unloaded power transformer

950 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 2, APRIL 2005

A Sequential Phase Energization Technique forTransformer Inrush Current Reduction—Part II:

Theoretical Analysis and Design GuideWilsun Xu, Senior Member, IEEE, Sami G. Abdulsalam, Student Member, IEEE, Yu Cui, and Xian Liu, Member, IEEE

Abstract—This paper presents a theory to explain the character-istics of a sequential phase energization based inrush current re-duction scheme. The scheme connects a resistor at the transformerneutral point and energizes each phase of the transformer in se-quence. It was found that the voltage across the breaker to be closedhas a significant impact on the inrush current magnitude. By ana-lyzing this voltage using steady-state circuit theory, the simulationand experimental results presented in a companion paper are ex-plained. The results lead to the establishment of a guide to selectthe optimal value of the neutral resistor. The applicability of theproposed scheme to different transformer configurations has alsobeen investigated in this paper. It is shown that the idea of sequen-tial phase energization leads to a new class of techniques for lim-iting switching transients.

Index Terms—Inrush current, power quality, transformer.

I. INTRODUCTION

ANEW, simple and low cost scheme to reduce transformerinrush currents has been presented in a companion paper.

The scheme uses a resistor connected at the transformer neutralpoint and energizes each phase of the transformer in sequence.Simulation and experimental results have shown that the schemeis quite effective [1]. The amount of inrush current reductionas a function of neutral resistor value was determined from theresults. It was found that there is an optimal value for the resistor.The paper, however, offers no quantitative theory to explain thephenomena.

The objective of this paper is to present a theoretical analysison the proposed scheme. The results lead to the establishmentof a design guide for the selection of the optimal resistor value.The theory also makes it possible to analyze the applicability ofthe proposed scheme to different types of transformer configu-rations.

A rigorous analysis on the proposed scheme needs to studya system of multi-variable nonlinear differential equations.Finding an analytical solution to the problem is probably im-possible. Even with many approximations, we still failed to getsome meaningful results. The process, however, led us to realizethat the steady-state voltage across the breaker to be closed

Manuscript received May 20, 2003; revised October 18, 2003. This work wassupported by the Alberta Energy Research Institute. Paper no. TPWRD-00241-2003.

W. Xu, Y. Cui, and S. G. Abdulsalam are with the Department of Electricaland Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4,Canada (e-mail: [email protected]).

X. Liu is with the University of Arkansas, Little Rock, AR 72204-1099 USA.Digital Object Identifier 10.1109/TPWRD.2004.843465

Fig. 1. Circuit for analyzing transformer energization.

has a significant impact on the inrush current magnitude. Thisvoltage can be determined from steady-state circuit analysis.Further investigation of the phenomena reveals that one of thereal causes behind the effectiveness of the proposed schemeis the reduction of this voltage through the neutral resistor,which is made possible by sequential phase energization. In thefollowing sections, a steady-state circuit theory is presented toanalyze the problem. The theory is then extended to establish adesign guide to determine the optimal resistor value.

II. STEADY-STATE ANALYSIS OF THE PROPOSED SCHEME

The proposed scheme involves the energization of threephases in sequence. The energization of the first phase isvery similar to the series resistor insertion scheme. This is astraightforward problem and it will not be considered furtherin subsequent sections. The challenge here is the analysisof the 2nd and 3rd phase energization. Using the 2nd phaseenergization as an example, the circuit shown in Fig. 1 can bedrawn. The variables shown in the circuit diagram are phasors.This notation will be followed throughout the paper.

Without losing generality, the unloaded transformer can berepresented as three coupled branches in the figure. In its steady-state form, the equation for the transformer can be written asfollows,

where and are the self and mutual impedances of thecoupled circuit respectively. is shown in Fig. 1. The above

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XU et al.: A SEQUENTIAL PHASE ENERGIZATION TECHNIQUE FOR TRANSFORMER INRUSH CURRENT REDUCTION PART II 951

equation assumes that the transformer is balanced among threephases and the resistive component is omitted. The secondaryside of the transformer has an impact on the value of the cou-pling matrix, but it does not change the structure of the circuit.

The most important variable of the above circuit is the voltageacross the phase B breaker before it is closed. This voltage is la-beled as in the figure and is called breaker contact voltagein this paper. Based on circuit theory, the following characteris-tics regarding to can be stated:

• If , closing of the phase B breaker would notresult in transient currents in the circuit.

• If the circuit were a linear circuit, the magnitude of thetransient currents in the circuit would be in proportionto if the breaker always closes at the same phaseangle of .

• If the circuit is a nonlinear circuit with transformer mag-netization characteristics, a larger will generallylead to a larger inrush current if the breaker always closesat the same phase angle of . The relationship betweenthe inrush current and is nonlinear.

It becomes clear, therefore, that we can use the magnitude ofto investigate indirectly the magnitude of the circuit tran-

sients. A larger should be avoided if one wants to reducethe inrush currents. This reasoning is the basis of the quanti-tative theory presented in this paper. The goal of our analysisis thus transformed into the one of finding the relationship be-tween and .

According to Fig. 1, the equation to determine is estab-lished as follows:

The above set of equations has five known variables. The re-sult for is shown in the following formula:

(1)

Similarly, we can develop a set of equations for the steady-state circuit condition before the phase C breaker is energized

This leads to the solution for the as follows:

(2)

The impact of on the magnitudes of and canbe assessed by plotting formulas (1) and (2). Using the test trans-former of [1] ( secondary) as an example, the results are shown

Fig. 2. Breaker contact voltages as affected by R .

Fig. 3. Comparison of breaker contact voltage curves and the inrush currentcurves.

in Fig. 2. It can be seen that decreases initially whenis small. On the other hand, always increases with

. The intersection point of the two curves gives a compro-mised reduction on both voltages. This is the optimal point forthe neutral resistor since we don’t want either voltage becomestoo high. The corresponding voltage is about 80% of the casewith solidly grounded transformer , or 66% of thephase to ground voltage of 120 V. Also included in the figureis the measured and results for the experimentaltransformer. There is a reasonable agreement between the re-sults. The difference is caused by the asymmetry and saturationof the transformer magnetic circuit. Note that the transformermodel shown in Fig. 1 is assumed to have the same mutual im-pedances.

Further inspection of the results shows that the curves arevery similar to the inrush current versus curves obtainedby experiments and simulations [1]. The main difference is onthe scale of the Y-axis. This is understandable since the mag-nitudes of inrush currents are approximately exponential func-tions of the breaker contact voltages and . Fig. 3compares the two sets of curves and the similarity can be clearlyseen. More importantly, the intersection points of the respectivecurves are very close. Accordingly, one can find the optimal re-sistance value using (1) and (2). For the test transformer, theoptimal resistance is found to be 1.8 with the steady-statemethod and 2.4 from the nonlinear simulation results. Thecorresponding reduction of breaker contact voltage is about 66%in this case.



In summary, (1) and (2) can be combined to establish a singleformula for the optimal resistance value as follows:

or

(3)There is no closed form solution for the above equation. But

it can be easily solved numerically. In the next section, approx-imate analytical expression for the optimal value is estab-lished by considering the relationship between and .

III. DESIGN GUIDE FOR DIFFERENT TRANSFORMERS

Equation (3) shows optimal resistor is a function ofand of the transformer. A general method to determine thesetwo parameters is as follows:

1) Ground the transformer neutral for the side where isto be inserted. This is typically the primary side of thetransformer. This side is also called the test side.

2) The secondary side of the transformer is left as it is. Forexample, if the transformer is connected, leave theconnection intact.

3) Apply a rated positive sequence voltage to the transformertest side and measure the current injected into the trans-former. The ratio of the voltage to the current is the stan-dard open circuit impedance of the transformer. The re-actance component of the impedance can be determinedaccordingly. This value is labeled as .

4) Apply a rated zero sequence voltage to the transformertest side and measure the current injected into the trans-former. The ratio of the voltage to the current is a zero se-quence impedance of the transformer. Depending on theconnection of the secondary side, this impedance is notnecessarily the zero sequence open circuit impedance. Ifthe secondary side is -connected, it is actually the shortcircuit zero sequence impedance of the transformer. Theresulting reactance is labeled as .

5) Parameter and can be calculated from the fol-lowing well known equation [5]:

Mathematically speaking, the above procedure is to findand using the following equations:

Fig. 4. Zero sequence test circuit for Y=� transformer.

With these understandings, the formulas for the optimal resis-tance are derived for different types of transformer connections.

A. Transformer

In this case, the positive sequence test gives the open-circuitreactance or magnetizing reactance of the transformer. The zerosequence test gives the short-circuit zero sequence reactance, asshown in Fig. 4.

Since the short-circuit impedance is much smaller than theopen circuit impedance

Substituting this condition into (3), the equation for the optimalneutral resistor can be established as follows:

which gives

(4)

There is a 32% voltage reduction in this case. If ,. The voltage reduction with respect to solidly

grounded case is about 20%.

B. Y/Y Transformer With 3-Limb

In this case, the positive sequence test also gives the standardopen circuit reactance or magnetizing reactance of the trans-former. For the zero sequence test, the flux has to flow outsideof the limb due to the fact that the flux of each phase has thesame direction (Fig. 5). The zero sequence impedance is there-fore very small. Comparing with , it can be neglected. Sothe formula for optimal neutral resistor is essentially identicalto (4).

C. Y/Y Transformer Consisting of Three Single-Phase Units

In this case, the positive sequence test also gives the standardopen circuit reactance of the transformer. The zero sequence testyields the same flux path as that of the positive sequence test.As a result, . This gives

The above condition does not produce an optimal resistancevalue from (3). It implies that the proposed scheme is not quiteworkable for this type of transformer. This result can be seenfrom the breaker contact voltage versus curves shown inFig. 6. The figure reveals that there is no low voltage intersectionpoint for the two curves. The figure also shows that the problemis caused by the curve, which does not start from zerovalue in this case. The physical explanation is that the 3rd phase



Fig. 5. Zero sequence flux path for a 3-limb transformer.

Fig. 6. Breaker contact voltages for Y/Y transformer consisting of threesingle-phase units.

is decoupled from the other two phases. A voltage cannot beinduced on that phase when the first two phases are energized.

D. Y/Y Transformer With 5-Limb

This case is very similar to the case of 3 single-phase trans-formers. The zero sequence flux can return from the iron core,resulting in a zero sequence impedance that is comparable to

. Accordingly, the proposed scheme may not work in thiscase either.

E. Summary and Examples

In summary, an optimal resistance exists for trans-former and for 3-limb Y/Y transformer. These transformersare characterized as having mutual coupling among threephases. The proposed scheme will work for these cases. Itcan be further inferred that the scheme will also work for 3winding transformers as long as it has a secondary or tertiary.Since most power transformers have a delta-connected tertiarywinding, the proposed scheme can be applied to a wide rangeof transformers. Furthermore, the same formula for the optimalneutral resistor can be used for all cases.

If the open circuit current at rated voltage is expressed in per-centage of the transformer rating and the resistance part is ig-nored, (4) can be further simplified as follows:

(5)

where is the per-unit transformer excitation current atrated supply voltage.

As an example, the experimental transformer used for thisproject has the following measured values:

TABLE INO-LOAD TEST DATA FOR A HYUNDAI TRANSFORMER

• Applied voltage ;• Average no load current ;• No load losses .The open circuit impedance is

and the open circuit resistance is. It gives

The corresponding optimal resistance is 1.8 . As a secondexample, a HYUNDAI 132.8 MVA, 72/13.8 kV, 3-limb,transformer is considered. The manufacturer provided the testdata from the 13.8 kV side given in Table I

Using a similar procedure and the average current amongthree phases, the and values are calculatedas 283 and 868 respectively. If referred to the pri-mary side where the neutral resistance is to be inserted,

. Using formula (4), the optimalneutral resistor is calculated as 2008 . If formula (5) is used,the resistance is 53 pu or 2068 . The values agree well withthe simulation determined optimal shown in Fig. 8 of thecompanion paper.

IV. NUMERICAL AND SENSITIVITY STUDIES

It is a significant claim that the optimal values for inrushcurrent reduction and for breaker contact voltage reduction arevery close. The design (4) and (5) are based on such a claim. Al-though this claim can be understood conceptually from the ex-planations presented in Section II, there is still a need to verify itfurther. To this end, two sensitivity studies have been conducted.The studies involve changing the slope of the transformer sat-uration curve. The first study examines the impact of changingthe slope of the unsaturated segment of the curve and the secondstudy examines the impact associated with the slope of the sat-urated segment. The inrush current results obtained from simu-lation are shown in Figs. 7 and 8.

It can be seen from Fig. 7 that the intersection points of theinrush current curves move horizontally when the slope of theunsaturated curve (i.e. ) changes from 50% to 200% ofthe measured value. It means that the unsaturated reactance canaffect the optimal resistance value. This result agrees well withthe conclusion drawn from the breaker contact voltage analysis.The analysis shows that is a function of the unsatu-rated reactance .

Fig. 8 reveals that the intersection points move verticallywhen the slope of the saturated segment of the saturation curveis changed from 30% to 100%. It implies that the slope hasno effect on the value of the optimal . This result furtherconfirms the adequacy of the breaker contact voltage analysis.The analysis does not indicate is affected by the



Fig. 7. Impact of changing the slope of the unsaturated segment of thetransformer magnetization curve.

Fig. 8. Impact of changing the slope of the saturated segment of thetransformer magnetization curve.

slope of the saturated segment of the transformer magnetizationcurve.

In addition to the above verification studies, the accuracyof the design formula is further evaluated by using a 3 limbY/Y transformer and a transformer consisting of threesingle-phase units. The results for the 3 limb Y/Y transformerare shown in Fig. 9. It can be seen that there is a good agreementbetween the steady-state analysis and the transient simulations.

For transformers consisting of three single-phase units,the case of 300 MVA, 13.8/199.2 kV transformer units de-scribed in [6] is simulated. Two cases are studied, one with thesingle-phase units connected in and the other connectedin Yg/Y. In both cases the high voltage side is the grounded Y.The results for connection are shown in Fig. 10. Thisfigure confirms the validity of the steady-state analysis method.

For the case of the Yg/Y connection, steady state analysisshow that the neutral resistor scheme is not as effective sincethe breaker contact voltage cannot be reduced. The simulationresults, however, showed that the proposed scheme has some ef-fects (Fig. 11). The effect could be explained with the followingequation:

where stands for the Laplace operator and the total circuitimpedance seen from the breaker contacts (the 3rd phase closing

Fig. 9. Comparison of simulation and theoretical results for a 3-limbtransformer with Y/Y connection.

Fig. 10. Comparison of simulation and theoretical results for a Yg=�transformer consisting of three single-phase units.

Fig. 11. Inrush current simulation results for a Yg/Y transformer consisting ofthree single-phase units.

is used as an example). Although this equation applies to a linearcircuit only, it is symbolically valid for a saturated transformer.It can be seen that a reduction on will reduce . Anincrease of could also reduce . It is likely that, in thecase of Y/Y transformer bank, the reduction on inrush current isdue to the increase of Z(s) by the neutral resistor. We are furtherinvestigating this phenomenon.

In order to understand the characteristics of the proposedscheme further, additional sensitivity studies have been con-ducted. Some of the results are presented in the following sub-sections.



A. Impact of Transformer Resistance

In the foregone derivations, the transformer resistance wasneglected. It would be useful to know what is the effect of thisapproximation. In this case, the transformer model becomes

where is the winding resistance. Using a procedure similarto that described in Section II, the breaker contact voltages arefound to be

Within a certain range of (0 to 20% of ),can be expressed as

It can be seen that the impact of is not significant. Thisconclusion has been validated by the example of the 132.8 MVAtransformer.

B. Sequence of Switching

The proposed scheme as it stands now requires a switchingsequence of phases A, B and C. In this study, we want to knowif a switching sequence of A, C and B would bring more inrushcurrent reduction. In this case, the breaker contact voltages aredetermined as follows

(6)

(7)

where subscripts 2 and 3 denote switching order. The resultingbreaker contact voltage curves are shown in Fig. 12. It can beseen that the trend of is different from that of .The voltage is always higher than the case of . Con-sequently, there is no intersection between the two curves. Theconclusion of this analysis is that the proper switching sequencefor the proposed scheme is A, B and C.

C. Neutral Impedance

The possibility of using a neutral impedanceto reduce the inrush current is also investigated. Adopting the

Fig. 12. Breaker voltages as affected by R for switching sequence ACB.

Fig. 13. Breaker contact voltages as affected by neutral reactance.

switching sequence of ABC, the breaker contact voltages aredetermined as follows for the transformer case:

The case of inserting a neutral reactor is examined first. Thecorresponding breaker contact voltage curves are shown inFig. 13 and are compared with those associated with the neutralresistor. The results show that does not have a valley.The intersection point of and is higher than thevalue of obtained with or equal to zero. As aresult, connecting a reactor to the transformer neutral is not asolution option.

The case of connecting a neutral impedance is alsoinvestigated. The breaker contact voltages for the cases of

, and are shown inFig. 14. The results indicate that the case of yields thelowest voltage. So a pure resistor as the neutral impedance is thebest option for the proposed scheme.



Fig. 14. Breaker contact voltages as affected by neutral impedance.

V. CONCLUSIONS

This paper has presented a theory to explain the character-istics of a proposed sequential phase energization based inrushcurrent reduction scheme. A formula to determine the optimalresistor value is established. Main findings of the work can besummarized as follows:

• The mechanism of the proposed scheme can be under-stood from the perspective of breaker contact voltage re-duction. These voltages can be determined using steady-state circuit analysis.

• The proposed scheme is most effective for transformerswith a delta winding or having three limbs, i.e. three wind-ings of the transformer are coupled electrically or magnet-ically.

• The optimal neutral resistance for these cases can bedetermined from formula ,where is the open-circuit positive-sequence reac-tance of the transformer. Selecting a precise value forthe neutral resistor is not necessary. As long as it is inthe neighborhood of , the scheme is equallyeffective.

• The sequence of switching should be as follows: phaseA first, followed by phase B and then by phase C. Thisswitching sequence will lead to 20% to 30% reductions onthe breaker contact voltages and 80% to 90% reductionson the inrush currents. Time delay between the switchingevents is in the range of 5 to 60 cycles.

• Although neutral impedance can also be used for the pro-posed scheme, study results show that the most effectiveoption is still the neutral resistor scheme.

Although a lot of results have been obtained for the pro-posed scheme, we feel more work is needed. For example, howto determine the current flowing through RN is still an opensubject. This current is important for assessing the transientwithstand capability of the resistor and the neutral voltage rise.There is also a need to field test the proposed scheme on largetransformers.

The proposed method compares favorably to the existingschemes of pre-insertion resistor and synchronous closing. It

is much cheaper than the pre-insertion resistor scheme sinceonly one resistor and one by-pass breaker are used. It is morerobust than the synchronous closing scheme. The scheme needsto determine the residual flux of transformer cores to workeffectively. There is no good solution to find residual flux yet.In view of the fact that a lot of distribution transformers havea neutral resistor for single-phase fault detection, the proposedscheme could be applied with very low cost—delayed closingof each phases of the transformer might be just sufficient.

We believe that another major contribution of this work is thediscovery of a new class of methods to reduce switching tran-sients. The method is to reduce the breaker contact (phasor) volt-ages through sequential phase energization. The true function ofthe neutral resistor is to minimize the breaker contact voltages.From this perspective, the potential of the proposed scheme isnot limited to transformer energization. In theory, it is also ap-plicable to capacitor energization and possibly motor starting.We are currently investigating these subjects as well.

ACKNOWLEDGMENT

The authors wish to thank C. Muskens of ATCO Electric andT. Martinich of BC Hydro for the suggestions and commentsthroughout the course of this project. The help of A. Terheide, atechnician in the University of Alberta Power Lab, with experi-mental investigations is fully acknowledged.

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, pp. 943–949, Apr. 2005.

[2] Members of the staff of the Department of Electrical Engineering,Massachusetts Institute of Technology, Magnetic Circuits and Trans-former. New York: Wiley, 1943, pp. 442–444.

[3] R. L. Bean, N. Chacken, H. R. Moore, and E. C. Wentz, Transformers forElectric Power Industry. New York: McGraw-Hill, 1959, pp. 317–321.

[4] M. Elleuch and M. Poloujadoff, “A contribution to the modeling of threephase transformers using reluctance,” IEEE Trans. Magn., vol. 32, no.2, pp. 335–343, Mar. 1996.

[5] H. M. Dommel, EMTP Theory Book, 2nd ed. Vancouver, British Co-lumbia: Microtran Power System Analysis Corporation, 1996.

[6] X. Chen, “Negative inductance and numerical instability of the saturabletransformer component in EMTP,” IEEE Trans. Power Del., vol. 15, no.4, pp. 1199–1204, Oct. 2000.

Wilsun Xu (M’90–SM’95) received the Ph.D. degree from the University ofBritish Columbia, Vancouver, Canada, in 1989.

He worked in BC Hydro from 1990 to 1996 as an engineer. Dr. Xu is presentlya Professor at the University of Alberta, Edmonton, Canada. His main researchinterests are power quality and harmonics.

Sami G. Abdulsalam (S’03) received the B.Sc. and M.Sc. degrees in electricalengineering from Elmansoura University, Egypt, in 1997 and 2001, respectively.He is currently pursuing his Ph.D. degree in electrical and computer engineeringat the University of Alberta, Edmonton, Canada.

Since 2001 he has been with Enppi Engineering Company, Cairo, Egypt.His current research interests are in modeling and simulation of power systemtransients.



Yu Cui received the B.Eng. degree from Tsinghua University, Beijing, China; anM.Sc. degree from Institute of Electrical Engineering, Chinese Academy of Sci-ences, Beijing, China; and an M.Sc. from University of Saskatchewan (Canada)in 1995, 2000, and 2003 respectively. He is currently working on his Ph.D. de-gree at University of Alberta.

His research areas include power system stability and power quality.

Xian Liu (M’95) obtained the Ph.D degree in computer engineering from theUniversity of British Columbia, Canada, in 1996.

Before joining the University of Arkansas at Little Rock, Little Rock, AR. Dr.Liu worked at NORTEL Networks, Ottawa, ON, Canada, and the University ofAlberta, Canada, from 1995 to 2001. To date he and his research collaboratorshave published more than 50 journal and conference papers, mainly in the areasof electrical machines, communication networks, and engineering optimization.


unloaded power transformer

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