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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
A Sequential Phase Energization Technique for
Transformer Inrush Current Reduction—Part II:
Theoretical Analysis and Design Guide
Wilsun Xu, Senior Member, IEEE, Sami G. Abdulsalam, Student Member, IEEE, Yu Cui, and Xian Liu, Member, IEEE
Abstract—This paper presents a theory to explain the characteristics of a sequential phase energization based inrush current reduction scheme. The scheme connects a resistor at the transformer
neutral point and energizes each phase of the transformer in sequence. It was found that the voltage across the breaker to be closed
has a significant impact on the inrush current magnitude. By analyzing this voltage using steady-state circuit theory, the simulation
and experimental results presented in a companion paper are explained. The results lead to the establishment of a guide to select
the optimal value of the neutral resistor. The applicability of the
proposed scheme to different transformer configurations has also
been investigated in this paper. It is shown that the idea of sequential phase energization leads to a new class of techniques for limiting switching transients.
Index Terms—Inrush current, power quality, transformer.
Fig. 1. Circuit for analyzing transformer energization.
I. INTRODUCTION
A
NEW, simple and low cost scheme to reduce transformer
inrush currents has been presented in a companion paper.
The scheme uses a resistor connected at the transformer neutral
point and energizes each phase of the transformer in sequence.
Simulation and experimental results have shown that the scheme
is quite effective [1]. The amount of inrush current reduction
as a function of neutral resistor value was determined from the
results. It was found that there is an optimal value for the resistor.
The paper, however, offers no quantitative theory to explain the
phenomena.
The objective of this paper is to present a theoretical analysis
on the proposed scheme. The results lead to the establishment
of a design guide for the selection of the optimal resistor value.
The theory also makes it possible to analyze the applicability of
the proposed scheme to different types of transformer configurations.
A rigorous analysis on the proposed scheme needs to study
a system of multi-variable nonlinear differential equations.
Finding an analytical solution to the problem is probably impossible. Even with many approximations, we still failed to get
some meaningful results. The process, however, led us to realize
that the steady-state voltage across the breaker to be closed
Manuscript received May 20, 2003; revised October 18, 2003. This work was
supported by the Alberta Energy Research Institute. Paper no. TPWRD-002412003.
W. Xu, Y. Cui, and S. G. Abdulsalam are with the Department of Electrical
and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4,
Canada (e-mail: wxu@ece.ualberta.ca).
X. Liu is with the University of Arkansas, Little Rock, AR 72204-1099 USA.
Digital Object Identifier 10.1109/TPWRD.2004.843465
has a significant impact on the inrush current magnitude. This
voltage can be determined from steady-state circuit analysis.
Further investigation of the phenomena reveals that one of the
real causes behind the effectiveness of the proposed scheme
is the reduction of this voltage through the neutral resistor,
which is made possible by sequential phase energization. In the
following sections, a steady-state circuit theory is presented to
analyze the problem. The theory is then extended to establish a
design guide to determine the optimal resistor value.
II. STEADY-STATE ANALYSIS OF THE PROPOSED SCHEME
The proposed scheme involves the energization of three
phases in sequence. The energization of the first phase is
very similar to the series resistor insertion scheme. This is a
straightforward problem and it will not be considered further
in subsequent sections. The challenge here is the analysis
of the 2nd and 3rd phase energization. Using the 2nd phase
energization as an example, the circuit shown in Fig. 1 can be
drawn. The variables shown in the circuit diagram are phasors.
This notation will be followed throughout the paper.
Without losing generality, the unloaded transformer can be
represented as three coupled branches in the figure. In its steadystate form, the equation for the transformer can be written as
follows,
where
and
are the self and mutual impedances of the
is shown in Fig. 1. The above
coupled circuit respectively.
0885-8977/$20.00 © 2005 IEEE
XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II
equation assumes that the transformer is balanced among three
phases and the resistive component is omitted. The secondary
side of the transformer has an impact on the value of the coupling matrix, but it does not change the structure of the circuit.
The most important variable of the above circuit is the voltage
across the phase B breaker before it is closed. This voltage is lain the figure and is called breaker contact voltage
beled as
in this paper. Based on circuit theory, the following characteriscan be stated:
tics regarding to
• If
, closing of the phase B breaker would not
result in transient currents in the circuit.
• If the circuit were a linear circuit, the magnitude of the
transient currents in the circuit would be in proportion
if the breaker always closes at the same phase
to
angle of
.
• If the circuit is a nonlinear circuit with transformer magwill generally
netization characteristics, a larger
lead to a larger inrush current if the breaker always closes
. The relationship between
at the same phase angle of
is nonlinear.
the inrush current and
It becomes clear, therefore, that we can use the magnitude of
to investigate indirectly the magnitude of the circuit transients. A larger
should be avoided if one wants to reduce
the inrush currents. This reasoning is the basis of the quantitative theory presented in this paper. The goal of our analysis
is thus transformed into the one of finding the relationship beand
.
tween
is estabAccording to Fig. 1, the equation to determine
lished as follows:
The above set of equations has five known variables. The result for
is shown in the following formula:
(1)
Similarly, we can develop a set of equations for the steadystate circuit condition before the phase C breaker is energized
This leads to the solution for the
as follows:
(2)
on the magnitudes of
and
can
The impact of
be assessed by plotting formulas (1) and (2). Using the test transformer of [1] ( secondary) as an example, the results are shown
Fig. 2.
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Breaker contact voltages as affected by R .
Fig. 3. Comparison of breaker contact voltage curves and the inrush current
curves.
in Fig. 2. It can be seen that
decreases initially when
is small. On the other hand,
always increases with
. The intersection point of the two curves gives a compromised reduction on both voltages. This is the optimal point for
the neutral resistor since we don’t want either voltage becomes
too high. The corresponding voltage is about 80% of the case
, or 66% of the
with solidly grounded transformer
phase to ground voltage of 120 V. Also included in the figure
and
results for the experimental
is the measured
transformer. There is a reasonable agreement between the results. The difference is caused by the asymmetry and saturation
of the transformer magnetic circuit. Note that the transformer
model shown in Fig. 1 is assumed to have the same mutual impedances.
Further inspection of the results shows that the curves are
curves obtained
very similar to the inrush current versus
by experiments and simulations [1]. The main difference is on
the scale of the Y-axis. This is understandable since the magnitudes of inrush currents are approximately exponential funcand
. Fig. 3
tions of the breaker contact voltages
compares the two sets of curves and the similarity can be clearly
seen. More importantly, the intersection points of the respective
curves are very close. Accordingly, one can find the optimal resistance value using (1) and (2). For the test transformer, the
optimal resistance is found to be 1.8 with the steady-state
method and 2.4 from the nonlinear simulation results. The
corresponding reduction of breaker contact voltage is about 66%
in this case.
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
In summary, (1) and (2) can be combined to establish a single
formula for the optimal resistance value as follows:
or
Fig. 4. Zero sequence test circuit for
(3)
There is no closed form solution for the above equation. But
it can be easily solved numerically. In the next section, approxvalue is estabimate analytical expression for the optimal
and
.
lished by considering the relationship between
III. DESIGN GUIDE FOR DIFFERENT TRANSFORMERS
is a function of
Equation (3) shows optimal resistor
and
of the transformer. A general method to determine these
two parameters is as follows:
is
1) Ground the transformer neutral for the side where
to be inserted. This is typically the primary side of the
transformer. This side is also called the test side.
2) The secondary side of the transformer is left as it is. For
example, if the transformer is connected, leave the
connection intact.
3) Apply a rated positive sequence voltage to the transformer
test side and measure the current injected into the transformer. The ratio of the voltage to the current is the standard open circuit impedance of the transformer. The reactance component of the impedance can be determined
.
accordingly. This value is labeled as
4) Apply a rated zero sequence voltage to the transformer
test side and measure the current injected into the transformer. The ratio of the voltage to the current is a zero sequence impedance of the transformer. Depending on the
connection of the secondary side, this impedance is not
necessarily the zero sequence open circuit impedance. If
the secondary side is -connected, it is actually the short
circuit zero sequence impedance of the transformer. The
.
resulting reactance is labeled as
and
can be calculated from the fol5) Parameter
lowing well known equation [5]:
Y=1 transformer.
With these understandings, the formulas for the optimal resistance are derived for different types of transformer connections.
A.
Transformer
In this case, the positive sequence test gives the open-circuit
reactance or magnetizing reactance of the transformer. The zero
sequence test gives the short-circuit zero sequence reactance, as
shown in Fig. 4.
Since the short-circuit impedance is much smaller than the
open circuit impedance
Substituting this condition into (3), the equation for the optimal
neutral resistor can be established as follows:
which gives
(4)
,
There is a 32% voltage reduction in this case. If
. The voltage reduction with respect to solidly
grounded case is about 20%.
B. Y/Y Transformer With 3-Limb
In this case, the positive sequence test also gives the standard
open circuit reactance or magnetizing reactance of the transformer. For the zero sequence test, the flux has to flow outside
of the limb due to the fact that the flux of each phase has the
same direction (Fig. 5). The zero sequence impedance is there, it can be neglected. So
fore very small. Comparing with
the formula for optimal neutral resistor is essentially identical
to (4).
C. Y/Y Transformer Consisting of Three Single-Phase Units
Mathematically speaking, the above procedure is to find
and
using the following equations:
In this case, the positive sequence test also gives the standard
open circuit reactance of the transformer. The zero sequence test
yields the same flux path as that of the positive sequence test.
. This gives
As a result,
The above condition does not produce an optimal resistance
value from (3). It implies that the proposed scheme is not quite
workable for this type of transformer. This result can be seen
curves shown in
from the breaker contact voltage versus
Fig. 6. The figure reveals that there is no low voltage intersection
point for the two curves. The figure also shows that the problem
curve, which does not start from zero
is caused by the
value in this case. The physical explanation is that the 3rd phase
XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II
953
TABLE I
NO-LOAD TEST DATA FOR A HYUNDAI TRANSFORMER
• Applied voltage
• Average no load current
• No load losses
The open circuit impedance is
and the open circuit resistance is
. It gives
Fig. 5. Zero sequence flux path for a 3-limb transformer.
Fig. 6. Breaker contact voltages for Y/Y transformer consisting of three
single-phase units.
is decoupled from the other two phases. A voltage cannot be
induced on that phase when the first two phases are energized.
D. Y/Y Transformer With 5-Limb
This case is very similar to the case of 3 single-phase transformers. The zero sequence flux can return from the iron core,
resulting in a zero sequence impedance that is comparable to
. Accordingly, the proposed scheme may not work in this
case either.
E. Summary and Examples
In summary, an optimal resistance exists for
transformer and for 3-limb Y/Y transformer. These transformers
are characterized as having mutual coupling among three
phases. The proposed scheme will work for these cases. It
can be further inferred that the scheme will also work for 3
winding transformers as long as it has a secondary or tertiary.
Since most power transformers have a delta-connected tertiary
winding, the proposed scheme can be applied to a wide range
of transformers. Furthermore, the same formula for the optimal
neutral resistor can be used for all cases.
If the open circuit current at rated voltage is expressed in percentage of the transformer rating and the resistance part is ignored, (4) can be further simplified as follows:
(5)
is the per-unit transformer excitation current at
where
rated supply voltage.
As an example, the experimental transformer used for this
project has the following measured values:
;
;
.
The corresponding optimal resistance is 1.8 . As a second
example, a HYUNDAI 132.8 MVA, 72/13.8 kV, 3-limb,
transformer is considered. The manufacturer provided the test
data from the 13.8 kV side given in Table I
Using a similar procedure and the average current among
and
values are calculated
three phases, the
and 868
respectively. If referred to the prias 283
mary side where the neutral resistance is to be inserted,
. Using formula (4), the optimal
neutral resistor is calculated as 2008 . If formula (5) is used,
the resistance is 53 pu or 2068 . The values agree well with
shown in Fig. 8 of the
the simulation determined optimal
companion paper.
IV. NUMERICAL AND SENSITIVITY STUDIES
values for inrush
It is a significant claim that the optimal
current reduction and for breaker contact voltage reduction are
very close. The design (4) and (5) are based on such a claim. Although this claim can be understood conceptually from the explanations presented in Section II, there is still a need to verify it
further. To this end, two sensitivity studies have been conducted.
The studies involve changing the slope of the transformer saturation curve. The first study examines the impact of changing
the slope of the unsaturated segment of the curve and the second
study examines the impact associated with the slope of the saturated segment. The inrush current results obtained from simulation are shown in Figs. 7 and 8.
It can be seen from Fig. 7 that the intersection points of the
inrush current curves move horizontally when the slope of the
) changes from 50% to 200% of
unsaturated curve (i.e.
the measured value. It means that the unsaturated reactance can
affect the optimal resistance value. This result agrees well with
the conclusion drawn from the breaker contact voltage analysis.
is a function of the unsatuThe analysis shows that
.
rated reactance
Fig. 8 reveals that the intersection points move vertically
when the slope of the saturated segment of the saturation curve
is changed from 30% to 100%. It implies that the slope has
. This result further
no effect on the value of the optimal
confirms the adequacy of the breaker contact voltage analysis.
is affected by the
The analysis does not indicate
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Fig. 7. Impact of changing the slope of the unsaturated segment of the
transformer magnetization curve.
Fig. 8. Impact of changing the slope of the saturated segment of the
transformer magnetization curve.
slope of the saturated segment of the transformer magnetization
curve.
In addition to the above verification studies, the accuracy
of the design formula is further evaluated by using a 3 limb
transformer consisting of three
Y/Y transformer and a
single-phase units. The results for the 3 limb Y/Y transformer
are shown in Fig. 9. It can be seen that there is a good agreement
between the steady-state analysis and the transient simulations.
For transformers consisting of three single-phase units,
the case of 300 MVA, 13.8/199.2 kV transformer units described in [6] is simulated. Two cases are studied, one with the
and the other connected
single-phase units connected in
in Yg/Y. In both cases the high voltage side is the grounded Y.
connection are shown in Fig. 10. This
The results for
figure confirms the validity of the steady-state analysis method.
For the case of the Yg/Y connection, steady state analysis
show that the neutral resistor scheme is not as effective since
the breaker contact voltage cannot be reduced. The simulation
results, however, showed that the proposed scheme has some effects (Fig. 11). The effect could be explained with the following
equation:
where stands for the Laplace operator and
the total circuit
impedance seen from the breaker contacts (the 3rd phase closing
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Fig. 9. Comparison of simulation and theoretical results for a 3-limb
transformer with Y/Y connection.
Fig. 10. Comparison of simulation and theoretical results for a
transformer consisting of three single-phase units.
Yg=1
Fig. 11. Inrush current simulation results for a Yg/Y transformer consisting of
three single-phase units.
is used as an example). Although this equation applies to a linear
circuit only, it is symbolically valid for a saturated transformer.
will reduce
. An
It can be seen that a reduction on
could also reduce
. It is likely that, in the
increase of
case of Y/Y transformer bank, the reduction on inrush current is
due to the increase of Z(s) by the neutral resistor. We are further
investigating this phenomenon.
In order to understand the characteristics of the proposed
scheme further, additional sensitivity studies have been conducted. Some of the results are presented in the following subsections.
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955
A. Impact of Transformer Resistance
In the foregone derivations, the transformer resistance was
neglected. It would be useful to know what is the effect of this
approximation. In this case, the transformer model becomes
where
is the winding resistance. Using a procedure similar
to that described in Section II, the breaker contact voltages are
found to be
Fig. 12.
Breaker voltages as affected by R for switching sequence ACB.
It can be seen that the impact of
is not significant. This
conclusion has been validated by the example of the 132.8 MVA
transformer.
Fig. 13.
Breaker contact voltages as affected by neutral reactance.
B. Sequence of Switching
switching sequence of ABC, the breaker contact voltages are
transformer case:
determined as follows for the
Within a certain range of
can be expressed as
(0 to 20% of
),
The proposed scheme as it stands now requires a switching
sequence of phases A, B and C. In this study, we want to know
if a switching sequence of A, C and B would bring more inrush
current reduction. In this case, the breaker contact voltages are
determined as follows
(6)
(7)
where subscripts 2 and 3 denote switching order. The resulting
breaker contact voltage curves are shown in Fig. 12. It can be
is different from that of
.
seen that the trend of
The voltage is always higher than the case of
. Consequently, there is no intersection between the two curves. The
conclusion of this analysis is that the proper switching sequence
for the proposed scheme is A, B and C.
C. Neutral Impedance
The possibility of using a neutral impedance
to reduce the inrush current is also investigated. Adopting the
The case of inserting a neutral reactor is examined first. The
corresponding breaker contact voltage curves are shown in
Fig. 13 and are compared with those associated with the neutral
does not have a valley.
resistor. The results show that
The intersection point of
and
is higher than the
obtained with
or
equal to zero. As a
value of
result, connecting a reactor to the transformer neutral is not a
solution option.
is also
The case of connecting a neutral impedance
investigated. The breaker contact voltages for the cases of
,
and
are shown in
yields the
Fig. 14. The results indicate that the case of
lowest voltage. So a pure resistor as the neutral impedance is the
best option for the proposed scheme.
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Fig. 14.
IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005
Breaker contact voltages as affected by neutral impedance.
V. CONCLUSIONS
This paper has presented a theory to explain the characteristics of a proposed sequential phase energization based inrush
current reduction scheme. A formula to determine the optimal
resistor value is established. Main findings of the work can be
summarized as follows:
•
The mechanism of the proposed scheme can be understood from the perspective of breaker contact voltage reduction. These voltages can be determined using steadystate circuit analysis.
• The proposed scheme is most effective for transformers
with a delta winding or having three limbs, i.e. three windings of the transformer are coupled electrically or magnetically.
• The optimal neutral resistance for these cases can be
,
determined from formula
is the open-circuit positive-sequence reacwhere
tance of the transformer. Selecting a precise value for
the neutral resistor is not necessary. As long as it is in
, the scheme is equally
the neighborhood of
effective.
• The sequence of switching should be as follows: phase
A first, followed by phase B and then by phase C. This
switching sequence will lead to 20% to 30% reductions on
the breaker contact voltages and 80% to 90% reductions
on the inrush currents. Time delay between the switching
events is in the range of 5 to 60 cycles.
• Although neutral impedance can also be used for the proposed scheme, study results show that the most effective
option is still the neutral resistor scheme.
Although a lot of results have been obtained for the proposed scheme, we feel more work is needed. For example, how
to determine the current flowing through RN is still an open
subject. This current is important for assessing the transient
withstand capability of the resistor and the neutral voltage rise.
There is also a need to field test the proposed scheme on large
transformers.
The proposed method compares favorably to the existing
schemes of pre-insertion resistor and synchronous closing. It
is much cheaper than the pre-insertion resistor scheme since
only one resistor and one by-pass breaker are used. It is more
robust than the synchronous closing scheme. The scheme needs
to determine the residual flux of transformer cores to work
effectively. There is no good solution to find residual flux yet.
In view of the fact that a lot of distribution transformers have
a neutral resistor for single-phase fault detection, the proposed
scheme could be applied with very low cost—delayed closing
of each phases of the transformer might be just sufficient.
We believe that another major contribution of this work is the
discovery of a new class of methods to reduce switching transients. The method is to reduce the breaker contact (phasor) voltages through sequential phase energization. The true function of
the neutral resistor is to minimize the breaker contact voltages.
From this perspective, the potential of the proposed scheme is
not limited to transformer energization. In theory, it is also applicable to capacitor energization and possibly motor starting.
We are currently investigating these subjects as well.
ACKNOWLEDGMENT
The authors wish to thank C. Muskens of ATCO Electric and
T. Martinich of BC Hydro for the suggestions and comments
throughout the course of this project. The help of A. Terheide, a
technician in the University of Alberta Power Lab, with experimental investigations is fully acknowledged.
REFERENCES
[1] Y. Cui, S. G. Abdulsalam, S. Chen, and W. Xu, “A sequential phase
energization method for transformer inrush current reduction—Part I:
Simulation and experimental results,” IEEE Trans. Power Del., vol. 20,
no. 2, pp. 943–949, Apr. 2005.
[2] Members of the staff of the Department of Electrical Engineering,
Massachusetts Institute of Technology, Magnetic Circuits and Transformer. New York: Wiley, 1943, pp. 442–444.
[3] R. L. Bean, N. Chacken, H. R. Moore, and E. C. Wentz, Transformers for
Electric Power Industry. New York: McGraw-Hill, 1959, pp. 317–321.
[4] 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.
[5] H. M. Dommel, EMTP Theory Book, 2nd ed. Vancouver, British Columbia: Microtran Power System Analysis Corporation, 1996.
[6] X. Chen, “Negative inductance and numerical instability of the saturable
transformer component in EMTP,” IEEE Trans. Power Del., vol. 15, no.
4, pp. 1199–1204, Oct. 2000.
Wilsun Xu (M’90–SM’95) received the Ph.D. degree from the University of
British Columbia, Vancouver, Canada, in 1989.
He worked in BC Hydro from 1990 to 1996 as an engineer. Dr. Xu is presently
a Professor at the University of Alberta, Edmonton, Canada. His main research
interests are power quality and harmonics.
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.
He is currently pursuing his Ph.D. degree in electrical and computer engineering
at the University of Alberta, Edmonton, Canada.
Since 2001 he has been with Enppi Engineering Company, Cairo, Egypt.
His current research interests are in modeling and simulation of power system
transients.
XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II
Yu Cui received the B.Eng. degree from Tsinghua University, Beijing, China; an
M.Sc. degree from Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China; and an M.Sc. from University of Saskatchewan (Canada)
in 1995, 2000, and 2003 respectively. He is currently working on his Ph.D. degree at University of Alberta.
His research areas include power system stability and power quality.
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Xian Liu (M’95) obtained the Ph.D degree in computer engineering from the
University of British Columbia, Canada, in 1996.
Before joining the University of Arkansas at Little Rock, Little Rock, AR. Dr.
Liu worked at NORTEL Networks, Ottawa, ON, Canada, and the University of
Alberta, Canada, from 1995 to 2001. To date he and his research collaborators
have published more than 50 journal and conference papers, mainly in the areas
of electrical machines, communication networks, and engineering optimization.