On the ringdown transient of transformersN. Chiesa, A. Avendano, H. K. Høidalen, B. A. Mork, D. Ishchenko, and A. P. Kunze.

Abstract–This paper details the analysis of transformer ring-down transients that determine the residual fluxes. A novel energyapproach is used to analyze the causes of transformer saturationduring de-energization. Coupling configuration, circuit breakerand shunt capacitor influence on residual flux have been studied.Flux-linked initialization suggestions are given at the end of thepaper.

Keywords: Power transformer, inrush current, ringdown tran-sient, residual flux, shunt capacitance.

I. I NTRODUCTION

T HE energization of a power transformer may result ina severe inrush current. A power transformer inrush

current is characterized by a high magnitude of the currentfirst peak. This current is damped by the dissipative elementsof the transformer and reaches a steady state value afterseveral cycles. The first peak can be in the same order ofmagnitude as the transformer short circuit current and maycause undesirable events (false operations of protective relays,mechanical damages to the transformer windings, excessivestress on the insulation and voltage dips that can influence thesystem’s power quality).

The scientific community is well aware of this problemand many papers have been published concerning inrushcurrent estimation, modeling and mitigation [1]–[6]. Inrushcurrent worst case is generally estimated based on air coreinductance method. The modeling of energization transients ischallenging and is an active topic in the research community;the preferred way of limiting inrush currents has been movedfrom resistor burden and shunt capacitor, to more effectivesynchronized switching techniques. However, optimal reduc-tion of the stresses can be achieved only with an accurateknowledge of the residual fluxes.

Residual fluxes are due to the remnant magnetization of thecore, after a transformer has been deenergized. The residualflux pattern is mostly unknown or not known precisely due tothe complexity of the ringdown transient itself [5]. Ringdowntransients are a little known issue and a proper understandingof these phenomena is of great importance for establishingsystem protection schemes and relay reclosing time philoso-phies, particularly in cases where shunt capacitor banks areinstalled on transmission lines.

N. Chiesa and H. K. Høidalen are with the Department of Electric Power En-gineering, Norwegian University of Technology (NTNU), Trondheim, Norway(e-mail of corresponding author: nicola.chiesa@elkraft.ntnu.no).A. Avendano, B. A. Mork, D. Ishchenko and A. P. Kunze are with theDepartment of Electrical and Computer Engineering, MichiganTechnologicalUniversity (MTU), Houghton, MI 49931 USA.

Presented at the International Conference on Power Systems Transients(IPST’07) in Lyon, France on June 4-7, 2007

Saturation curve

Time

Flu

x-lin

ked,

Cur

rent Flux-linked

Current

Time

Flu

x-lin

ked,

Vol

tage

Voltage

Flux-linked λFlux-linked λ + λ0

Current

Tim

e

Current f(λ + λ0 )

Current f(λ)

Fig. 1. Qualitative representation of the inrush current phenomenon; theeffect of the residual flux.

The purpose of this paper is to investigate the ringdownphenomenon that occurs when a transformer is deenergizedand leads to the creation of residual fluxes.

II. T HE RINGDOWN TRANSIENT PHENOMENA

The residual flux value is a fundamental parameter duringthe re-energization of a transformer since it affects the firstpeak of the inrush current. Assuming a sinusoidal waveformand neglecting the dissipative elements, it is possible to outlinethe fundamental relations that lead to the creation of an inrushcurrent:

v(t) = v sin(ωt + φ) (1)

λ(t) = λ0 +

∫ t

0

v(t) dt = (2)

= λ0 +v

ω(cos(φ) − cos(ωt + φ))

i(t) = L(λ) λ(t) (3)

whereλ0 is the residual flux present at the energization instant.Fig. 1 qualitatively represents the inrush current worst case;with t = T

2andφ = 0, (2) becomes:

λ(T/2) = λ0 + 2v

ω= λ0 + 2 λ (4)

with λ = vω

being the peak of the rated flux-linked. Thus,switching at zero voltage crossing causes the doubling of theflux-linked first-peak.

Due to the flat nature of the saturation curve, a smallincrease of flux peak (residual flux) can drive the iron coreof the transformer into heavy saturation. The plot in the lowerleft corner of Fig. 1 shows a complete inrush transient andcan be noticed how the DC flux offset is slowly damped tozero together with the current by the dissipative elements aswinding resistance and core losses. Winding resistance hasmore importance in the initial part of the ringdown: highcurrent produces highRi2 losses. Hysteresis losses do not

V V

I

UI

Rz Xz

RLC

50 Hz

Fig. 2. ATP circuit for inrush/ringdown transient simulations.

Time [ms]

0 40 80 120 160 200

Ene

rgy

[J]

0

400

800

1200

1600

Ene

rgy

[J]

0.00

0.04

0.08

0.12

0.16

Parallel resistance

Series resistance

Fig. 3. Simulation of energy dissipated from the resistive elements,(C = 5 µF); 290-MVA transformer.

add noticeable damping to the inrush current and only affectthe magnitude of the residual magnetization [7].

The residual flux is created when a transformer is discon-nected from the power grid. At the end of a de-energizationtransient both the voltages and currents decrease to zero,however the flux in the core retains a certain value definedas residual flux. A ringdown transient is a natural LC re-sponse that appears as the stored energy dissipates whenevera transformer is deenergized and can be simulated with theATP/EMTP circuit shown in Fig. 2. The transformer corehas been modeled with a type-98 nonlinear inductor (L) anda linear resistor (R). The use of a non-hysteretic inductordoes not allow the estimation of residual flux. ATP offersa type-96 hysteretic inductor, however it has been dismisseddue to the proved poor quality of this model [8]–[10]. Thetransformer short circuit impedance is modeled by the windingresistance (RZ) and the leakage reactance (XZ). Sources ofcapacitance (C) include transformer winding capacitances,capacitor banks, and transmission lines and cables connectedto the transformer terminals during the de-energization. Theparameters of the circuit are extracted from a 290-MVA three-phase power transformer whose test report is shown in Tab. Iin the Appendix.

Fig. 3 shows the energy dissipated by the resistive elementsof the circuit during a ringdown transient. The energy dissi-pated by the series resistance (RZ) is much smaller than theone dissipated by the parallel resistance (R). Thus, the circuitcan be simplified in a parallel RLC circuit, disregarding theseries resistance and reactance (RZ = 0 andXZ = 0).

Fig. 4 shows the energy dissipated by the resistance andstored in the reactive elements of the circuit in steady stateconditions. The energy dissipated constantly increases asitrepresents the active energy drawn from the source and con-sumed by the circuit (losses). The analysis of the energy storedin the capacitor (EC) and in the inductor (EL) is of particularinterest and three main situations can be pointed out:

• maximum energy stored in the capacitor:EC = max,EL = 0, voltage peak (tSW = 20 ms);

• maximum energy stored in the inductor:EL = max,EC = 0, voltage zero crossing (tSW = 25 ms);

Energy dissipated Capacitive energy

Inductive energy Total stored energy

Time [ms]

0.015 0.020 0.025 0.030 0.035

Ene

rgy

[J]

0

500

1000

1500

2000

2500E C = max

V peak

E L =max

V zero crossE C = E L

Fig. 4. Simulated energy at steady state (C = 5µF); 290-MVA transformer.

• equal energy stored in capacitor and inductor:EC = EL

(tSW = 23.75 ms for this particular L-C configuration).

Fig. 5 shows the energy transient when the circuit isswitched out at these three different instants. At any instantduring the transient the energy conservation law is valid:

ER + EC + EL = 0 (5)

with ER being the energy dissipated by the resistor. A com-parison of Figs. 4 and 5 reveals that the total energy dissipatedby the resistor is equal to the total energy stored at steady stateby the reactive elements of the circuit:

|EC(tSW ) + EL(tSW )| = |ER(t∞) − ER(tSW )| (6)

with tSW being the switching instant andt∞ being the endof the transient. When switching at voltage peak the netenergy released by the inductor is zero. However, during thetransient some energy is exchanged between the capacitor andthe inductor. Analogous considerations can be made for thesecond case, with switching at zero voltage. For this particularconfiguration the maximum energy stored in the inductor issmaller then the maximum energy stored in the capacitorcausing lower energy dissipation in the resistive element.Dueto the nonlinear characteristic of the inductor the point whereEC = EL does not always represent the minimum total energystored as in a linear system.

Fig. 6 shows flux-linked and current ringdown transientsfor different values of capacitanceC, zero crossing and peakvoltage switching instants. It is important to notice how theringdown natural frequency decreases as the value of thecapacitance increases. For a parallel RLC circuit the ringdowncharacteristic is described by:

ω0 =1

√

L(i) C(7)

α =1

2 R C(8)

ωN =√

ω2

0− α2 (9)

ξ =α

ω0

=1

2 R

√

L(i)

C(10)

where ω0 is the undamped resonant frequency,α is thedamping coefficient,ωN is the natural frequency, andξ is thedamping ratio (ξ < 1 underdamped,ξ = 1 critically damped,

-1500

-750

0

750

1500

Ene

rgy

[J]

-400

-200

0

200

400

Time [ms]

0 50 100 150 200-200

0

200

400

Energy dissipated

Inductive energy

Capacitive energy

tSW =23.75 ms

tSW =25 ms

tSW =20 ms

Fig. 5. Simulation of energy during ringdown transients at differentdisconnection instants (C=5µF), 290-MVA transformer.

ξ > 1 overdamped). Due to the large winding capacitance,large transformers usually haveξ << 1 thus ωN ≈ ω0. Ahigher value of capacitance reduces the value of the dampingcoefficient α, increasing the duration of the ringdown tran-sient. For a fixed value of inductance, the ringdown naturalfrequency will be inversely proportional to the square rootofthe installed capacitance. In case of a nonlinear inductance thevalue of the synchronous frequencyωN is not constant. Theminimum of the natural frequency (ωN min) is obtained whenthe magnetization level is small enough and the inductance ismagnetized in the linear area of the saturation curve.

A lower natural frequency causes a higher flux density inthe core. However, it is inaccurate to deduce that this is thecause of the increase of flux-linked and current peaks as shownin Fig. 6 (C = 5 µF and10 µF with tSW = 20 ms). Due tothe nonlinearity of the core inductance, the natural frequency(ωN ) reduces from the synchronous frequency (ωS = 50 Hz)to the minimum natural frequency (ωN min). Fig. 7 shows that

Time [ms]

0 50 100 150 200

Fre

quen

cy [H

z]

0

20

40

60

20ms, 10µF25ms, 10µF

ωS

ωNmin

Fig. 7. Simulation of frequency variation during ringdown; 290-MVAtransformer.

the time (resolution = one half period) required to reach theminimum natural frequency is not constant and is related to thedisconnection instant. Since the minimum natural frequency isreached at the end of the de-energization transient, the gradualreduction of the frequency cannot justify the core saturation.

Referring to Figs. 4 and 5, and disconnection instanttSW = 20 ms, the total energy at the disconnection instantis equal to the maximum capacitive energy. After a quarterof period some of the capacitive energy has been dissipatedby the resistive element, but the remaining energy must betransfered to the inductance. This quota part is higher thanthemaximum steady state inductive energy. In order to store alarger amount of energy in the same inductor the current hasto increase considerably:

EL =1

2L I2 (11)

The effect is emphasized by the nonlinear characteristic oftheinductor. Thus, core saturation during ringdown is experiencedonly when the total energy stored in the reactive elements(inductances and capacitances) at the disconnection instant ishigher than the maximum inductive energy at steady state.

III. L ABORATORY MEASUREMENTS

Laboratory measurements of residual flux have been per-formed on three distribution transformers with the followingcharacteristics:

• 3-legged, 15-kVA, 60 Hz, 240(120)/208 V, Dyn/Yyn ;• 5-legged, 150-kVA, 60 Hz, 12470/208 V, YNYn (with an

airgap between the main legs and the outer legs);• 3-legged, 500-kVA 60 Hz, 21600(12470)/480 V,

YNyn/Dyn (amorphous core).

0 40 80 120 160 200-90

-60

-30

0

30

60

90

-60

-40

-20

0

20

40

60

Time [ms]0 40 80 120 160 200

-90

-60

-30

0

30

60

90

-60

-40

-20

0

20

40

60

0 40 80 120 160 200-90

-60

-30

0

30

60

90

-60

-40

-20

0

20

40

60-90

-60

-30

0

30

60

90

Cur

rent

[A]

-300

-200

-100

0

100

200

300

-90

-60

-30

0

30

60

90

-150

-100

-50

0

50

100

150

Link

age

Flu

x [W

b-t]

-90

-60

-30

0

30

60

90

-60

-40

-20

0

20

40

60C=1µF, tSW=20ms

C=1µF, tSW=25ms

C=5µF, tSW=20ms

C=5µF, tSW=25ms

C=10 µF, tSW=20ms

C=10 µF, tSW=25ms

Current

Linkage Flux

Fig. 6. Simulation of flux-linked and current waveforms duringringdown; 290-MVA transformer.

X Data

-1

0

1

Ph. 1

Ph. 2

Ph. 3

Zero seq.

Flu

x-lin

ked

p.u.

-0.4

-0.2

0.0

0.2

0.4

Sw.B Dyn

Sw.A Yyn

Sw.B Yyn

-0.4

-0.2

0.0

0.2

0.4

Sw.C Yyn

Sw.B Yyn

Time [ms]0 4 8 12 16

-0.4

-0.2

0.0

0.2

0.4

Sw.C Dyn

Sw.C Yyn

Sw.D Yyn

(a) Rated Flux

(b) 15-kVA three-leg

(d) 500-kVA three-leg

(c) 150-kVA five-leg

Fig. 8. Residual flux as function of the disconnection time; measured on15-150-500 kVA transformers.

Two series of tests have been performed to analyze specificbehaviors of the ringdown transient. In the first test a totalof four different types of molded-case circuit breakers havebeen used to examine the relation between the results and theswitching gear used. The impact of the winding connectionconfiguration is also verified. The second set of tests studiesthe influence of shunt capacitances on the ringdown transient.

A. Connection configuration and circuit breaker influence

Fig. 8 shows the relation between residual fluxes (calculatedfrom the integral of the phase voltage) of the different phasesas function of the disconnection instant for the 15-kVA, 150-kVA and 500-kVA transformer respectively. No synchronizedswitching device has been used; the various points have beenmeasured with random operations of the circuit breakers. Analternative to Fig. 8 is to establish a complementary cumulativeprobability distribution to answer how often the residual flux isabove a particular level, but in this case the phase correlationis lost.

The results of these tests show that the maximum residualflux lies between 0.2 and 0.4 p.u. of the rated flux-linked.Moreover, the maximum residual flux of the central phase

results slightly higher than in the other two phases for the15 and 500-kVA transformers.

For the smallest test object the curves representing the resid-ual magnetization as function of the disconnection instantarein phase with the rated flux waveforms. The phase correlationis reduced as the rating of the transformer increases. Withthe increase of the transformer’s physical size, the windingsize increases, leading to an increased winding capacitance.The winding capacitance of the 15-kVA transformer is verylow so the circuit behaves as a pure inductive circuit insteadas a parallel LC circuit. A breaker is unable to chop aninductive current, thus the disconnection is postponed untilthe first current zero crossing. In a parallel LC circuit thecurrent can be chopped since the parallel capacitance providesan alternative circulation path for the current. This has beenverified analyzing the line current waveforms of the threetransformers: the currents are not chopped for the 15-kVAtransformer, but are chopped for the two larger transformers.Moreover, when a shunt capacitor is attached to the terminalof the 15-kVA transformer, tests have shown that the currentsare chopped and the residual flux is not anymore in phasewith the rated flux and resembles more the behavior seen inthe larger transformers.

The sum of the residual flux is always zero. This means thatno zero sequence flux is present during the ringdown transient.A three-legged core inhibits zero sequence flux because itconstrains the sum of the flux to be equal to zero and potentialflux in the air cannot retain magnetization. A delta windinghas an analogous effect imposing the sum of the voltages tobe zero. In the case of five-legged core without any deltawinding, a zero sequence residual flux cannot be neglectedas it can be stored in the outer legs. However, the particularcore configuration of the five-legged transformer used in thesetests did not allow us to reproduce this effect (an air gap ispresent between the three main limbs and the outer limbs).

These results show that neither the circuit breaker northe winding coupling (wye or delta) seems to influence theresidual flux as the different configurations produce verysimilar results. The interruption process can be differentforlarger transformer and high-voltage circuit breakers. A broaderinvestigation of larger transformers is required before weareable to generalize these results.

B. Influence of shunt capacitor

The influence of the capacitance has been verified byattaching a variable shunt capacitor to the 15-kVA transformer.Fig. 9 shows the residual flux as function of the capacitance.The maximum residual flux is reduced by one third whena shunt capacitance of 1µF is attached to the transformerterminals. The line in Fig. 9 shows that the maximum residualflux decreases approximately proportional to the logarithmofthe shunt capacitance:

max(λ0) ∝ −log(C) (12)

Fig. 10 shows some measured flux-linked and current wave-forms during ringdown transients. These waveforms qualita-tively verify the behavior observed from the simulations: largervalue of capacitance gives longer ringdown time and can drive

Shunt capacitance [µF]1 10 100

Flu

x [p

.u.]

0.0

0.1

0.2

0.3

(No C)

Fig. 9. Residual flux as function of the connected shunt capacitor (0-70µF);measured on a 15-kVA three-legged transformer.

the core into high saturation. Residual fluxes (that could notbe obtained with the simulation) are here present at the end ofthe transient. The hysteresis loop of one phase is also shown.During the ringdown transient current and flux-linked followminor hysteresis loops. Higher number of loops are requiredfor reaching steady state if a large capacitance is installed. Thefinal point of the hysteresis loops lies on the zero current axis,but retain a certain value of flux.

IV. RESIDUAL FLUX-LINKED ESTIMATION AND

INITIALIZATION

A hysteretic core model that can handle the demagnetizationis required to accurately simulate the ringdown transient.Few hysteretic-nonlinear-inductor models appear to have therequired property; two models that may be worth to verify withmeasurements are the Jiles-Atherton and Preisach models [11],[12]. However, their implementation in a simulation programis demanding both for modeling challenges and parameterestimation.

If the simulation interest is only inrush current estimation,the core model can be simpler because it does not need torepresent the demagnetization transient. However, an accurateinrush estimation requires residual flux-linked initialization ofevery section of the core. The following recommendationsshould be taken into account:

• Maximum residual flux-linked for small distributiontransformers lies in the range of 0.2-0.4 p.u. of the ratedflux-linked, with slightly higher value for the centralphase. If a shunt capacitance is connected to the trans-former during the de-energization this range is decreasedsubstantially.

• Residual fluxes in the different sections of the core ofthree-phase transformers are related on the basis of thecore type. In three-legged transformers the residual fluxesof the three legs must sum to zero; the yokes share thesame residual flux of the transformer leg that they aremagnetically in parallel with. In five-legged transformersthe residual fluxes of the three main legs plus the twoouter legs must sum to zero. In banks of three single-phase transformers the residual flux can be initializedindependently for each unit.

The extension of the results to medium/large power trans-former is challenging due to the limited measurements pre-sented in literature. Moreover, the use of improved corematerial in newer transformers reduces the validity of old

measurements. In a large Cigre survey (on more than 500transformers) [13] carried out in 1984 the maximum residualflux is given only for two transformers (0.75 and 0.9 p.u).Reference [2] dated 1986 suggests different remanent fluxrange cases varying between 0.4 and 0.8 p.u. The residual fluxfor a 545 MVA transformer is measured to be slightly higherthen 0.4 p.u. (worst case out of 10 random de-energization) in[14]. One single measurement of the de-energizarion of a 170MVA transformer is reported in [3] and has a residual flux of0.31 p.u.

V. CONCLUSION

A ringdown transient can be easily replicated in the lab-oratory; however few if any of the existing EMTP type ofmodels are capable of properly arriving at the value of theresidual flux. A comparison between measured and simulatedwaveforms has not been presented due to the inferior qualityofthe ATP model used. The poor agreement between simulationand lab results shows the necessity of developing an improvedmodel for ringdown transient simulation.

ATP simulations were useful to understand and qualitativelyreplicate the ringdown phenomena. A novel energy approachhas been presented as a key to investigate the saturation behav-ior during ringdown; a transformer may be driven into heavysaturation by the energy stored in the capacitive elements ofthe circuit.

A proper residual flux estimation is difficult since the phasecorrelation between rated flux-linked and residual magneti-zation is no longer valid as the transformer size increases.Residual flux ranges and guidelines for flux initialization aregiven in the paper. When synchronized switching is used tomitigate inrush current, it is important to take into account thatthe central phase may have the highest peak of the residualflux. Thus, it is wise to avoid the energization of the centralphase as first phase.

It has been observed that shunt capacitance has a maininfluence in residual magnetization and ringdown transientduration. If a large capacitance is connected to the transformerduring the de-energization, longer time is required for reachingthe end of the transient. This is an important aspect to takeinto account during protection scheme and relay reclosing-time strategies planing. A longer ringdown time also resultsin a lower residual flux.

APPENDIX

TABLE IGENERATORSTEP-UP TRANSFORMERTEST-REPORT.

Main data [kV] [MVA] [A] CouplingHS 432 290 388 YNLS 16 290 10465 d5

Open-circuit E0[kV,(%)] [MVA] I0[%] P0[kW]LS 12(75) 290 0.05 83.1

14(87.5) 290 0.11 118.815(93.75) 290 0.17 143.616(100) 290 0.31 178.617(106.25) 290 0.67 226.5

Short-circuit [kV] [MVA] ek, er[%] Pk[kW]HS/LS 432/16 290 14.6, 0.24 704.4

Current [A]-6 -3 0 3 6

-0.50

-0.25

0.00

0.25

0.50Time [ms]

-20 0 20 40 60 80-0.6

-0.3

0.0

0.3

0.6

Cur

rent

[A]

-10

-5

0

5

10

Time [ms]-20 0 20 40

-0.6

-0.3

0.0

0.3

0.6

-6

-3

0

3

6

Current [A]-6 -3 0 3 6

-0.50

-0.25

0.00

0.25

0.50

Current [A]-6 -3 0 3 6

Link

age

flux

[Wb-

t]

-0.50

-0.25

0.00

0.25

0.50

Phase 3

Time [ms]-20 0 20 40

Link

age

flux

[Wb-

t]

-0.6

-0.3

0.0

0.3

0.6

-6

-3

0

3

6

Linkge fluxCurrent

(a) 2 Fµ (b) 8 Fµ (c) 60 Fµ

Ph.3Ph.2

Ph.1 Ph.1

Ph.1Ph.2 Ph.3 Ph.2Ph.3

Fig. 10. Ringdown transient measured on a 15-kVA transformer;flux-linked, current waveforms and hysteresis loops.

REFERENCES

[1] J. Holcomb, “Distribution transformer magnetizing inrushcurrent,”Transactions of the American Institute of Electrical Engineers, Part III(Power Apparatus and Systems), vol. 80, no. 57, pp. 697–702, Dec.1961.

[2] R. Yacamini and A. Abu-Nasser, “The calculation of inrushcurrent inthree-phase transformers,”IEE Proceedings B (Electric Power Applica-tions), vol. 133, no. 1, pp. 31 – 40, Jan. 1986.

[3] Y. Husianycia and M. Rioual, “Determination of the residual fluxeswhen de-energizing a power transformer/comparison with on-site tests,”2005 IEEE Power Engineering Society General Meeting (IEEE Cat. No.05CH37686), vol. 3, pp. 2492 – 2497, 2005.

[4] R. Apolonio, J. C. de Oliveira, H. S. Bronzeado, and A. B. de Vas-concellos, “Transformer controlled switching: a strategy proposal andlaboratory validation,” in11th International Conference on Harmonicsand Quality of Power, IEEE, Ed., Sep. 2004, pp. 625 – 630.

[5] L. Prikler, G. Banfai, G. Ban, and P. Becker, “Reducing the magnetizinginrush current by means of controlled energization and de-energizationof large power transformers,”Electric Power Systems Research EP-SRDN, vol. 76, no. 8, pp. 642 – 649, May 2006.

[6] L. M. Ganatra, P. G. Mysore, K. K. Mustaphi, A. Mulawarman,B. A.Mork, and G. Gopakumar, “Application of reclosing schemes in thepresence of capacitor bank ringdown,”Proc Am Power Conf, vol. 61-2,pp. 967 – 972, 1999.

[7] F. de Leon and A. Semlyen, “A simple representation of dynamichysteresis losses in power transformers,”IEEE Trans Power Delivery,vol. 10, no. 1, pp. 315 – 321, 1995.

[8] H. W. Dommel and et.al.,Electromagnetic Transients Program Refer-ence Manual (EMTP Theory Book). Portland, OR: Prepared for BPA,Aug. 1986.

[9] S. Dennetiere, J. Mahseredjian, M. Martinez, M. Rioual, A. Xemard,and P. Bastard, “On the implementation of a hysteretic reactormodelin emtp,” in International Conference on Power Systems Transients,IPST03, Ed., New Orleans, USA, 2003.

[10] J. G. Frame, N. Mohan, and T. Liu, “Hysteresis modeling in an electro-magneting transient program,”IEEE Trans Power Appar Syst, vol. PAS-101, pp. 3403 – 3412, Sep. 1982.

[11] F. Liorzou, B. Phelps, and D. L. Atherton, “Macroscopicmodels ofmagnetization,”IEEE Trans. on Magnetics, vol. 36, no. 2, pp. 418 –428, Mar. 2000.

[12] M. Popov, L. Van Der Sluis, G. C. Paap, and P. H. Schavemaker, “Ona hysteresis model for transient analysis,”IEEE Power EngineeringReview, vol. 20, no. 5, pp. 53 – 55, May 2000.

[13] E. Colombo and G. Santagostino, “Results of the enquiries on actualnetwork conditions when switching magnetizing and small inductivecurrents and on transformer and shunt reactor saturation characteristics,”Electra, vol. 94, pp. 35 – 53, May 1984.

[14] H. Kohyama, K. Kamei, and H. Ito, “Application of controlled switchingsystem for transformer energization taking into account a residual fluxin transformer core,” inCIGRE SC A3&B3 Joint Colloquium in Tokyo,2005.

Nicola Chiesa was born in Cenate Sotto, Italy, on October 27, 1980. Hereceived the M.S. degree in Electrical Engineering from Politecnico di Milanoin 2005. In September 2005 he joined the Department of ElectricPowerEngineering at the Norwegian University of Science and Technology as aPh.D. candidate.

Alejandro Avendano was born in Tjuana, Mexico, on January 19, 1982.He received the B.S. degree in Electromechanical Engineering from InstitutoTecnologico de Tjuana in 2004. In 2005 he joined the Department of Electric& Computer Engineering at the Michigan Technological University as aPh.D. candidate sponsored by the National Research Councilof Mexico(CONACYT).

Hans K. Høidalen was born in Norway in 1967. He received his MSc andPhD from the Norwegian University of Science and Technologyin 1990 and1998 respectively. He is now a professor at the same institution with a specialinterest of electrical stress calculations and modeling.

Bruce A. Mork (M’82) was born in Bismarck, ND, on June 4, 1957. Hereceived the BSME, MSEE, and Ph.D. from North Dakota State Universityin 1979, 1981 and 1992 respectively. He joined the faculty ofMichiganTechnological University in 1992, where he is now AssociateProfessor ofElectrical Engineering, and Director of the Power & Energy Research Center.

Dmitry Ishchenko (M’04) was born in Krasnodar, Russia. He receivedhis M.S. and Ph.D. degrees in Electrical Engineering from Kuban StateTechnological University, Russia in 1997 and 2002 respectively. In Feb. 2003he joined the Electrical and Computer Engineering Departmentof MTU as apostdoctoral researcher.

Andrew P. Kunze (M’06) was born in Mahtowa, USA on November 28, 1983.He received a B.S. in Electrical Engineering from Michigan TechnologicalUniversity in 2006. He is currently pursuing an M.S. in Electrical Engineeringat MTU.