as the series resistor scheme and is sufficient for intended application. If one increases the size of the
resistor, the series resistor scheme can reduce the inrush current further. The inrush current will increase with the proposed
scheme. This is because that the neutral resistor is no longer the
optimal one.
are slightly
Note that the maximum inrush currents at
different between the two schemes in Fig. 6. This is due to the
fact that a simultaneous closing of three breakers was simulated
for the series resistor scheme, while for the proposed scheme, it
is a sequential closing.
C. Impact of the Neutral Resistance on Current Duration
The above equation implies that the induced voltage is equal to
the supply voltage. As a result, there are no transients when the
third winding is switched on to the supply. As will be shown in
the companion paper, this is an important requirement for the
proposed scheme to be effective. When R becomes very large,
the case is similar to energizing the second phase.
Accordingly, we can conclude that there are conflicting requirements for the size of the neutral resistor for each energization event. The optimal neutral resistance is the one that
can yield compromised reduction of the inrush current for all
events. Such an optimal value is the interaction point of the
In addition to reducing magnitude of inrush current, the neutral resistor can also reduce the duration of the inrush current.
This postulation was investigated and the results are shown in
Fig. 7. This figure shows the decaying peak current of each cycle
as a function of time. The curves correspond to the largest inrush current case for the first phase switching.
It can be seen that inrush current is damped quickly when
there is a resistor in the circuit. This is another benefit of the
proposed scheme. We also checked the time constant associated with the second phase switching. A similar phenomenon
was observed. But the reduction of time constant is not as significant as the first phase switching. This is due to the fact that
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Fig. 7. Decay of peak inrush current with time.
Fig. 9. Experimental transformer (30 kVA, 120/208 V).
TABLE I
NO-LOAD TEST DATA FOR A HYUNDAI TRANSFORMER
Fig. 10.
Fig. 8.
Simulation results of a 72/13.8-kV transformer.
there is a second path for the inrush current. In theory, the neutral
resistor has no impact on the time constant associated with the
third phase switching. This is because the inrush current does
not flow through the resistor once the third phase is closed. In
summary, the neutral resistor has some positive effects on reducing the duration of inrush currents. Since the resistor has reduced the magnitude of inrush current so significantly, the effect
on duration can be considered as a secondary benefit.
D. Simulation Results of a Large Transformer
Simulation studies have also been conducted on a 138 MVA,
transformer. The nameplate of this trans72/13.8 kV,
former is shown in Table I. The transformer is energized from
the 72 kV side and the simulation results are shown in Fig. 8.
A significant reduction of the inrush current can be seen. The
optimal resistor value is about 2000 , which is approximately
10% of the magnetizing impedance of the transformer.
IV. EXPERIMENTAL RESULTS
The proposed scheme has also been investigated through
extensive laboratory experiments. The experiments were conducted on the same transformer used for simulation studies,
Typical current waveforms when the second phase is energized.
which is shown in Fig. 9. The main difficulties encountered for
experiments are 1) the switching instant cannot be controlled at
will, 2) there is an unknown amount of residual flux when the
first phase is energized, 3) the supply system has an impedance
and 4) the supply voltage is distorted with harmonics. To
overcome the first difficulty, each switching event was repeated
more than 100 times. The results are then grouped according to
the recorded phase angles of the supply voltage. The maximum
inrush current was extracted from the results.
A. Inrush Current Waveforms
Due to space limitation, only shown in this paper are the
sample results for the 2nd and 3rd phase switching when
. The 1st phase switching is similar to the series resistor
scheme and is omitted here. Fig. 10 shows the phase B and neutral current when phase B is energized. It can be seen that the
neutral current is larger than phase B current. There is nothing
special about this phenomenon since, depending on the instant
of switching, phase A current could add to phase B current to
yield a larger neutral current.
Fig. 11 shows the Phase C and neutral current when phase C
is energized. The most interesting information one can extract
from this figure is that the neutral current reduces to zero almost instantly once the 3rd phase is energized. It justifies why
the neutral resistor has no direct impact on reducing the inrush
current in this case. However, as will be shown in a companion
paper, the neutral resistor contributes to the inrush current reduction through reducing the voltage across the 3rd breaker before
it is closed.
CUI et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION—PART I
Fig. 11.
Typical inrush current waveforms when 3rd phase is energized.
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Fig. 13. Magnitude of inrush current as affected by the neutral resistor (Y-Y
connection).
simulation studies cannot take into account the (unknown)
impedance of the supply system. The ‘far end’ of the saturation
curve is not exactly known because of limitations of experimental facility. The harmonic distortion in the supply voltage
is another significant factor. The supply voltage has a harmonic
voltage THD around 4%. This factor is likely the main cause
leading to the fluctuation of the curve representing the second
phase energization. This judgment is supported by an open
delta experiment for the transformer. In this experiment, the
curves are determined for the test
inrush currents versus
transformer when its delta-connected secondary is open. In this
case, the transformer cannot trap zero sequence current from
the system. The resultant 2nd phase energization curve has
more noticeable fluctuation (Fig. 13).
In spite of the differences, the effectiveness of the proposed
inrush current suppression scheme has been verified by both
simulation and experimental results. The resultant optimal value
for the neutral resistor has a good agreement.
V. CONCLUSIONS
Fig. 12. Magnitude of inrush current as affected by the neutral resistor.
B. Impact of Neutral Resistance on the Current
The maximum inrush current as a function of the neutral resistance is also determined from experimental results. As discussed earlier, each switching event was repeated more than 100
times. Approximate maximum inrush current was determined.
The results are shown in Fig. 12.
It can be seen that Fig. 12 is quite similar to the one derived
from simulation studies. The results are good confirmation to
the validity of the simulation technique. The optimal resistance
is in the range between 2 and 8 . This value is comparable
with that derived from simulation. One can also find that there is
a relatively wide range to select the value for the neutral resistor.
A resistance value in the range of 2 to 10 has almost the same
effectiveness. Use of exact optimal value is not essential for the
proposed scheme.
The difference between the simulation and experimental
results is due to a number of factors. For example, the experimental results cannot catch the highest inrush current. The
This paper has presented a new technique to reduce inrush
current caused by transformer energization. Extensive simulations and experimental results have confirmed the effectiveness
of the proposed scheme. Main conclusions can be summarized
in the following.
i) There is an optimal neutral resistor value for the proposed
scheme. This value is a compromised value between the
need to suppress the inrush currents when the first two
phases are energized and the need to suppress the current
when the 3rd phase is energized. It is not essential to use
an exact optimal value. Resistances around the optimal
value are almost equally effective.
ii) With the proposed resistance value(s), the neutral resistor
based scheme can lead to 80% to 90% reduction on the
inrush current. The results also show that it is as effective
as the series resistor scheme. As a result, the proposed
scheme has the potential to fully eliminate the power
quality concerns caused by transformer energization.
It is important to note that the proposed time delay for sequential energization is a simple mechanical delay of 5 to 60 cycles.
There are no strict requirements on the delay time. High voltage
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Fig. A1. Fluxes diagram of a three-phase three-limb transformer.
Fig. A4.
Exciting characteristic of three phases.
A. Transformer Model
Fig. A2. Equivalent magnetic circuit of a three-phase three-limb transformer.
The transformer model is a set of nonlinear differential
equations as shown below. In these equations all secondary-coil
quantities have been referred to the primary side. N is the
number of turns of the primary side windings.
Fig. A3. Equivalent electric circuit of phase j of a three-phase three-limb
transformer.
circuit breakers are typically set up with independent operating
mechanism for each phase. A delayed closing of phases is
therefore achievable. In the case of a three-phase operated
circuit breaker equipped with a common operating mechanism,
the breaker typically has a built-in mechanical delay among
three phases. This feature can be used to implement the proposed scheme. The voltage or current imbalance introduced by
the delayed operation should not be a concern. This is because
the transformer is unloaded and the duration of imbalance is
very short.
APPENDIX
In this appendix information about the simulation model is
presented along with experiments used to determine the model
parameters. The model was published in [10]. Fig. A1–A3
show the fluxes diagram, the equivalent magnetic circuit and
the equivalent electric circuit of a 3-phase 3-limb transformer.
Magnetic fluxes associated with the transformer can be subdivided into the following categories as indicated in Fig. A1.
• Magnetic fluxes that link different phases and follow the
magnetic circuit ( , , , , and ). They are associated with the nonlinear reluctances , , , ,
and ;
• Phase leakage fluxes which link all the windings of one
,
, and
).
phase, and partially go through air (
They are associated with constant reluctances
,
,
.
and
and
are the winding resistor and leakage
In Fig. A3,
and
are those of the
inductor of the primary side, while
secondary side, but refereed to the primary side, respectively.
The above equations have taken into account the delta connection in the transformer secondary, which gives
. This model consists of 13 equations. It is solved using
the Matlab as well as MathCAD tools. Two independent programs were developed for this purpose.
B. Model Parameters
Parameters needed for the above model were determined
from experiments. The parameters include the winding resistances, leakage inductances, inductances of limb and yoke and
the reluctances. The winding resistances and leakage inductances were determined from standard short-circuit tests on
each winding [11]. The average values among three phases are
,
.
A zero sequence open-circuit test was used to deter. Measured average value is
mine the air path reluctance
, which is used for all three phases.
To measure the nonlinear reluctances of the limbs and yokes,
the transformer was reconnected into Y/Y connection and
was supplied by a 3-phase balanced voltage. A set of open
circuit tests is conducted to find the saturation curves, which
.
are then converted to the nonlinear equation of
Fig. A4 shows the exciting characteristic of different phases.
Limited by the test facility, we could only get the ‘front’ part
CUI et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION—PART I
Fig. A5.
Computed inrush current waveforms for a transformer of [10].
of the saturation curve. The deep-saturation part of the curve is
extrapolated according to the trend.
949
[5] Westinghouse, Electrical Transmission and Distribution Reference
Book. Chicago: The Lakeside Press, R. R. Donnelley & Sons Company, 1944, pp. 411–417.
[6] B. Holmgrem, R. S. Jenkins, and J. Rinbrugent, “Transformer inrush
current,” in CIGRE Proc. 22nd Session, vol. 1, 1968, pp. 1–13.
[7] R. Yacamini and A. Abu-Nasser, “The calculation of inrush current in
three-phase transformers,” IEE Proc. Electr. Power Appl., vol. 133, no.
1, pp. 31–40, Jan. 1986.
[8] L. Cipcigan, W. Xu, and V. Dinavahi, “A new technique to mitigate inrush current caused by transformer energization,” in Proc. IEEE 2002
PES Summer Meeting, Chicago, USA, Jul. 2002.
[9] H. M. Dommel, EMTP Theory Book, 2nd ed. Vancouver, British Columbia: Microtran Power System Analysis Corporation, 1996.
[10] M. Elleuch and M. Poloujadoff, “A contribution to the modeling of three
phase transformers using reluctance,” IEEE Trans. Magn., vol. 32, no.
2, pp. 335–343, Mar. 1996.
[11] Members of the staff of the Department of Electrical Engineering,
Massachusetts Institute of Technology, Magnetic Circuits and Transformer. New York: Wiley, 1943, pp. 443–453.
C. Model Verification
To verify the model, a test case shown in [10], which is a
10 kVA, 232 V, 3-phase 3-limb transformer with grounded Y/Y
connection, is used. The inrush current waveforms computed
by this project is shown as Fig. A5. The waveforms have a close
agreement with the results shown in Fig. 9 of [10].
Due to the various factors described in Section IV, we could
not produce inrush current waveforms that can exactly match
the experimental results. However, there is an acceptable agreement for the general shape of the waveforms and their decaying
trends. Furthermore, the validity of the model is confirmed by
curves.
the close similarity of inrush current versus
ACKNOWLEDGMENT
The authors wish to thank C. Muskens of ATCO Electric and
T. Martinich of BC Hydro for the suggestions and comments
during the course of this project. The help of A. Terheide, a technician at the University of Alberta power lab, on experimental
investigations is fully acknowledged.
REFERENCES
[1] T. Specht, “Transformer inrush and rectifier transient currents,” IEEE
Trans. Power App. Syst., vol. 88, no. 4, pp. 269–276, Apr. 1969.
[2] CIGRE working group task force 13.07, Controlled switching of HVAC
circuit breakers, in 1st Part Elektra, no. 183, pp. 43–73, Apr. 1999.
[3]
, “Controlled switching of HVAC circuit breakers,” 2nd Part
Elektra, no. 185, pp. 37–57, Aug. 1999.
[4] K. Smith, L. Ran, and B. Leyman, “Analysis of transformer inrush
transients in offshore electrical systems,” Proc. Inst. Elect. Eng., Gen.
Transm. Distrib., vol. 146, no. 1, pp. 89–95, Jun. 1999.
Yu Cui received the B.Eng. degree from Tsinghua University, Beijing, China
in 1995; the M.Sc. degree from Institute of Electrical Engineering, Chinese
Academy of Sciences, Beijing, China in 2000; and the M.Sc. degree from University of Saskatchewan (Canada) in 2003. He is currently working on his Ph.D.
degree at University of Alberta.
His research areas include power system stability and power quality.
Sami G. Abdulsalam (S’03) received the B.Sc. and M.Sc. degrees in electrical
engineering from Elmansoura University, Egypt in 1997 and 2001, respectively.
Since 2001 he has been with Enppi Engineering Company, Cairo, Egypt. He is
currently pursuing the Ph.D. degree in electrical and computer engineering at
the University of Alberta.
His current research interests are in modeling and simulation of power system
transients.
Shiuming Chen (M’02–SM’02) received the B.Sc. degree in 1990 and M.Sc.
degree in 1993 in electrical engineering from Zhejiang University, and the Ph.D.
degree in 1997 from Tsinghua University, Beijing, P R China.
He is currently an Associate Professor of the Tsinghua University and is
working at the University of Alberta as a post-doctoral fellow. His research interests are over-voltage protection in power systems and electromagnetic compatibility in power and electronic systems.
Wilsun Xu (M’90–SM’95) received the Ph.D. degree from the University of
British Columbia, Vancouver, BC, Canada, in 1989.
Currently he is a Professor with the University of Alberta, Edmonton, AB,
Canada. He was an Engineer with BC Hydro, Vancouver, BC, Canada, from
1990 to 1996. His main research interests are power quality and harmonics.