A Sequential Phase Energization Method for Transformer Inrush

A Sequential Phase Energization Method for
Transformer Inrush Current Reduction—Transient
Performance and Practical Considerations
Sami G. Abdulsalam, Student Member, IEEE, and Wilsun Xu, Fellow, IEEE
Abstract—This paper presents an improved design method for
a novel transformer inrush current reduction scheme. The scheme
energizes each phase of a transformer in sequence and uses a neutral resistor to limit the inrush current. Although experimental
and simulation results have demonstrated the effectiveness of the
scheme, the problem of how to select the neutral resistor for optimal performance has not been fully solved. In this paper, an analytical method that is based on nonlinear circuit transient analysis
is developed to solve this problem. The method models transformer
nonlinearity using two linear circuits and derives a set of analytical
equations for the waveform of the inrush current. In addition to
establishing a set of formulas for optimal resistor determination,
the results also reveal useful information regarding the inrush behavior of a transformer and the characteristics of the sequential
energization scheme. This paper also proposed a method, the use of
surge arrester, to solve the main limitation of the sequential phase
energization scheme—the rise of neutral voltage. Performance of
the improved scheme is presented.
Index Terms—Inrush current, power quality, transformer.
A sequential phase energization-based scheme to reduce
transformer inrush currents has been proposed by the authors
in [1] and [2] (Fig. 1). The method uses an optimally-sized
grounding resistor. 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. It was found that a neutral resistor that is 8.5% of
the unsaturated magnetizing reactance would lead 80% to 90%
inrush currents reduction. However, the resistor sizing issue
was not investigated from the transient performance perspective
due to difficulties in conducing transient analysis of nonlinear
Our further study of the scheme revealed that a much lower
resistor size is equally effective. The steady-state theory developed for neutral resistor sizing [2] is unable to explain this phenomenon. Extensive investigation showed that the phenomenon
must be understood using transient analysis. If we select the neutral resistor to minimize the peak of the actual inrush current
Manuscript received September 6, 2005; revised March 6, 2006. This work
was supported by the Alberta Energy Research Institute. Paper no. TPWRD00521-2005.
The authors are with the Department of Electrical and Computer Engineering,
University of Alberta, Edmonton, AB T6G 2V4 Canada (e-mail: [email protected]
ualberta.ca; [email protected]).
Color versions of Figs. 2, 4–7, and 9–16 are available online at http://ieeexplore.org.
Digital Object Identifier 10.1109/TPWRD.2006.881450
Fig. 1. Sequential phase energization technique for inrush current reduction.
directly, we can obtain a much lower resistor value. It was also
found that the first phase energization leads to the highest inrush current among the three phases and, as a result, the resistor
can be sized according to its effect on the first phase energization. With the help of nonlinear circuit theory [3], we managed
to derive an analytical relationship between the peak of the inrush current and the size of the resistor, which results in a transient-analysis based theory for the resistor selection. One of the
objectives of this paper is to present the analytical work and the
resultant design guide for the scheme. The developed analytical
method is an improvement over the one published in the classic
Westinghouse T&D Reference Book [4] and can be used to analyze general inrush current phenomenon of transformers and
In addition, this paper also addresses the main limitation of
the proposed scheme—the rise of neutral voltage. The use of
surge arrester is proposed to overcome the limitation. Performance of the improved scheme is presented.
The significance of this work is that it is a rigorous analytical study of the transformer energization phenomenon. The results reveal a good deal of information on inrush behavior of
transformers and the characteristics of the sequential energization scheme. In addition, the developed analytical method made
it possible to accurately estimate energy requirements for the
grounding resistor and the voltage limiting surge arrester.
Since the scheme adopts sequential switching, each switching
stage can be discussed separately. For first phase switching, the
scheme performance is straightforward. The neutral resistor is
in series with the energized phase and its effect will be similar to
a pre-insertion resistor. When the third phase is energized, the
voltage across the breaker contacts to be closed is essentially
close to zero due to the existence of delta secondary or three-
0885-8977/$20.00 © 2006 IEEE
Fig. 3. (a) Transformer electrical equivalent circuit (per-phase) referred to the
primary side. (b) Simplified, two slope saturation curve.
Fig. 2. Maximum inrush current as affected by the neutral resistor for a 30
, 3 limb transformer, [1]. (Top: experimental, bottom:
kVA, 208/208,
Y 01
legged core. So there will be minimal switching transients for
when the 3rd phase is energized [1], [2].
The 2nd phase energization is the one most difficult to analyze. Fortunately, we discovered from numerous experimental
and simulation studies that the inrush current due to 2nd phase
energization is lower than those due to 1st phase energization
(Fig. 2). This is true for the region
for the same value of
where the inrush current of the 1st phase is decreasing rapidly
As a result, we should focus on analyzing the first phase energization to develop more precise sizing criteria for the neutral
as function of the operating flux linklinear inductance
ages is represented as a linear inductor in unsaturated “ ”
and saturated “ ” modes of operation respectively, Fig. 3(b).
Secondary side resistance
and leakage reactance
as reand
represent the
ferred to primary side are also shown.
primary and secondary phase to ground terminal voltages, respectively.
During first phase energization, the differential equation describing the behavior of the transformer with saturable iron core
can be written as follows:
In order to represent the highest saturation level without losing
generality, switching angle of zero on the applied sinusoidal
voltage waveform together with a positive residual flux polarity
is assumed throughout the analysis. In this case, saturation takes
place at the positive side of the saturation curve. Accordingly,
the general inrush current waveform in unsaturated and saturated modes of operation can be given by
One of the main focal points of this paper is to develop a solid
design methodology for the neutral resistor size. Our approach
presented here is based on deriving an analytical expression relating the amount of inrush current reduction directly to the neutral resistor size. Preliminary results have been presented earlier by the authors in [5]. An accurate expression for inrush current will eliminate the requirement of computer simulation on
a case-by-case basis. Few investigations in this field have been
done and some formulas were given to predict the general wave
shape, harmonic content or the maximum peak current [3]–[9].
For the presented application, it was required that the expression
can accurately present the inrush current waveform over a wide
range of neutral resistance values taking into account system
impedance, residual flux value and the neutral resistor itself.
A. Inrush Current Expression
The transformer behavior during first phase energization can
be modeled through the simplified equivalent electric circuit
shown in Fig. 3 together with an approximate two-slope saturation curve, [3]–[8]. In Fig. 3(a), and present the total primary side resistance and leakage reactance. The iron core non-
Generally, transformers operate in unsaturated mode immediately after energization since the initial “or residual” flux is
below the saturation flux level . For small neutral resistor
values, the magnetizing impedance of the switched phase will
Fig. 4. Analytical and simulation inrush current waveforms (first cycle) for 30
Yg 0 1
be very high compared to other linear elements in the series circuit and the supply voltage will be mainly distributed across the
magnetizing branch until saturation is reached. The saturation
time can be calculated as follows:
Fig. 5. I
72/13.8 kV
(R ) compared to the simulation peak current for 132.8 MVA,
Yg 0 1 3 limb transformer.
The inrush peak expression (3) can be rewritten as follows:
in (5) is a dimensionless factor which depends on
) as well as
transformer saturation characteristics (
ratio during saturation
the total
, and
are the nominal peak flux linkages,
supply voltage, and angular frequency, respectively. Fig. 4
shows the first cycle, analytical and simulation waveforms for
the 30 kVA transformer with neutral resistor values of 0.1, 0.5,
and 1.0 (Ohm), respectively, and a residual flux of 0.75 (p.u.).
The inrush waveform will reach its peak during saturation
close to when the sinusoidal term peaks. This assumption is
valid for two reasons; first, the exponential term coefficient
is fractional as compared to the sinusoidal term amplitude
. Second, the saturation time
, is small as
increases which will introduce
a small shift in the peak current to appear slightly before the sinusoidal peak value. The saturation current “ ” is small as compared to the inrush peak and can be neglected. Accordingly, the
can be
peak time and the peak inrush current as function of
expressed as follows:
, the total
For the maximum inrush current condition
energized phase
ratio including system impedance is high
and accordingly, the damping of the exponential term in (5)
during the first cycle can be neglected
Typical saturation and residual flux magnitudes for power
transformers are in the range
Accordingly, switching at voltage zero instant with a polarity
that matches the maximum possible residual flux, the saturation
are within the
angle “ ” w.r.t. instant of switching and
following ranges, respectively
analytical and simulation curves for the 132.8
MVA transformer described in [1] during first phase switching
are shown in Fig. 5.
values leading to considerable inrush reduction will reHigh
ratios. It is clear from (6) and (8) that
rasult in low
tios equal to or less than 1 ensure negative dc component factor
” and hence the exponential term shown in (5) can be
conservatively neglected. Accordingly, (5) can be rewritten as
B. Neutral Resistor Sizing
Based on (3), it is now possible to select a neutral resistor size
that can achieve a specific inrush current reduction ratio
given by
Using (7) and (10) to evaluate (4), the neutral resistor size
which corresponds to a specific reduction ratio can be given
Equations (9) and (11) reveal that transformers with less
severe saturation characteristics “high saturation flux and low
maximum residual flux values” require a higher neutral resistor
value to achieve the desired inrush current reduction rate. Based
on (9) and (11), the inrush current reduction of 90% can be
achieved within the range of
Based on (12), a small resistor “less than 10 times the saturation series reactance” can achieve more than 90% reduction in
inrush current. The amount of reduction in flux during the first
cycle can be found from (2) as follows:
Fig. 6. Simulation of the 3 300 MVA, Yg-Y transformer [10], during second
phase switching for R = 150:0 (Ohm).
Within the optimum neutral resistor value defined by (12), the
total flux reduction during first phase switching is within
As the second cycle starts, an initial flux level of
will exist. This results in the absence of
inrush current after the first cycle since the maximum flux
is close to—or below—the saturation flux.
Transformer behavior during second phase switching was
observed through simulation and experiments to vary with respect to connection and core structure type. However, a general
behavior trend exists within low neutral resistor values where
the scheme can effectively limit inrush current magnitude.
For cases with delta winding or multi-limb core structure,
the second phase inrush current is lower than that during first
phase switching. Single phase units connected in Yg–Y have
a different performance as both first and second stage inrush
currents has almost the same magnitude until a maximum reduction rate of about 80% is achieved. Generally, based on the
well-known saturation characteristics of power transformers,
any reduction in inrush current is a result of limiting the maximum flux that can build up in the core. In this section, the
performance of the proposed inrush mitigation scheme during
second stage switching will be qualitatively analyzed and com. It will
pared to the first switching stage for small values of
be shown that the transformer saturation level during second
phase switching is less than that during first phase switching.
A. Three Single Phase Units Connected in Yg–Y
For this condition, the transformer can be modeled using two
saturable inductor circuits representing each phase. The coupling between both switched phases is introduced only through
the neutral resistor. For any energized phase , the flux
function of the primary phase voltage
can be given by
and the neutral voltage
Phase B will start operating in the unsaturated region with
its own residual flux. As a result, both phase currents will be
low and the neutral voltage remains close to zero,
As soon as Phase B reaches saturation, its current will increase
and the neutral voltage will start to build up. The neutral current
will be mainly due to the contribution of phase B. Hence, the
neutral resistor can be assumed to be in series with phase B
and a similar inrush reduction performance, to that of first phase
switching, will hold. The process will continue until the neutral
voltage integral “amount of reduction” becomes sufficient to
drive Phase A into saturation. With phase A originally in steady
state, a disturbance in flux equal to the difference between the
rated and saturation flux values is required for phase A to reach
saturation. Conservatively assuming that the reduction in flux in
Phase B results in an increase of the same amount in phase A,
to achieve at least 20 to 35%
it will be possible to increase
reduction in its flux before disturbing phase A, Fig. 6.
is increased further, more inrush current reduction can
be achieved in phase B until both phases reach the same satu. As the difference beration level for a specific value of
tween saturation and rated flux values increases, more reduction
in phase B current can be achieved. The same conditions apply
during third switching stage.
B. Transformers With Delta Winding and/or 3-Limb Structures
The performance during sequential switching for this type
, banks
will be quite different than for single phase,
transformers due to the following reasons:
• dynamic flux will exist in un-energized phases;
• inrush current can exist in one phase due to external saturation in un-energized phase (return path of the flux).
The existence of dynamic flux in un-energized phases will make
the initial flux in the switched phase dependent on the instant
of switching. In order to maximize the flux of the switched
Fig. 7. Simulation of the 30 kVA transformer during second phase switching
condition showing the phase fluxes and effect of delta winding current for small
values of R = 0:1 (Ohm).
phase and consequently represent highest saturation condition,
the critical switching instant “ ” should be found. The flux in
phase B after switching can be calculated as follows:
Fig. 8. Modeling the delta winding during the saturation condition of phase C.
instant of switching
The maximum theoretical flux that can be reached in phase B
can accordingly be given by
For the maximum flux condition
on phase B voltage waveform
The switching angle of
corresponds to a zero initial flux value in phase A and, as a result,
no initial flux exists when the second phase is energized. This
finding is of importance since it proves that the maximum theoretical saturation level during second phase energization will be
lower than that during the energization of the first phase which
Immediately after 30 of the switching instant, the fluxes in
phases A and B are both positive and determined by the terminal voltage integral of both phases. This will lead phase C
which represents the return path of both fluxes to saturate first.
As shown in Figs. 7 and 8, the saturation of phase C will drive a
delta winding current equal to the magnetizing current of phase
C under saturation. The induced delta winding current will be reflected as zero sequence current of the same magnitude flowing
through phases A and B and a neutral current equal to twice the
delta current.
For phase B, both integrals of the terminal and the neutral
voltages have the same polarity and hence the delta winding
will help reducing saturation level further in phase B. For phase
A, the supply voltage waveform will have opposite polarity to
the neutral voltage, however, due to the difference between the
saturation and rated flux values, the disturbance in phase A will
be less than that observed in switched phase B.
In case of multi limb transformers with no delta winding,
the second and third switching stages behavior depends on the
number of core limbs. For 3-Limb transformers, the flux in the
two energized limbs will add up into the third limb. As the third
limb saturates, the return flux path of phase A and B will experience saturation and as a result a neutral current equals twice the
phase current will flow. This will result in a similar effect to that
from a delta winding. On the other hand, for transformers with
4 or 5 limbs, and shell form cores, the return path of the flux
from phases A and B will be unsaturated to some degree and
the performance of the scheme will be similar to that of three
single phase units connected in Yg–Y.
From simulation studies carried out on various transformer
types and connections, it was found that the peak neutral voltage
will reach values up to 1 (p.u.) rapidly as the neutral resistor
value is increased. Typical neutral voltage peak profile against
neutral resistor size is shown in Fig. 9 for the 132.8 MVA transformer during 1st and 2nd phase switching.
The scheme performance during the complete switching sequence is shown in Fig. 10 with optimum neutral resistor of 50
. A delay of one second between each switching stage is
Fig. 9. Neutral voltage peak as a function of R during the first and second
switching stages for the 132.8 MVA transformer.
Fig. 11. I
(R )=I (0) percentage inrush current peak for different arrester saturation voltages R = 50 (
Fig. 10. Phase currents, neutral current and neutral voltage during complete
switching sequence for the 132.8, 72/13.8 kV, Yg-D transformer R = 50 (
quency insulation level at neutral for liquid immersed transformers at system voltages of 25 kV or below is 10 kV but not
less than the nominal line voltage. In this case, the proposed
scheme can be applied without modification for this type at interconnection levels of 25 kV or below. For voltages higher than
25 kV and up to 69 kV, the neutral voltage rise need to be limited to 50% of the nominal line voltage in order to comply with
the insulation requirement at neutral, [12]. In case of dry type
transformers, the minimum insulation level at neutral should be
at least 4 kV at system voltages of 1.2 kV and extends to 10 kV
at higher voltage levels. If the transformer is designed for ungrounded Y connection, the neutral insulation level should be
the same as the line terminal level [13].
B. Neutral Resistor With Neutral Voltage Limiting Arrester
required to allow phase fluxes to lose most of the dc component. The neutral voltage during the first cycle will reach 85%
of the rated phase voltage. Quickly after the first cycle, the transformer is unsaturated and the neutral voltage is negligible since
. The unsaturated magnetizing reactance is about
900 times the saturation reactance of a transformer, [11].
Accordingly, with the transformer operating in unsaturated
mode, the neutral resistor voltage is negligible. Within the optimum resistor value, the neutral voltage peak is less than 0.5
(p.u.) during second phase energization. As soon as the third
phase is switched in, the neutral voltage will remain close to
It is a common industry practice to grade the insulation over
the Yg winding for solidly grounded transformers [11]–[14].
This can introduce limitations to the applicability of the proposed scheme at high voltage levels. The following section addresses the standard requirements and limitations for the application of the proposed scheme to both dry-type and liquid immersed transformers.
A. IEEE Standards Requirements
A review of the IEEE/ANSI standards [12]–[14] has been carried out in order to evaluate the acceptable neutral voltage rise
limit on different power transformer types. The main application of the proposed scheme is the generator’s step up transformers for IPP “Independent Power Producer” which are interconnected to the system at the distribution or sub transmission levels. The interconnection transformer is preferably Wyegrounded on the system side and Delta connected on the generator side [15], [16]. According to [12], the minimum low fre-
Arrester(s) connected in parallel with the neutral resistor
could limit the neutral voltage rise to the standard level. Actually, the resistor-arrester arrangement presents a nonlinear
resistor saturating at the arrester’s saturation voltage. According
to (15), limiting the neutral voltage rise will reduce the neutral
voltage integral and hence, reduce the technique’s efficiency.
Limiting the neutral voltage rise to 0.5 (p.u.) will have effect
only during first phase switching, Figs. 9 and 10 which is more
desirable in order to limit the energy dissipated through the
curves of the arrester-neutral resistor
arrester. The
arrangement is shown in Fig. 11 for the 132.8 MVA transformer.
A similar deduction procedure to the one presented in section
III leads to the following inrush expression:
Accordingly, the peak inrush current during arrester operation
can be expressed as
From (18), the amount of reduction in current will depend
. However,
on how fast the arrester will become saturated,
since the neutral voltage will start rising after the transformer
Fig. 12. Phase currents, neutral current, and neutral voltage during complete
switching sequence R = 50 (
). Arrester saturation voltage is 0.5 (p.u.).
Fig. 14. Accumulated energy during different switching stages. Results for the
132.8 MVA transformer with infinite system.
sorbed by the neutral resistor during the complete switching sequence for the 132.8 MVA transformer for the case shown in
Fig. 10. It is clear from Figs. 14 and 10 that negligible neutral
voltage will exist after the first cycle of the 1st phase energization and the energy dissipated through the resistor can accordingly be calculated as follows:
Fig. 13. Phase currents, fluxes, neutral current and neutral voltage during complete switching sequence for the 132.8 MVA with 1000 MVAsc system.
saturates at , the neutral voltage integral will have a maximum
approaches . This
limit as the arrester saturation time
clarifies the “almost” steady profile of the inrush current as
increases shown in Fig. 11. The resistor-arrester arrangement
performance during complete switching sequence is shown in
Fig. 12. The results shown in Figs. 10 and 12 were obtained
assuming an infinite system bus.
The scheme performance with 1000 MVA short circuit
impedance, assuming 10% of this impedance to be resistive
is shown in Fig. 13. It is shown that inrush current reduction
to less than 3 times the nominal current can be achieved considering a relatively small source impedance and at the same
time limiting the neutral voltage to 0.5 (p.u.). In addition, the
scheme will have much better performance with regards to the
settling time of inrush currents.
C. Energy Requirements
Simulation studies can provide an accurate calculation of energy requirement level for the scheme. In this section, approximate formulas will be given for a quick—but accurate—estimate of the energy withstand capability for both the resistor and
the resistor-arrester arrangements. As mentioned earlier, there
will be negligible neutral voltage across the resistor after the
third phase switching. Accordingly, our focus will be on the assessment of energy requirements during first and second phase
switching stages. Fig. 14 shows the accumulated energy ab-
For the second phase, as can be seen from Figs. 6 and 7, the
neutral current can be presented using two sinusoidal half-waves
of twice the frequency. Since the neutral voltage rise during
second phase is around 0.5 (p.u.) with the same neutral resistor,
the energy during 60-cycle period of the second phase switching
can be calculated as follows:
As can be seen from (20), most of the energy absorbed by the
grounding resistor will be during second phase switching. After
the third phase is switched in, the neutral current will be very
close to zero and energy dissipation through the resistor can be
For the resistor-arrester arrangement, the arrester will be active only during the first cycle of the first switching stage. As
shown in (17) the total current through the switched phase will
be composed of a dc component through the resistor and an ac
component through the arrester.
Accordingly, the energy dissipated through the resistor and
the arrestor can be calculated, respectively, as follows:
Fig. 15. Accumulated energy during different switching stages (J). Arrester set
at 0.5 (p.u.) saturation voltage with the 1000 MVAsc system.
Fig. 16. Voltage at the primary side of a 22/0.48, 160 kVa, Y-D transformer
due to energizing Phase A. Top: isolated neutral. Bottom: neutral grounding.
The arrester will not be active for saturation voltages of 0.5
(p.u.) or higher within the optimal neutral resistor value. The
neutral resistor energy is the same as that of the original scheme
during second switching stage for the same
. As shown in
Fig. 15, the total energy absorbed by the resistor during all
switching stages is about 1.30 MJ, and 250 kJ for the surge arrester(s).
Neutral grounding resistors capable of handling 1000–1500
A root mean square (rms) continuous current for 10 s at voltage
levels of 33 kV or more are commercially available today. Arresters can handle less energy dissipation (absorption) than resistors. This is due to the fact that they are originally designed
for short period operation duration. However, a way of stacking
a number of arresters in parallel in order to handle a higher energy rating has been suggested in [17]. Typical energy capability for arrester class up to 48 kV is 4 to 4.9 kJ/kV [11] and
The proposed sequential energization scheme could expose a
transformer to ferroresonance. Fortunately, the neutral resistor
is in series of the resonant circuit and will provide sufficient
damping to prevent ferroresonance from happening. In fact, [20]
proposed the idea of using a neutral resistor to mitigate ferroresonance. Based on numerous TNA studies, [20] found that a neuis sufficient to prevent the occurtral resistor less than 0.05
rence of ferroresonance in Yg–D transformer banks. Based on
the finding, we can conclude that the proposed scheme will not
experience ferroresonance problem. Our simulation studies on
22/0.48 kV, 4.5%, 160 kVA, Y–D transformer, also confirmed
this conclusion. Fig. 16 shows the voltage waveforms at the energizing side of the transformer due to energizing phase A. It
is clear that using the optimal resistor successfully damped the
overvoltage at un-energized phases B and C within one cycle.
This paper presented an improved and more complete design criterion for a novel transformer inrush current reduction
scheme. It was shown that a small neutral resistor size of less
than ten times the transformer series saturation reactance can
achieve 80–90% reduction in inrush currents among the three
phases. The transient performance of the scheme was presented
and it was demonstrated through detailed analysis that the first
phase switching leads to the highest inrush current level. The
paper has also addressed the main practical limitation of the
scheme as the permissible rise of neutral voltage. A feasible
application range for both dry type and liquid immersed transformer has been proposed and the use of surge arresters to extend the application range of the scheme has also been presented. Formulas were also given to estimate the required energy withstand capability for both the neutral resistor and the
arrestor if applicable.
[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, pt. 1, pp. 943–949, Apr. 2005.
[2] W. Xu, S. G. Abdulsalam, Y. Cui, S. Liu, and X. Liu, “A sequential
phase energization method for transformer inrush current reduction—part II: Theoretical analysis and design guide,” IEEE Trans.
Power Del., vol. 20, no. 2, pt. 1, pp. 950–957, Apr. 2005.
[3] A. Boyajian, “Mathematical analysis of nonlinear circuits,” General
Electric Rev., pp. 531–537, 745–751, Sep. and Dec. 1931.
[4] Westinghouse Electric Corporation, Electric Transmission and Distribution Reference Book, 4th ed. East Pittsburgh, PA, 1964.
[5] S. G. Abdulsalam and W. Xu, “Analytical study of transformer inrush
currents and its applications,” in Proc. Int. Conf. Power System Transients, Montreal, QC, Canada, 2005.
[6] B. Holmgrem, R. S. Jenkins, and J. Riubrugent, Transformer inrush
current CIGRE paper 12-03, CIGRE. Paris, France, pp. 1-13, 1968.
[7] H. A. Peterson, Transients in Power Systems. New York: General
Publishing Co., General Electric, 1951.
[8] L. F. Blume, G. Camilli, S. B. Farnham, and H. A. Peterson, “Transformer magnetizing inrush currents and influence on system operation,” AIEE Trans. Power App. Syst., vol. 63, pp. 366–375, Jan. 1944.
[9] P. C. Y. Ling and A. Basak, “Investigation of magnetizing inrush current in a single-phase transformer,” IEEE Trans. Magn., vol. 24, no. 6,
pp. 3217–3222, Nov. 1988.
[10] 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.
[11] A. Greenwood, Electrical Transients in Power Systems, 2nd ed. New
York: Wiley, 1991.
[12] IEEE Standard General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE Std. C57.12.00-2000,
2000, pp. 1-53.
[13] IEEE Standard General Requirements for Dry-Type Distribution and
Power Transformers Including Those With Solid Cast and/or ResinEncapsulated Windings, IEEE Std. C57.12.01-1998, Dec. 31, 1998.
[14] IEEE standard requirements, terminology, and test procedure for neutral grounding devices, ANSI/IEEE Std. 32-1972, 1972.
[15] British Columbia Transmission Corporation, 69 kV to 500 kV interconnection requirements for power generators, May 2004.
[16] BC Hydro, 35 kV and below interconnection requirements for power
generators, Jun. 2004.
[17] J. J. Lee and M. S. Cooper, “High-energy solid-state electrical surge
arrestor,” IEEE Trans. Parts, Hybrids Packag., vol. PHP-13, no. 4, pp.
413–419, Dec. 1977.
[18] M. L. B. Martinez and L. C. Zanetta, Jr., “A proposal to evaluate the
energy withstand capacity of metal oxide resistors,” in Proc. 11th
Int. Symp. High Voltage Engineering, Aug. 23–27, 1999, vol. 2, pp.
[19] M. Martinez and L. Zanetta, “On modeling and testing metal oxide
resistors to evaluate the arrester withstanding energy,” presented at the
IEEE Dielectr. Mater., Meas. Appl. Conf., 2000, Publ. No. 473.
[20] R. H. Hopkinson, “Ferroresonant overvoltage control based on TNA
tests on three-phase wye-delta transformer banks,” IEEE Trans. Power
App. Syst., vol. PAS-87, no. 2, pp. 353–361, Feb. 1968.
Sami G. Abdulsalam (S’03) received the B.Sc. and M.Sc. degrees in electrical
engineering from El-Mansoura University, El-Mansoura, Egypt, in 1997 and
2001, respectively. He is currently pursuing the Ph.D. degree in electrical and
computer engineering from the University of Alberta, Edmonton, AB, Canada.
Currently, he is with the Enppi Engineering Company, Cairo, Egypt. His research interests are in electromagnetic transients in power systems and power
Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the University
of British Columbia, Vancouver, BC, Canada, in 1989.
He was an Engineer with BC Hydro, Burnaby, BC, Canada, from 1990 to
1996. Currently, he is a Professor with the University of Alberta, Edmonton,
AB, Canada, and a Changjiang Professor of Shangdong University, Shangdong,
China. His research interests are power quality and harmonics.
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