1077-2618/10/$26.00©2010 IEEE

Harmonic analysis ininterconnectedpower systems

BY RYAN A . TURNER& KENNETH S . SM I TH

THIS ARTICLE PRESENTSTHEHARMONICANAL-

ysis of transformer inrush currents in offshore power

systems. Offshore production facilities interconnected

by subsea cables are becoming increasingly common,

either as new projects or as extensions to existing facilities. Interconnec-

tion via a subsea cable introduces a significant shunt capacitance to the

source power system, giving rise to low natural or resonant frequency.

One source of harmonic currents is the system transformer. When ini-

tially energized, the transformer may draw a transient inrush current

that contains all harmonic components. If one of the harmonic compo-

nents in the inrush current is close to the resonant frequency of the

Digital Object Identifier 10.1109/MIAS.2010.937440

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power system depending upon the damping levels, a sus-tained overvoltage may be produced. This has recentlycaused operational problems on a number of newly inter-connected offshore systems. Analysis tools and methodol-ogies are presented in this article that can be used duringdetailed engineering design to assess the likelihood ofsuch dangerous events and to identify whether mitigationis required, long before the problems are encounteredduring system commissioning.

Typically, an interconnector is composed of a subsea cablecircuit supplied via step-up and step-down transformersbetween offshore platforms or between an offshore platformand onshore production facility. During a black-start orlight-system loading conditions, it is sometimes necessaryto energize a remote transformer against minimum genera-tion with a subsea interconnector cable circuit in service.This particular network configuration can result in a lowsystem-resonant frequency, possibly coincident with one ofthe harmonic components present in the transformer inrushcurrent. The harmonic content of the transformer inrushcurrent can excite the power system-resonant frequency,resulting in overvoltages that may last for a substantialperiod of time. This has recently been experienced on anumber of new installations during system commissioning.

The analysis presented was undertaken by the authors tounderstand the system conditions that may be problematicand hence develop an operational switching philosophythat avoids such problematic cases for existing systems. Themethodology could be applied during the detailed design offuture systems to anticipate and mitigate potential problemsbefore they are experienced during actual plant commission-ing. The PSCAD-EMTDC electromagnetic transient simu-lation program version 4.2 produced by the ManitobaHydro HVDCResearch Center was used for this analysis.

The transformer inrush currents have been known toelectrical engineers from the very early days of ac transmis-sion, having first been observed by Ferranti when commis-sioning the Depford to London 11-kV link in 1890 [1].More than 100 years later, transformer inrush currents con-tinue to cause operational problems on power systems. Thephenomena of inrush currents exciting power system reso-nances has been identified when energizing the convertertransformers associated with high-voltage (HV) direct cur-rent schemes [2] and in systems with transformers andsignificant lengths of HV cables [3]. This inrush has alsobeen experienced during power system restoration of HVtransmission networks when the load on the system isnegligible [4], [5]. In industrial distribution systems,transformer inrush has excited power system resonanceswhere power factor correction capacitors have been applied[6], [7]. In these examples, the presence of a relativelyweak-source system and considerable shunt capacitanceleads to a relatively low system-resonant frequency. This isan inherent feature of interconnected offshore power sys-tems due to the capacitance of the subsea cable [8]. Bydesign, harmonic-producing loads such as variable-speeddrives must not excite this resonance, but transformerinrush is often neglected as a source of harmonic currents.

Transformer InrushWhen a transformer is energized, it may draw a high-magnitude transient current from the supply. This current,

which is characterized as being almost entirely unidirec-tional, rises abruptly to its maximum value in the firsthalf cycle after the transformer is energized, and it slowlydecays until the normal steady-state magnetizing condi-tions in the transformer are reached. In a three-phaseunit, the peak magnitude of this asymmetric current canbe more than 13 times the rated line current for thewinding being energized [9]. The magnitude and dura-tion of the transient inrush current depend upon fourfactors [10]:

n the point on the voltage wave at the instant the trans-former circuit is energized (i.e., switching angle)

n the impedance of the circuit supplying the transformern the value and sign of the residual flux linkage in thetransformer core

n the nonlinear magnetic saturation characteristics ofthe transformer core.

The first two factors depend on the electric circuit towhich the transformer is connected and the switchingarrangements; the other two factors depend upon the charac-teristics of the magnetic circuit of the transformer core.Residual magnetic fluxes are due to the remanent magnetiza-tion of the core after a transformer has been de-energized. Atthe end of a de-energization transient, both the voltages andcurrents decay to zero; however, the flux in the core retains acertain value defined as residual flux [11]. Although thecharacteristics of the electrical circuits are normally known,the details of the magnetic circuit are rarely available, andhence, lumped reluctance models based on core geometry[12] cannot be always utilized.

Modeling Transformer Core SaturationThe transformer representation used for these studies is theclassical model in which each phase of the transformer isrepresented by a separate single-phase transformer modelwith no coupling between phases. Magnetic core saturationis represented by a current source [13], as shown by a block-diagram format in Figure 1.

The flux linkage is the integral of the winding voltage,i.e., US(t) ¼

RVL (t) dt. Saturation is modeled on the low-

voltage (LV) winding, as this is closest to the transformercore. The magnetizing current represented by the currentsource IS(t) is related to the flux linkage through the non-linear US-IS characteristic, which can be derived from the

1S

φS(t)VL(t)

IS(t)

IS

1

φS

Modeling of transformer saturation in PSCAD-EMTDC.15

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voltage and current measurements taken during a no-load(open circuit) test. At higher values of flux linkage, theslope of the US-IS curve tends toward the saturated coreinductance of the transformer winding. This asymptoticfunction is programmed internally within the PSCAD-EMTDC program, based on the magnetizing current atrated voltage, the position of the knee point on the charac-teristic, and the air-cored reactance of the winding. An air-cored solenoid of overall diameter D, length l, radial thick-ness d, andN turns has an inductance given by [14]

LA ¼6:4l0N

2D2

3:5Dþ 8l3

D� 2:25d

D½H�: (1)

The peak inrush current can be estimated by determin-ing the instantaneous ampere turns necessary to support theflux that passes through the air path between the iron coreand transformer winding [9]. The flux in the saturated ironcore is Ac 3Bs, the residual flux is Ac 3Br, and switchingat the least favorable point on the voltage wave requires thetime-varying component of flux to reach twice the nominalvalue or Ac32Bn. The peak instantaneous flux in the airpath is thereforeAc 3 (2Bnþ Br – Bs), and dividing the airpath by area results in air-flux density. For the nonsaturat-ing air path, B ¼ l0H, from which the following equationfor the peak instantaneous inrush current can be derived:

ipeak ¼Bairl

l0N¼ l

l0N3

Ac

Aair(2Bn þ Br � Bs)½A�, (2)

where Bair is the magnetic flux density outside the saturatediron core, Bn the nominal peak iron core magnetization, Bt

and Bs the residual and saturation magnetization of the ironcore, l the length of magnetic flux in air, N the number ofturns,Ac the cross-section of iron core,Aair the cross-sectionof the air path, and l0 is the permeability of air.

Data on the transformer core or windings are not oftenavailable, and so the air-core saturated inductance or thepeak inrush current cannot be calculated. An alternativeapproach used by authors for modeling purposes is toassume a maximum peak inrush current for the least favor-able switching angle and residual flux-linkage conditionsand to select the air-core-saturated inductance to replicatethis current when energized against an ideal, zero-imped-ance source [15].

Residual flux linkage can be included in the model byinserting a dc current source in parallel with each LVtransformer winding; the current is chosen to establish thedesired level of residual flux linkage. During normal opera-tion, the flux linkage in each phase winding will vary sinu-soidally; the magnitude in each phase will be identical,each displaced in time phase from the next by 120�. Whende-energized, the winding flux linkage will be frozen atthe instant of disconnection from the supply. To representthis remanence state, it is assumed that one limb of thetransformer has þ80%, the second –80%, and the thirdzero residual flux linkage. This is the worst case that mightbe expected upon any random transformer energization.

Harmonic Analysisof Transformer Inrush CurrentThe harmonic content of the transformer inrush currentwith time has been calculated by Bronzeado et al. [16]. Itwas shown that the peak value of any individual harmoniccomponent during one cycle is generally different from itspeak during another cycle. Because of the nonsymmetricalwaveshape, the transformer inrush current contains all har-monic components, i.e., fundamental, second, third, fourth,fifth, etc., as well as a dc (zero frequency) component.

As an example, the peak inrush current experiencedwhen energizing a 4.5-MVA, 6/0.72-kV, 7.0%, 50-Hz,Dy11 transformer against an ideal zero impedance sourceon the HV side is shown in Figure 2. These waveshapeswere produced using the PSCAD-EMTDC modelingmethodology described earlier. The results presented arefor the least favorable point on wave switching and worst-case residual flux linkage in the transformer core (i.e., 80%residual flux linkage). The transformer-saturated, air-coredinductance was chosen to give a peak inrush current equalto nine times the rated line current based on the tablepresented in [9]. The peak inrush current drawn fromphase A of the source is therefore

ipeak ¼ 934:5 MVAffiffiffi3p

3 6 kV¼ 3:897 kA:

The harmonic content of the phase A transient inrushcurrent was calculated using a discrete Fourier transform(DFT) with a moving window. As shown in Figure 3, themost significant components are the fundamental, which isinitially 1.5-kA rms, and the second harmonic is initially200-A rms. It is this second harmonic current that is used

5

4

3

Cur

rent

(kA

)

Time (s)

2

1

0

–1

–2

–31.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30

2Peak inrush current for a 6.0/0.72-kV, 4.5-MVA transformerenergized against an ideal source.

Cur

rent

(kA

)

Time (s)101 2 3 4 5 6 7 8 9

0.30

0.25

0.20

0.15

0.10

0.05

0.00

FirstSecondThirdFourthFifthSixth

3Harmonic content present in phase A inrush current.

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by transformer differential protection schemes to differen-tiate between transformer inrush and an internal windingfault [17]. The fifth harmonic current reaches a peak valueof approximately 50-A rms, four times smaller than thesecond harmonic and 30 times smaller than the fundamen-tal component. In this case, where there is no interactionbetween the transformer and power system, the second har-monic is by far the dominant one. Generally, the harmoniccomponents decay as the inrush transient decays towardthe normal steady-state operating conditions. Note thatthe harmonics of order three and above show discontinu-ities, with their peak values decreasing to zero and thenincreasing again. These harmonics change their phaseangle from positive to negative and vice versa as theirmagnitude passes through zero [18]. Neglecting the thirdharmonic (which is a special case due to winding arrange-ments), the higher the harmonic order the smaller themagnitude of the corresponding current component in theinrush current.

System Description and Simulation StudiesThe results obtained from a PSCAD-EMTDC study of a sys-tem typical with the authors’ experience are presented. Inthis study, the 6.0/0.72-kV, 4.5-MVA transformer discussedearlier is energized at the remote offshore platform, as shownin Figure 4. The platform is supplied via a 50-Hz intercon-nector circuit, consisting of an 11/35-kV, 25-MVA, 8.8%step-up transformer, 30 km subsea cable operating at 35 kV,and a 35/6.0-kV, 16-MVA, 6.4% step-down transformer.One meter of the subsea cable has a shunt capacitive react-ance of 15.3 MX. The onshore plant operates at 11 kV andis supplied by up to four 11-kV, 30-MVA gas turbine gener-ators (GTGs), each with a subtransient reactance of 32%.The full PSCAD-EMTDC dynamic machine model [19]was used to represent each generator as well as their auto-matic voltage regulators (AVRs) via transfer function-blockdiagrams. The subsea cable was represented by cascadedmutu-ally coupled pi sections.

The initial 11-kV system voltage waveshape after switch-ing in the 4.5-MVA transformer for the least-favorable pointon wave switching against a 30-MVA GTG is shown inFigure 5. The system is unloaded, and the transformer ini-tially had 80% residual flux linkage. High levels of distor-tion are present in the 11-kV voltage waveshape, as shownin the zoomed trace in Figure 5, corresponding to themaximum voltage envelope around t¼ 0.75 s.

The harmonic components present in the voltage in the11-kV system voltage waveform are illustrated in Figure 6,which shows the variation of the harmonic content withtime calculated using a traveling sample window DFT.During the inrush transient, the largest voltage compo-nents are at the fifth and sixth harmonics of the supplyfrequency. The sixth harmonic rms voltage reaches a peak

of approximately 2.25 kV or 35% of the fundamentalcomponent, approximately 300 ms after switching in thetransformer. This component decays quite quickly and isnegligible 10 s after the initial switching transient. Theinitial overvoltage evident on the 11-kV system voltagewaveshape in Figure 5 corresponds to the sum of the har-monic voltages around t ¼ 0.75 s in Figure 6, and, in par-ticular, the high magnitude of the sixth harmonic voltage.

The fifth harmonic rms voltage reaches a peak of0.72 kV (11% of the fundamental component) approxi-mately 7 s after switching in the transformer and decaysrelatively slowly. (Note that the initial magnitude of thefifth harmonic voltage is nonzero before switching in the

30-MVAGTG

35-kVSubsea Cable 4.5-MVA

Transformer

11 kV 6 kV

0.72 kV

4Case study single-line diagram.

Vol

tage

(kV

)

–150.70 0.72 0.74

Time (s)0.76 0.78 0.80

–10

–5

0

10

5

15

Vol

tage

(kV

)

–150.00 0.50 1.00

Time (s)

(b)

(a)

1.50 2.00 2.50 3.00

–10

–5

0

10

5

15

5An 11-kV system-instantaneous phase-to-neutral voltagewhen energizing the transformer against 13GTG.(a) Overall 11-kV voltage envelope. (b) Expansionof transient around maximum envelope.

Vol

tage

(kV

)

2.50

2.00

1.50

1.00

0.50

0.000 1 2 3 4 5

Time (s)6 7 8 9 10

SecondThirdFourthFifthSixth

6Variation of harmonic content in the 11-kV system voltage.

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transformer, indicating the presence of some fifth harmonicdistortion in the steady state due to the magnetizing cur-rent of the other online transformers in the network.)

The peak overvoltages are very dependent on the amountof system damping present and the system impedance. Theabsence of load results in longer decay times for the har-monic overvoltages. However, it is necessary to investigatethe frequency-dependent system impedance to account forthe sustained fifth harmonic voltage (Figure 6). A plot ofthe variation of the system impedance (using the PSCAD-EMTDC impedance scanning tool) for different generationlineups looking into the 11-kV switchboard is given in Fig-ure 7. This shows a parallel resonance close to the fifth har-monic for the system configuration with a single GTGconnected. The resonant circuit at the fifth harmonic com-prises of the inductances of the generator and the step-uptransformer and the capacitance of the subsea cable. Notethat as the number of online generators increases, i.e., thesystem becomes stronger from a fault-level perspective, theresonant frequency increases. As the total load on the sys-tem increases, the magnitude of the impedance peaks willtend to decrease (those shown in the Figure 7 are for light-load conditions). Additional load on the system is thereforebeneficial by reducing the overvoltages produced by excita-tion of the power system resonance. The somewhat highlevel of the fifth harmonic in Figure 6 before the transformeris switched in is explained by the fact that the system-resonantfrequency is at the fifth harmonic.

When the transformer at the remote installation is ener-gized, the fifth harmonic current component of the inrushcurrent injected into the system excites the resonantfrequency, resulting in the sustained fifth harmonic over-voltage, as shown in Figures 5 and 6.

Although the sixth harmonic current component hasa lower magnitude compared with the fifth harmonic inFigure 3, the maximum peak harmonic overvoltage pre-dicted in Figure 6 occurs at the sixth harmonic. This sug-gests that the equivalent system impedance varies duringthe transient event. Energizing a transformer may result in atransient interaction between the incoming and other trans-formers connected to the system, known as sympatheticinteraction [20]. The dc component of current in the inrushcurrent drawn by the incoming transformer flows throughthe resistive component of the system impedance, whichproduces a dc component of voltage. This dc voltage is seenby all other online transformers, which are then forced intomagnetic saturation as their flux linkage (or time integralof voltage) develops an offset. All the system transformers,including the unit being energized, are therefore driven tosome extent into magnetic saturation, and, consequently,the magnetizing reactance of each transformer falls and theydraw increased fundamental frequency magnetizing currentor reactive power. The increase in lagging reactive powerdemand partially compensates for the leading reactive powergenerated by the subsea cable, i.e., there is a net decrease inthe effective capacitance, which gives rise to an increase inthe system-resonant frequency. This mechanism explainswhy (Figure 6) the magnitude of the sixth harmonic voltageis initially higher than the fifth. The system impedance plot(Figure 7) produced using the PSCAD-EMTDC impedance-scanning tool corresponds to the unsaturated conditions inthe system transformers.

Energization of the interconnector link itself can also beproblematic. In the particular case presented here wherethere are no circuit breakers at 35 kV on the submarine cable(as is common practice), it is necessary to energize the step-uptransformer, the subsea cable, and the step-down transformersimultaneously. Simulation studies confirm that energizingthe link against a single GTG is extremely onerous, both interms of the fundamental frequency voltage drop and alsothe excitation of the fifth harmonic resonance in the system,which reaches a peak of 1.1 kV, or 17% of the fundamental,and only decays very slowly (with a time constant of approx-imately 4 s) toward the steady-state value, as indicated inFigure 8. The final steady-state value for the fifth harmonicvoltage is equivalent to the initial steady-state value presentedin Figure 6. Based on extensive simulation studies, theauthors were able to recommend the minimum generationand load levels necessary before energizing the interconnec-tor and also when energizing individual transformers toensure that both the system-voltage dip and any temporaryharmonic overvoltages were within acceptable limits.

Methods have been proposed in the technical literatureto eliminate inrush currents, including preinsertion resis-tors [9], point-on-wave circuit breakers [21], [22], and acombination technique [23]. These have been applied onutility systems; however, the authors are only aware of oneinterconnected offshore installation where they have beenused so far. In this case, preinsertion resistors have been usedto reduce the voltage dip experienced when energizing the

Impe

danc

e (Ω

)

0

20

40

80

100

120

140

0 5 10 15 20 25Harmonic Number

30 35 40

4 x GTGs3 x GTGs2 x GTGs1 x GTG

7Variation of system impedance with frequency seen at an11-kV switchboard for different-generation lineups.

Vol

tage

(kV

)

4.00

3.00

2.50

3.50

2.00

1.50

1.00

0.50

0.000 2 4 6 8 10

Time (s)12 14 16 18 20

SecondThirdFourthFifthSixth

8Variation of harmonic content in an 11-kV system voltagewhen energizing the interconnector.

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transformers and cables of an ac interconnection between thetwo platforms. The drawbacks of these methods are theirincreased capital cost, physical space requirements, decreasedreliability, and increasedmaintenance costs. It is essential thatthese requirements are identified early in the design process.

ConclusionsThe inrush current of a power transformer is almost entirelyunidirectional and can be many times larger than the fullload current. Analysis of a typical inrush current waveformusing a traveling window DFT shows that all harmoniccomponents are present. Interconnected offshore systemswith limited generation and long subsea cable feeders willhave relatively low resonance frequencies. The harmonic com-ponents present in transformer inrush currents may coincidewith the power system-resonant frequency, leading to signifi-cant temporary overvoltages. This problem is particularlyacute during a black-start scenario when there is limitedonline generation and system load.

The example studies presented in this article wereundertaken by the authors to analyze and understand therecently experienced problems when commissioning a realinterconnected offshore system. In general, problems are lesslikely to occur with increased levels of generation and loadon the system. Increased online generation raises the system-resonant frequency, tending to move it away from the lower-order harmonic components that are characteristic oftransformer inrush currents. Increased loading on the sys-tem introduces very valuable damping, which reduces themagnitude of any overvoltages produced. For the systemthe authors studied, the minimum generation and loadlineup required to ensure that both voltage dip and har-monic overvoltage are within acceptable limits were iden-tified. Operational experience has subsequently confirmedthe validity of these recommendations.

To avoid experiencing difficulties during commissioningof future offshore-interconnected systems, the methodologypresented in this article should be used during the detailedengineering design phase of the project to identify possibleproblems and investigate practical engineering solutions. Sys-tem impedance/frequency scans, with peaks close to or coinci-dent with low-order harmonic numbers, give an indicationthat individual transformer or interconnector link energiza-tion may well be problematic and that detailed electromag-netic transient modeling using a tool such as PSCAD-EMTDC should be undertaken. All transformers and theirsaturation characteristics as well as system controllers suchas AVRs should be modeled. If problem scenarios cannotbe avoided by only permitting switching during certainsystem configurations or if this is not operationally practi-cal (due to process constraints), advanced techniques asdescribed in the technical literature must be adopted.

References[1] J. A. Fleming, “Experimental researches on alternating current trans-

formers,” J. Inst. Electr. Eng., vol. 21, pp. 677–685, 1892.[2] J. P. Bowles, “Overvoltages in HVDC transmission systems caused by

transformer magnetizing inrush currents,” IEEE Trans. Power App. Syst.,vol. 93, pp. 487–493, Jan. 1974.

[3] D. Povh and W. Schultz, “Analysis of overvoltages caused bytransformer magnetizing inrush current,” IEEE Trans. Power App. Syst.,vol. 97, no. 4, pp. 1355–1365, July 1978.

[4] A. Ketabi, A. M. Ranjbar, and R. Feuillet, “Analysis and control oftemporary overvoltages for automated restoration planning,” IEEETrans. Power Delivery , vol. 17, no. 4, pp. 1121–1127, Oct. 2002.

[5] G. H. Cheng and Z. Xu, “Analysis and control of harmonic overvoltagesduring power system restoration,” in IEEE/PES Transmission and Distribu-tion Conf. Exhibition: Asia and Pacific Region, Dalian, China, 2005, pp. 1–7.

[6] J. F. Witte, F. P. Decesaro, and S. R. Mendis, “Damaging long-termovervoltages on industrial capacitor banks due to transformer energizationinrush currents,” IEEE Trans. Ind. Applicat., vol. 30, no. 4, pp. 1107–1115, July 1994.

[7] A. M. Miri and C. Sihler, “Damping of resonances at energization oftransformers serving large pulse-type loads,” IEEE Trans. Ind. Appli-cat., vol. 40, no. 6, pp. 1694–1699, Nov. 2004.

[8] K. S. Smith, L. Ran, and R. Yacamini, “Electrical inter-connection off-shore: The benefits and the limitations,” Trans Inst. Marine Eng., vol. 110,no. pt. 4, pp. 207–228, 1998.

[9] L. F. Blume, G. Camilli, S. B. Farnham, and H. A. Peterson,“Transformer magnetizing inrush currents and its influence on systemoperation,” AIEE Trans., vol. 63, no. 6, pp. 366–375, 1944.

[10] A. A. Hudson, “Transformer magnetising invisible current: A resumeof published information,” Elect. Res. Assoc., Rep. No. 5152, 1966.

[11] N. Chiesa, H. K. Avendano, B. A. Mork, D. Ishchenko, and A. P.Kunze, “On the ringdown transient of transformers,” in Proc. Int. Conf.Power Systems Transients, Lyon, France, June 4–7, 2007, pp. 1–6.

[12] K. S. Smith, L. Ran, and B. Leyman, “Analysis of transformer inrushtransients in offshore electrical systems,” IEE Proc. Generat. Transm. Dis-trib., vol. 146, no. 1, pp. 89–95, Jan. 1999.

[13] H. W. Dommel, “Transformer models in the simulation of electro-magnetic transients,” in Proc. 5th Power Systems Computation Conf., Cam-bridge, U.K., Sept. 1–5, 1975, pp. 3:1/4:1–16.

[14] M. A. Laughton and M. G. Say, Electrical Engineer’s Reference Book,14th ed. London: Butterworths, 1985.

[15] K. S. Smith, “Transformer inrush studies for wind farm grid con-nections,” in Proc. Int. Conf. Power System Transients, June 19–23, 2005,Paper No. IPST05-026.

[16] H. Bronzeado, P. B. Brogan, and R. Yacamini, “Harmonic analysis oftransient currents during sympathetic interaction,” IEEE Trans. PowerSyst. , vol. 11, no. 4, pp. 2051–2056, Nov. 1996.

[17] C. J. Mozina, “Protection and commissioning of multifunction digitaltransformer relays at medium voltage industrial facilities,” IEEE Trans.Ind. Applicat., vol. 41, no. 6, pp. 1420–1429, Nov. 2005.

[18] R. Yacamini and A. Abu-Nasser, “Numerical calculation of inrush cur-rent in single-phase transformer,” Proc. Inst. Elect. Eng., vol. 128, no. 6,pp. 327–334, Nov. 1981.

[19] A. M. Gole, R. W. Menzies, H. M. Turanli, and D. A. Woodford,“Improved interfacing of electrical machine models to electromagnetictransients programs,” IEEE Trans. Power App. Syst., vol. 103, no. 9,pp. 2446–2451, Sept. 1984.

[20] H. Bronzeado and R. Yacamini, “Phenomenon of sympathetic interac-tion between transformers caused by inrush currents,” IEE Proc. Sci.Meas. Technol., vol. 142, no. 4, pp. 323–329, July 1995.

[21] J. C. Oliveira, C. E. Tavares, R. Apolonio, A. B. Vasconcellos, and H.S. Bronzeado, “Transformer controlled switching to eliminate inrushcurrent–Part I: Theory and laboratory validation,” in Proc. IEEE/PESTransmission Distribution Conf. Exposition (TDC’06), Latin America, Aug.2006, pp. 1–5.

[22] J. H. Brunke and K. J. Frohlich, “Elimination of transformer inrushcurrents by controlled switching,” IEEE Trans. Power Delivery, vol. 16,no. 2, pt. 1 and 2, pp. 276–280, Apr. 2002.

[23] S. G. Abdulsalam and X. Wilsun, “A sequential phase energizationmethod for transformer inrush current reduction—Transient perform-ance and practical considerations,” IEEE Trans. Power Delivery, vol. 22,no. 1, pp. 208–216, Jan. 2007.

Ryan A. Turner (ryan.turner@mottmac.com) and Kenneth S.Smith are with Mott MacDonald in Glasgow, United King-dom. Turner is a Member of the IEEE. Smith is a Senior Mem-ber of the IEEE. This article first appeared as “ResonanceExcited by Transformer Inrush Current in Interconnected Off-shore Power Systems” at the 2008 Industry Applications SocietyAnnual Meeting.

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