208 ieee transactions on power delivery, …apic/papers/power_quality/pq-inrushreductionp...208 ieee...

208 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

A Sequential Phase Energization Method forTransformer Inrush Current Reduction—Transient

Performance and Practical ConsiderationsSami G. Abdulsalam, Student Member, IEEE, and Wilsun Xu, Fellow, IEEE

Abstract—This paper presents an improved design method fora novel transformer inrush current reduction scheme. The schemeenergizes each phase of a transformer in sequence and uses a neu-tral resistor to limit the inrush current. Although experimentaland simulation results have demonstrated the effectiveness of thescheme, the problem of how to select the neutral resistor for op-timal performance has not been fully solved. In this paper, an ana-lytical method that is based on nonlinear circuit transient analysisis developed to solve this problem. The method models transformernonlinearity using two linear circuits and derives a set of analyticalequations for the waveform of the inrush current. In addition toestablishing a set of formulas for optimal resistor determination,the results also reveal useful information regarding the inrush be-havior of a transformer and the characteristics of the sequentialenergization scheme. This paper also proposed a method, the use ofsurge arrester, to solve the main limitation of the sequential phaseenergization scheme—the rise of neutral voltage. Performance ofthe improved scheme is presented.

Index Terms—Inrush current, power quality, transformer.

I. INTRODUCTION

A sequential phase energization-based scheme to reducetransformer inrush currents has been proposed by the authorsin [1] and [2] (Fig. 1). The method uses an optimally-sizedgrounding resistor. By energizing each phase of the transformerin sequence, the neutral resistor behaves as a series-insertedresistor and thereby significantly reduces the energization in-rush currents. It was found that a neutral resistor that is 8.5% ofthe unsaturated magnetizing reactance would lead 80% to 90%inrush currents reduction. However, the resistor sizing issuewas not investigated from the transient performance perspectivedue to difficulties in conducing transient analysis of nonlinearcircuits.

Our further study of the scheme revealed that a much lowerresistor size is equally effective. The steady-state theory devel-oped for neutral resistor sizing [2] is unable to explain this phe-nomenon. Extensive investigation showed that the phenomenonmust be understood using transient analysis. If we select the neu-tral resistor to minimize the peak of the actual inrush current

Manuscript received September 6, 2005; revised March 6, 2006. This workwas supported by the Alberta Energy Research Institute. Paper no. TPWRD-00521-2005.

The authors are with the Department of Electrical and Computer Engineering,University of Alberta, Edmonton, AB T6G 2V4 Canada (e-mail: [email protected]; [email protected]).

Color versions of Figs. 2, 4–7, and 9–16 are available online at http://ieeex-plore.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 alsofound that the first phase energization leads to the highest in-rush current among the three phases and, as a result, the resistorcan be sized according to its effect on the first phase energiza-tion. With the help of nonlinear circuit theory [3], we managedto derive an analytical relationship between the peak of the in-rush current and the size of the resistor, which results in a tran-sient-analysis based theory for the resistor selection. One of theobjectives of this paper is to present the analytical work and theresultant design guide for the scheme. The developed analyticalmethod is an improvement over the one published in the classicWestinghouse T&D Reference Book [4] and can be used to an-alyze general inrush current phenomenon of transformers andreactors.

In addition, this paper also addresses the main limitation ofthe proposed scheme—the rise of neutral voltage. The use ofsurge arrester is proposed to overcome the limitation. Perfor-mance of the improved scheme is presented.

The significance of this work is that it is a rigorous analyt-ical study of the transformer energization phenomenon. The re-sults reveal a good deal of information on inrush behavior oftransformers and the characteristics of the sequential energiza-tion scheme. In addition, the developed analytical method madeit possible to accurately estimate energy requirements for thegrounding resistor and the voltage limiting surge arrester.

II. PERFORMANCE OF THE SEQUENTIAL PHASE

ENERGIZATION INRUSH MITIGATION SCHEME

Since the scheme adopts sequential switching, each switchingstage can be discussed separately. For first phase switching, thescheme performance is straightforward. The neutral resistor isin series with the energized phase and its effect will be similar toa pre-insertion resistor. When the third phase is energized, thevoltage across the breaker contacts to be closed is essentiallyclose to zero due to the existence of delta secondary or three-

0885-8977/$20.00 © 2006 IEEE

ABDULSALAM AND XU: A SEQUENTIAL PHASE ENERGIZATION METHOD 209

Fig. 2. Maximum inrush current as affected by the neutral resistor for a 30kVA, 208/208, Y � �, 3 limb transformer, [1]. (Top: experimental, bottom:simulation).

legged core. So there will be minimal switching transients forwhen the 3rd phase is energized [1], [2].

The 2nd phase energization is the one most difficult to ana-lyze. Fortunately, we discovered from numerous experimentaland simulation studies that the inrush current due to 2nd phaseenergization is lower than those due to 1st phase energizationfor the same value of (Fig. 2). This is true for the regionwhere the inrush current of the 1st phase is decreasing rapidlyas increases.

As a result, we should focus on analyzing the first phase en-ergization to develop more precise sizing criteria for the neutralresistor.

III. ANALYTICAL STUDY OF FIRST PHASE SWITCHING

One of the main focal points of this paper is to develop a soliddesign methodology for the neutral resistor size. Our approachpresented here is based on deriving an analytical expression re-lating the amount of inrush current reduction directly to the neu-tral resistor size. Preliminary results have been presented ear-lier by the authors in [5]. An accurate expression for inrush cur-rent will eliminate the requirement of computer simulation ona case-by-case basis. Few investigations in this field have beendone and some formulas were given to predict the general waveshape, harmonic content or the maximum peak current [3]–[9].For the presented application, it was required that the expressioncan accurately present the inrush current waveform over a widerange of neutral resistance values taking into account systemimpedance, residual flux value and the neutral resistor itself.

A. Inrush Current Expression

The transformer behavior during first phase energization canbe modeled through the simplified equivalent electric circuitshown in Fig. 3 together with an approximate two-slope satu-ration curve, [3]–[8]. In Fig. 3(a), and present the total pri-mary side resistance and leakage reactance. The iron core non-

Fig. 3. (a) Transformer electrical equivalent circuit (per-phase) referred to theprimary side. (b) Simplified, two slope saturation curve.

linear inductance as function of the operating flux link-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 re-ferred to primary side are also shown. and represent theprimary and secondary phase to ground terminal voltages, re-spectively.

During first phase energization, the differential equation de-scribing the behavior of the transformer with saturable iron corecan be written as follows:

(1)

In order to represent the highest saturation level without losinggenerality, switching angle of zero on the applied sinusoidalvoltage waveform together with a positive residual flux polarityis assumed throughout the analysis. In this case, saturation takesplace at the positive side of the saturation curve. Accordingly,the general inrush current waveform in unsaturated and satu-rated modes of operation can be given by

(2)where

Generally, transformers operate in unsaturated mode imme-diately after energization since the initial “or residual” flux isbelow the saturation flux level . For small neutral resistorvalues, the magnetizing impedance of the switched phase will


Fig. 4. Analytical and simulation inrush current waveforms (first cycle) for 30kVA Yg �� transformer.

be very high compared to other linear elements in the series cir-cuit and the supply voltage will be mainly distributed across themagnetizing branch until saturation is reached. The saturationtime can be calculated as follows:

where , , and are the nominal peak flux linkages,supply voltage, and angular frequency, respectively. Fig. 4shows the first cycle, analytical and simulation waveforms forthe 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 saturationclose to when the sinusoidal term peaks. This assumption isvalid for two reasons; first, the exponential term coefficientis fractional as compared to the sinusoidal term amplitudesince and . Second, the saturation timeconstant, , is small as increases which will introducea small shift in the peak current to appear slightly before the si-nusoidal peak value. The saturation current “ ” is small as com-pared to the inrush peak and can be neglected. Accordingly, thepeak time and the peak inrush current as function of can beexpressed as follows:

(3)

The analytical and simulation curves for the 132.8MVA transformer described in [1] during first phase switchingare shown in Fig. 5.

B. Neutral Resistor Sizing

Based on (3), it is now possible to select a neutral resistor sizethat can achieve a specific inrush current reduction ratiogiven by

(4)

Fig. 5. I (R ) compared to the simulation peak current for 132.8 MVA,72/13.8 kV Yg �� 3 limb transformer.

The inrush peak expression (3) can be rewritten as follows:

(5)

where in (5) is a dimensionless factor which depends ontransformer saturation characteristics ( and ) as well asthe total ratio during saturation

(6)

For the maximum inrush current condition , the totalenergized phase ratio including system impedance is highand accordingly, the damping of the exponential term in (5)during the first cycle can be neglected

(7)

Typical saturation and residual flux magnitudes for powertransformers are in the range

and

Accordingly, switching at voltage zero instant with a polaritythat matches the maximum possible residual flux, the saturationangle “ ” w.r.t. instant of switching and are within thefollowing ranges, respectively

(8)

(9)

High values leading to considerable inrush reduction will re-sult in low ratios. It is clear from (6) and (8) that ra-tios equal to or less than 1 ensure negative dc component factor“ ” and hence the exponential term shown in (5) can beconservatively neglected. Accordingly, (5) can be rewritten asfollows:

(10)

Using (7) and (10) to evaluate (4), the neutral resistor sizewhich corresponds to a specific reduction ratio can be givenby

(11)


Equations (9) and (11) reveal that transformers with lesssevere saturation characteristics “high saturation flux and lowmaximum residual flux values” require a higher neutral resistorvalue to achieve the desired inrush current reduction rate. Basedon (9) and (11), the inrush current reduction of 90% can beachieved within the range of

(12)

Based on (12), a small resistor “less than 10 times the satura-tion series reactance” can achieve more than 90% reduction ininrush current. The amount of reduction in flux during the firstcycle can be found from (2) as follows:

where

(13)

Within the optimum neutral resistor value defined by (12), thetotal flux reduction during first phase switching is within

(14)

As the second cycle starts, an initial flux level ofwill exist. This results in the absence of

inrush current after the first cycle since the maximum fluxis close to—or below—the satura-

tion flux.

IV. SECOND PHASE SWITCHING

Transformer behavior during second phase switching wasobserved through simulation and experiments to vary with re-spect to connection and core structure type. However, a generalbehavior trend exists within low neutral resistor values wherethe 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 firstphase switching. Single phase units connected in Yg–Y havea different performance as both first and second stage inrushcurrents has almost the same magnitude until a maximum re-duction rate of about 80% is achieved. Generally, based on thewell-known saturation characteristics of power transformers,any reduction in inrush current is a result of limiting the max-imum flux that can build up in the core. In this section, theperformance of the proposed inrush mitigation scheme duringsecond stage switching will be qualitatively analyzed and com-pared to the first switching stage for small values of . It willbe shown that the transformer saturation level during secondphase 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 twosaturable inductor circuits representing each phase. The cou-pling between both switched phases is introduced only throughthe neutral resistor. For any energized phase , the flux as

Fig. 6. Simulation of the 3� 300 MVA, Yg-Y transformer [10], during secondphase switching for R = 150:0 (Ohm).

function of the primary phase voltage and the neutral voltagecan be given by

(15)

Phase B will start operating in the unsaturated region withits own residual flux. As a result, both phase currents will below and the neutral voltage remains close to zero, .As soon as Phase B reaches saturation, its current will increaseand the neutral voltage will start to build up. The neutral currentwill be mainly due to the contribution of phase B. Hence, theneutral resistor can be assumed to be in series with phase Band a similar inrush reduction performance, to that of first phaseswitching, will hold. The process will continue until the neutralvoltage integral “amount of reduction” becomes sufficient todrive Phase A into saturation. With phase A originally in steadystate, a disturbance in flux equal to the difference between therated and saturation flux values is required for phase A to reachsaturation. Conservatively assuming that the reduction in flux inPhase B results in an increase of the same amount in phase A,it will be possible to increase to achieve at least 20 to 35%reduction in its flux before disturbing phase A, Fig. 6.

As is increased further, more inrush current reduction canbe achieved in phase B until both phases reach the same satu-ration level for a specific value of . As the difference be-tween saturation and rated flux values increases, more reductionin phase B current can be achieved. The same conditions applyduring third switching stage.

B. Transformers With Delta Winding and/or 3-Limb Structures

The performance during sequential switching for this typewill be quite different than for single phase, , bankstransformers due to the following reasons:

• dynamic flux will exist in un-energized phases;• inrush current can exist in one phase due to external satu-

ration in un-energized phase (return path of the flux).The existence of dynamic flux in un-energized phases will makethe initial flux in the switched phase dependent on the instantof switching. In order to maximize the flux of the switched


Fig. 7. Simulation of the 30 kVA transformer during second phase switchingcondition showing the phase fluxes and effect of delta winding current for smallvalues of R = 0:1 (Ohm).

phase and consequently represent highest saturation condition,the critical switching instant “ ” should be found. The flux inphase B after switching can be calculated as follows:

instant of switching

The maximum theoretical flux that can be reached in phase Bcan accordingly be given by

For the maximum flux condition

and (16)

The switching angle of on phase B voltage waveformcorresponds to a zero initial flux value in phase A and, as a result,no initial flux exists when the second phase is energized. Thisfinding is of importance since it proves that the maximum theo-retical saturation level during second phase energization will belower than that during the energization of the first phase whichequals .

Immediately after 30 of the switching instant, the fluxes inphases A and B are both positive and determined by the ter-minal voltage integral of both phases. This will lead phase Cwhich represents the return path of both fluxes to saturate first.As shown in Figs. 7 and 8, the saturation of phase C will drive adelta winding current equal to the magnetizing current of phaseC under saturation. The induced delta winding current will be re-flected as zero sequence current of the same magnitude flowing

Fig. 8. Modeling the delta winding during the saturation condition of phase C.

through phases A and B and a neutral current equal to twice thedelta current.

For phase B, both integrals of the terminal and the neutralvoltages have the same polarity and hence the delta windingwill help reducing saturation level further in phase B. For phaseA, the supply voltage waveform will have opposite polarity tothe neutral voltage, however, due to the difference between thesaturation and rated flux values, the disturbance in phase A willbe 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 thenumber of core limbs. For 3-Limb transformers, the flux in thetwo energized limbs will add up into the third limb. As the thirdlimb saturates, the return flux path of phase A and B will experi-ence saturation and as a result a neutral current equals twice thephase current will flow. This will result in a similar effect to thatfrom a delta winding. On the other hand, for transformers with4 or 5 limbs, and shell form cores, the return path of the fluxfrom phases A and B will be unsaturated to some degree andthe performance of the scheme will be similar to that of threesingle phase units connected in Yg–Y.

V. NEUTRAL VOLTAGE RISE: STANDARD REQUIREMENTS

AND MITIGATION TECHNIQUES

From simulation studies carried out on various transformertypes and connections, it was found that the peak neutral voltagewill reach values up to 1 (p.u.) rapidly as the neutral resistorvalue is increased. Typical neutral voltage peak profile againstneutral resistor size is shown in Fig. 9 for the 132.8 MVA trans-former during 1st and 2nd phase switching.

The scheme performance during the complete switching se-quence 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 secondswitching stages for the 132.8 MVA transformer.

Fig. 10. Phase currents, neutral current and neutral voltage during completeswitching sequence for the 132.8, 72/13.8 kV, Yg-D transformerR = 50 ().

required to allow phase fluxes to lose most of the dc compo-nent. The neutral voltage during the first cycle will reach 85%of the rated phase voltage. Quickly after the first cycle, the trans-former is unsaturated and the neutral voltage is negligible since

. The unsaturated magnetizing reactance is about900 times the saturation reactance of a transformer, [11].

Accordingly, with the transformer operating in unsaturatedmode, the neutral resistor voltage is negligible. Within the op-timum resistor value, the neutral voltage peak is less than 0.5(p.u.) during second phase energization. As soon as the thirdphase is switched in, the neutral voltage will remain close tozero.

It is a common industry practice to grade the insulation overthe Yg winding for solidly grounded transformers [11]–[14].This can introduce limitations to the applicability of the pro-posed scheme at high voltage levels. The following section ad-dresses the standard requirements and limitations for the appli-cation of the proposed scheme to both dry-type and liquid im-mersed transformers.

A. IEEE Standards Requirements

A review of the IEEE/ANSI standards [12]–[14] has been car-ried out in order to evaluate the acceptable neutral voltage riselimit on different power transformer types. The main applica-tion of the proposed scheme is the generator’s step up trans-formers for IPP “Independent Power Producer” which are in-terconnected to the system at the distribution or sub transmis-sion levels. The interconnection transformer is preferably Wye-grounded on the system side and Delta connected on the gener-ator side [15], [16]. According to [12], the minimum low fre-

Fig. 11. I (R )=I (0) percentage inrush current peak for different ar-rester saturation voltages R = 50 ().

quency insulation level at neutral for liquid immersed trans-formers at system voltages of 25 kV or below is 10 kV but notless than the nominal line voltage. In this case, the proposedscheme can be applied without modification for this type at in-terconnection levels of 25 kV or below. For voltages higher than25 kV and up to 69 kV, the neutral voltage rise need to be lim-ited to 50% of the nominal line voltage in order to comply withthe insulation requirement at neutral, [12]. In case of dry typetransformers, the minimum insulation level at neutral should beat least 4 kV at system voltages of 1.2 kV and extends to 10 kVat higher voltage levels. If the transformer is designed for un-grounded Y connection, the neutral insulation level should bethe same as the line terminal level [13].

B. Neutral Resistor With Neutral Voltage Limiting Arrester

Arrester(s) connected in parallel with the neutral resistorcould limit the neutral voltage rise to the standard level. Ac-tually, the resistor-arrester arrangement presents a nonlinearresistor saturating at the arrester’s saturation voltage. Accordingto (15), limiting the neutral voltage rise will reduce the neutralvoltage integral and hence, reduce the technique’s efficiency.Limiting the neutral voltage rise to 0.5 (p.u.) will have effectonly during first phase switching, Figs. 9 and 10 which is moredesirable in order to limit the energy dissipated through thearrester. The curves of the arrester-neutral resistorarrangement is shown in Fig. 11 for the 132.8 MVA trans-former.

A similar deduction procedure to the one presented in sectionIII leads to the following inrush expression:

(17)

Accordingly, the peak inrush current during arrester operationcan be expressed as

(18)

From (18), the amount of reduction in current will dependon how fast the arrester will become saturated, . However,since the neutral voltage will start rising after the transformer


Fig. 12. Phase currents, neutral current, and neutral voltage during completeswitching sequence R = 50 (). Arrester saturation voltage is 0.5 (p.u.).

Fig. 13. Phase currents, fluxes, neutral current and neutral voltage during com-plete switching sequence for the 132.8 MVA with 1000 MVAsc system.

saturates at , the neutral voltage integral will have a maximumlimit as the arrester saturation time approaches . Thisclarifies the “almost” steady profile of the inrush current asincreases shown in Fig. 11. The resistor-arrester arrangementperformance during complete switching sequence is shown inFig. 12. The results shown in Figs. 10 and 12 were obtainedassuming an infinite system bus.

The scheme performance with 1000 MVA short circuitimpedance, assuming 10% of this impedance to be resistiveis shown in Fig. 13. It is shown that inrush current reductionto less than 3 times the nominal current can be achieved con-sidering a relatively small source impedance and at the sametime limiting the neutral voltage to 0.5 (p.u.). In addition, thescheme will have much better performance with regards to thesettling time of inrush currents.

C. Energy Requirements

Simulation studies can provide an accurate calculation of en-ergy requirement level for the scheme. In this section, approx-imate formulas will be given for a quick—but accurate—esti-mate of the energy withstand capability for both the resistor andthe resistor-arrester arrangements. As mentioned earlier, therewill be negligible neutral voltage across the resistor after thethird phase switching. Accordingly, our focus will be on the as-sessment of energy requirements during first and second phaseswitching stages. Fig. 14 shows the accumulated energy ab-

Fig. 14. Accumulated energy during different switching stages. Results for the132.8 MVA transformer with infinite system.

sorbed by the neutral resistor during the complete switching se-quence for the 132.8 MVA transformer for the case shown inFig. 10. It is clear from Figs. 14 and 10 that negligible neutralvoltage will exist after the first cycle of the 1st phase energiza-tion and the energy dissipated through the resistor can accord-ingly be calculated as follows:

(19)

For the second phase, as can be seen from Figs. 6 and 7, theneutral current can be presented using two sinusoidal half-wavesof twice the frequency. Since the neutral voltage rise duringsecond phase is around 0.5 (p.u.) with the same neutral resistor,the energy during 60-cycle period of the second phase switchingcan be calculated as follows:

(20)

As can be seen from (20), most of the energy absorbed by thegrounding resistor will be during second phase switching. Afterthe third phase is switched in, the neutral current will be veryclose to zero and energy dissipation through the resistor can beneglected.

For the resistor-arrester arrangement, the arrester will be ac-tive only during the first cycle of the first switching stage. Asshown in (17) the total current through the switched phase willbe composed of a dc component through the resistor and an accomponent through the arrester.

Accordingly, the energy dissipated through the resistor andthe arrestor can be calculated, respectively, as follows:

(21)


Fig. 15. Accumulated energy during different switching stages (J). Arrester setat 0.5 (p.u.) saturation voltage with the 1000 MVAsc system.

(22)

The arrester will not be active for saturation voltages of 0.5(p.u.) or higher within the optimal neutral resistor value. Theneutral resistor energy is the same as that of the original schemeduring second switching stage for the same . As shown inFig. 15, the total energy absorbed by the resistor during allswitching stages is about 1.30 MJ, and 250 kJ for the surge ar-rester(s).

Neutral grounding resistors capable of handling 1000–1500A root mean square (rms) continuous current for 10 s at voltagelevels of 33 kV or more are commercially available today. Ar-resters can handle less energy dissipation (absorption) than re-sistors. This is due to the fact that they are originally designedfor short period operation duration. However, a way of stackinga number of arresters in parallel in order to handle a higher en-ergy rating has been suggested in [17]. Typical energy capa-bility for arrester class up to 48 kV is 4 to 4.9 kJ/kV [11] and[17]–[19].

VI. CONSIDERATIONS ON FERRORESONANCE

The proposed sequential energization scheme could expose atransformer to ferroresonance. Fortunately, the neutral resistoris in series of the resonant circuit and will provide sufficientdamping to prevent ferroresonance from happening. In fact, [20]proposed the idea of using a neutral resistor to mitigate ferrores-onance. Based on numerous TNA studies, [20] found that a neu-tral resistor less than 0.05 is sufficient to prevent the occur-rence of ferroresonance in Yg–D transformer banks. Based onthe finding, we can conclude that the proposed scheme will notexperience ferroresonance problem. Our simulation studies on22/0.48 kV, 4.5%, 160 kVA, Y–D transformer, also confirmedthis conclusion. Fig. 16 shows the voltage waveforms at the en-ergizing side of the transformer due to energizing phase A. Itis clear that using the optimal resistor successfully damped theovervoltage at un-energized phases B and C within one cycle.

Fig. 16. Voltage at the primary side of a 22/0.48, 160 kVa, Y-D transformerdue to energizing Phase A. Top: isolated neutral. Bottom: neutral grounding.

VII. CONCLUSIONS

This paper presented an improved and more complete de-sign criterion for a novel transformer inrush current reductionscheme. It was shown that a small neutral resistor size of lessthan ten times the transformer series saturation reactance canachieve 80–90% reduction in inrush currents among the threephases. The transient performance of the scheme was presentedand it was demonstrated through detailed analysis that the firstphase switching leads to the highest inrush current level. Thepaper has also addressed the main practical limitation of thescheme as the permissible rise of neutral voltage. A feasibleapplication range for both dry type and liquid immersed trans-former has been proposed and the use of surge arresters to ex-tend the application range of the scheme has also been pre-sented. Formulas were also given to estimate the required en-ergy withstand capability for both the neutral resistor and thearrestor if applicable.

REFERENCES

[1] Y. Cui, S. G. Abdulsalam, S. Chen, and W. Xu, “A sequential phaseenergization 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 sequentialphase energization method for transformer inrush current reduc-tion—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,” GeneralElectric Rev., pp. 531–537, 745–751, Sep. and Dec. 1931.

[4] Westinghouse Electric Corporation, Electric Transmission and Distri-bution Reference Book, 4th ed. East Pittsburgh, PA, 1964.

[5] S. G. Abdulsalam and W. Xu, “Analytical study of transformer inrushcurrents and its applications,” in Proc. Int. Conf. Power System Tran-sients, Montreal, QC, Canada, 2005.

[6] B. Holmgrem, R. S. Jenkins, and J. Riubrugent, Transformer inrushcurrent CIGRE paper 12-03, CIGRE. Paris, France, pp. 1-13, 1968.

[7] H. A. Peterson, Transients in Power Systems. New York: GeneralPublishing Co., General Electric, 1951.

[8] L. F. Blume, G. Camilli, S. B. Farnham, and H. A. Peterson, “Trans-former magnetizing inrush currents and influence on system opera-tion,” AIEE Trans. Power App. Syst., vol. 63, pp. 366–375, Jan. 1944.

[9] P. C. Y. Ling and A. Basak, “Investigation of magnetizing inrush cur-rent 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 sat-urable 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. NewYork: Wiley, 1991.

[12] IEEE Standard General Requirements for Liquid-Immersed Distribu-tion, Power, and Regulating Transformers, IEEE Std. C57.12.00-2000,2000, pp. 1-53.

[13] IEEE Standard General Requirements for Dry-Type Distribution andPower Transformers Including Those With Solid Cast and/or Resin-Encapsulated Windings, IEEE Std. C57.12.01-1998, Dec. 31, 1998.

[14] IEEE standard requirements, terminology, and test procedure for neu-tral grounding devices, ANSI/IEEE Std. 32-1972, 1972.

[15] British Columbia Transmission Corporation, 69 kV to 500 kV inter-connection requirements for power generators, May 2004.

[16] BC Hydro, 35 kV and below interconnection requirements for powergenerators, Jun. 2004.

[17] J. J. Lee and M. S. Cooper, “High-energy solid-state electrical surgearrestor,” 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 theenergy withstand capacity of metal oxide resistors,” in Proc. 11thInt. Symp. High Voltage Engineering, Aug. 23–27, 1999, vol. 2, pp.309–312.

[19] M. Martinez and L. Zanetta, “On modeling and testing metal oxideresistors to evaluate the arrester withstanding energy,” presented at theIEEE Dielectr. Mater., Meas. Appl. Conf., 2000, Publ. No. 473.

[20] R. H. Hopkinson, “Ferroresonant overvoltage control based on TNAtests on three-phase wye-delta transformer banks,” IEEE Trans. PowerApp. 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 electricalengineering from El-Mansoura University, El-Mansoura, Egypt, in 1997 and2001, respectively. He is currently pursuing the Ph.D. degree in electrical andcomputer engineering from the University of Alberta, Edmonton, AB, Canada.

Currently, he is with the Enppi Engineering Company, Cairo, Egypt. His re-search interests are in electromagnetic transients in power systems and powerquality.

Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the Universityof British Columbia, Vancouver, BC, Canada, in 1989.

He was an Engineer with BC Hydro, Burnaby, BC, Canada, from 1990 to1996. 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.

208 ieee transactions on power delivery, …apic/papers/power_quality/pq-inrushreductionp...208 ieee...

Documents