A Current-Based Solution for Transformer Differential Protection—Part I Problem Statement

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 16, NO. 4, OCTOBER 2001 485

A Current-Based Solution for TransformerDifferential Protection—Part I: Problem StatementArmando Guzmán, Member, IEEE, Stan Zocholl, Life Fellow, IEEE, Gabriel Benmouyal, Member, IEEE, and

Héctor J. Altuve, Senior Member, IEEE

Abstract—This paper analyzes the problem of transformerdifferential protection. First, we review the concept of trans-former differential protection. We then analyze magnetizinginrush, overexcitation, and current transformer (CT) saturationphenomena as possible causes of relay misoperation. Finally, wesummarize the existing methods for discriminating internal faultsfrom inrush and overexcitation conditions. In Part II of the paper,we propose a new approach for transformer differential protectionand describe the relay that is based on this approach.

Index Terms—Differential protection, power transformer pro-tection, protective relaying.

I. INTRODUCTION

T HREE characteristics generally provide means fordetecting transformer internal faults [1]. These char-

acteristics include an increase in phase currents, an increasein the differential current, and gas formation caused by thefault arc. When transformer internal faults occur, immediatedisconnection of the faulted transformer is necessary to avoidextensive damage and/or preserve power system stability andpower quality. Three types of protection are normally used todetect these faults: overcurrent protection for phase currents,differential protection for differential currents, and gas accu-mulator or rate-of-pressure-rise protection for arcing faults.

This analysis will focus primarily on differential protection.Transformer differential relays are prone to misoperation in thepresence of transformer inrush currents, which result from tran-sients in transformer magnetic flux. The first solution to thisproblem was to introduce an intentional time delay in the dif-ferential relay [2], [3]. Another proposal was to desensitize therelay for a given time, to override the inrush condition [3], [4].Others suggested adding a voltage signal to restrain [2] or to su-pervise the differential relay [5].

Researchers quickly recognized that the harmonic content ofthe differential current provided information that helped differ-entiate faults from inrush conditions. Kennedy and Haywardproposed a differential relay with only harmonic restraint for busprotection [6]. Hayward [7] and Matthews [8] further developedthis method by adding percentage differential restraint for trans-former protection. These early relays used all the harmonics torestrain. With a relay that used only the second harmonic to

Manuscript received January 19, 2000.A. Guzmán, S. Zocholl, and G. Benmouyal are with Schweitzer Engineering

Laboratories, Pullman, WA, USA.H. J. Altuve is with Universidad Autónoma de Nuevo León, Monterrey, N.L.,

México.Publisher Item Identifier S 0885-8977(01)08528-4.

Fig. 1. Typical differential relay connection diagram.

block, Sharp and Glassburn introduced the idea of harmonicblocking instead of restraining [9].

Many modern transformer differential relays use eitherharmonic restraint or blocking methods. These methods en-sure relay security for a very high percentage of inrush andoverexcitation cases. However, these methods do not work incases with very low harmonic content in the operating current.Common harmonic restraint or blocking, introduced by Einvaland Linders [10], increases relay security for inrush, but coulddelay operation for internal faults combined with inrush in thenonfaulted phases.

Transformer overexcitation may also cause differential relaymisoperation. Einval and Linders proposed the use of an ad-ditional fifth-harmonic restraint to prevent such misoperations[10]. Others have proposed several methods based on waveshape recognition to distinguish faults from inrush and have ap-plied these methods in transformer relays [11]–[14]. However,these techniques do not identify transformer overexcitationconditions.

This paper analyzes the problem of transformer differentialprotection. We discuss magnetizing inrush, overexcitation, andCT saturation phenomena as possible causes of relay misoper-ation. We then summarize the existing methods for discrimi-nating internal faults from inrush and overexcitation conditions.In Part II of the paper, we propose a new approach for trans-former differential protection and describe the relay that is basedon this approach.

II. TRANSFORMERDIFFERENTIAL PROTECTION

Percentage restraint differential protective relays [3] havebeen in service for many years. Fig. 1 shows a typical differen-tial relay connection diagram. Differential elements comparean operating current with a restraining current. The operatingcurrent (also called differential current), , can be obtained

0885–8977/01$10.00 © 2001 IEEE

486 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 16, NO. 4, OCTOBER 2001

Fig. 2. Differential relay with dual slope characteristic.

from the phasor sum of the currents entering the protectedelement:

(1)

is proportional to the fault current for internal faults andapproaches zero for any other operating (ideal) conditions.

There are different alternatives for obtaining the restrainingcurrent, . The most common ones include the following:

(2)

(3)

(4)

where is a compensation factor, usually taken as 1 or 0.5.Equations (3) and (4) offer the advantage of being applicable

to differential relays with more than two restraint elements.The differential relay generates a tripping signal if the oper-

ating current, , is greater than a percentage of the restrainingcurrent, :

(5)

Fig. 2 shows a typical differential relay operating character-istic. This characteristic consists of a straight line having a slopeequal to and a horizontal straight line defining the relayminimum pickup current, . The relay operating region islocated above the slope characteristic [equation (5)], and the re-straining region is below the slope characteristic.

Differential relays perform well for external faults, as longas the CTs reproduce the primary currents correctly. When oneof the CTs saturates, or if both CTs saturate at different levels,false operating current appears in the differential relay andcould cause relay misoperation. Some differential relays usethe harmonics caused by CT saturation for added restraint andto avoid misoperations (6). In addition, the slope characteristicof the percentage differential relay provides further securityfor external faults with CT saturation. A variable-percentageor dual-slope characteristic, originally proposed by Sharpand Glassburn, further increases relay security for heavy CTsaturation. Fig. 2 shows this characteristic as a dotted line.

CT saturation is only one of the causes of false operatingcurrent in differential relays. In the case of power transformerapplications, other possible sources of error are the following:

• Mismatch between the CT ratios and the power trans-former ratio

• Variable ratio of the power transformer caused by a tapchanger

• Phase shift between the power transformer primary andsecondary currents for delta-wye connections

• Magnetizing inrush currents created by transformer tran-sients because of energization, voltage recovery after theclearance of an external fault, or energization of a paralleltransformer

• High exciting currents caused by transformeroverexcitation.

The relay percentage restraint characteristic typically solvesthe first two problems. A proper connection of the CTs or emula-tion of such a connection in a digital relay (auxiliary CTs histor-ically provided this function) addresses the phase shift problem.A very complex problem is that of discriminating internal faultcurrents from the false differential currents caused by magne-tizing inrush and transformer overexcitation.

III. M AGNETIZING INRUSH, OVEREXCITATION, AND CTSATURATION

Inrush or overexcitation conditions of a power transformerproduce false differential currents that could cause relay misop-eration. Both conditions produce distorted currents becausethey are related to transformer core saturation. The distortedwaveforms provide information that helps to discriminateinrush and overexcitation conditions from internal faults. How-ever, this discrimination can be complicated by other sourcesof distortion such as CT saturation, nonlinear fault resistance,or system resonant conditions.

A. Inrush Currents

Magnetizing inrush occurs in a transformer whenever thepolarity and magnitude of the residual flux do not agree withthe polarity and magnitude of the ideal instantaneous value ofsteady-state flux [15]. Transformer energization is a typicalcause of inrush currents, but any transient in the transformercircuit may generate these currents. Other causes includevoltage recovery after the clearance of an external fault or theenergization of a transformer in parallel with a transformerthat is already in service. The magnitudes and waveforms ofinrush currents depend on a multitude of factors, and are almostimpossible to predict [16]. The following summarizes the maincharacteristics of inrush currents:

• Generally contain dc offset, odd harmonics, and even har-monics [15], [16].

• Typically composed of unipolar or bipolar pulses, sepa-rated by intervals of very low current values [15], [16].

• Peak values of unipolar inrush current pulses decreasevery slowly. Time constant is typically much greaterthan that of the exponentially decaying dc offset of faultcurrents.

GUZMÁN et al.: A CURRENT-BASED SOLUTION FOR TRANSFORMER DIFFERENTIAL PROTECTION—PART I: PROBLEM STATEMENT 487

Fig. 3. Exciting current of an overexcited transformer; overvoltage of150 percent applied to a 5 KVA, 230/115 V single-phase transformer.

• Second-harmonic content starts with a low value and in-creases as the inrush current decreases.

• Relay currents are delta currents (a delta winding is en-countered in either the power- or current-transformer con-nections, or is simulated in the relay), which means thatcurrents of adjacent windings are subtracted, and:

DC components are subtractedFundamental components are added at 60Second harmonics are added at 120Third harmonics are added at 180(they cancel out),and so forth.

Sonnemannet al. initially claimed that the second-harmoniccontent of the inrush current was never less than 16–17 percentof the fundamental [15]. However, transformer energizationwith reduced voltages may generate inrush currents withsecond-harmonic content less than 10 percent, as will bediscussed in Part II of this paper.

B. Transformer Overexcitation

The magnetic flux inside the transformer core is directlyproportional to the applied voltage and inversely proportionalto the system frequency. Overvoltage and/or underfrequencyconditions can produce flux levels that saturate the transformercore. These abnormal operating conditions can exist in any partof the power system, so any transformer may be exposed tooverexcitation.

Transformer overexcitation causes transformer heating andincreases exciting current, noise, and vibration. A severelyoverexcited transformer should be disconnected to avoidtransformer damage. Because it is difficult, with differentialprotection, to control the amount of overexcitation that a trans-former can tolerate, transformer differential protection trippingfor an overexcitation condition is not desirable. Use separatetransformer overexcitation protection, instead, and the differen-tial element should not trip for these conditions. One alternativeis a V/Hz relay that responds to the voltage/frequency ratio.

Overexcitation of a power transformer is a typical case of acsaturation of the core that produces odd harmonics in the ex-citing current. Fig. 3 shows the exciting current recorded duringa real test of a 5 kVA, 230/115 V, single-phase laboratory trans-former [17]. The current corresponds to an overvoltage con-dition of 150 percent at nominal frequency. For comparisonpurposes, the peak value of the transformer nominal current is61.5 A, and the peak value of the exciting current is 57.3 A.

TABLE IHARMONIC CONTENT OF THECURRENT SIGNAL SHOWN IN FIG. 3

Table I shows the most significant harmonics of the currentsignal depicted in Fig. 3. Harmonics are expressed as a per-centage of the fundamental component. The third harmonic isthe most suitable for detecting overexcitation conditions, but ei-ther the delta connection of the CTs or the delta connection com-pensation of the differential relay filters out this harmonic. Thefifth harmonic, however, is still a reliable quantity for detectingoverexcitation conditions.

Einval and Linders [10] were first to propose using the fifthharmonic to restrain the transformer differential relay. They rec-ommended setting this restraint function at 35 percent of fifthharmonic with respect to the fundamental. This ensures secu-rity for overvoltage conditions less than 140 percent. For greaterovervoltages, which could destroy the transformer in a few sec-onds, it is desirable to have the differential relay fast trippingadded to that of the transformer overexcitation relay.

C. CT Saturation

The effect of CT saturation on transformer differential pro-tection is double-edged. For external faults, the resulting falsedifferential current may produce relay misoperation. In somecases, the percentage restraint in the relay addresses this falsedifferential current. For internal faults, the harmonics resultingfrom CT saturation could delay the operation of differential re-lays having harmonic restraint or blocking.

The main characteristics of CT saturation are the following:

• CTs reproduce faithfully the primary current for a giventime after fault inception [18]. The time to CT saturationdepends on several factors, but is typically one cycle orlonger.

• The worst CT saturation is produced by the dc componentof the primary current. During this dc saturation period,the second-ary current may contain dc offset and odd andeven harmonics [7], [19].

When the dc offset dies out, the CT has only ac saturation,characterized by the presence of odd harmonics in the secondarycurrent [6], [7], [20]. Fig. 4 shows a typical secondary currentwaveform for computer-simulated ac CT saturation. This figurealso depicts the harmonic content of this current. The figureconfirms the presence of odd harmonics and the absence of evenharmonics in the secondary current.

IV. M ETHODS FORDISCRIMINATING INTERNAL FAULTS FROM

INRUSH AND OVEREXCITATION CONDITIONS

Early transformer differential relay designs used time delay[2], [3] or a temporary desensitization of the relay [3], [4] to


Fig. 4. Typical secondary current for symmetrical CT saturation and itsharmonic content.

override the inrush current. An additional voltage signal to re-strain [2] or to supervise (block) [5] the differential relay hasalso been proposed. These proposals increased operating speedat the cost of higher complexity. Recent methods use voltageinformation to provide transformer protection [21]–[24]. It isrecognized, however, that while an integrated digital substationprotection system provides voltage information, this is not thecase for a stand-alone differential relay. Adding voltage signalsto such a relay requires potential transformers that are normallynot available in the installation.

The current-based methods for discriminating internal faultsfrom inrush and overexcitation conditions fall into two groups:those using harmonics to restrain or block [6]–[10] and thosebased on wave-shape identification [11]–[14].

A. Harmonic-Based Methods

The harmonic content of the differential current can be used torestrain or to block the relay, providing a means to differentiatebetween internal faults and inrush or overexcitation conditions.The technical literature on this topic has not clearly identifiedthe differences between restraint and blocking.

The first harmonic-restrained differential relays used all har-monics to provide the restraint function [6]–[8]. The resultinghigh level of harmonic restraint provided security for inrushconditions at the expense of operating speed for internal faultswith CT saturation.

Kennedy and Hayward [6] designed a differential relay withonly harmonic restraint for bus protection. The operating equa-tion can be expressed as:

(6)

where represents the fundamental component of the oper-ating current; , are the higher harmonics; and areconstant coefficients.

Hayward [7] and Matthews [8] enhanced this method byadding percentage differential restraint for transformer protec-tion. The differential relay operating condition is:

(7)

Einval and Linders [10] designed a three-phase differentialrelay with second- and fifth-harmonic restraint. This designcomplemented the idea of using only the second harmonicto identify inrush currents (originally proposed by Sharp andGlassburn [9]), by using the fifth harmonic to avoid misopera-tions for transformer overexcitation conditions.

The relay [10] includes air-gap auxiliary current transformersthat produce voltage secondary signals and filter out the dccomponents of the input currents. A maximum voltage detectorproduces the percentage differential restraint voltage, so therestraint quantity is of the form shown in (4). The relay formsan additional restraint voltage by summing the second- andfifth-harmonic components of a voltage proportional to theoperating current. The basic operation equation for one phasecan be expressed according to the following:

(8)

Einval and Linders first introduced the concept of commonharmonic restraint in this relay. The harmonic restraint quan-tity is proportional to the sum of the second- and fifth-harmoniccomponents of the three relay elements. The relay operationequation is of the following form:

(9)

Sharp and Glassburn [9] were first to propose harmonicblocking. They designed a relay consisting of a percentagedifferential unit, DU, and a harmonic blocking unit, HBU.Differential relay tripping requires operation of both DU andHBU units.

In the harmonic blocking unit the fundamental componentand higher harmonics of the operating current are passed to twoparallel circuits, rectified, and applied to the operating and re-straint coils of a polarized relay unit. The circuit supplying theoperating coil of the polarized relay unit includes a notch-typeparallel filter tuned to 120 Hz. The circuit supplying the restraintcoil of the polarized relay contains a low-pass filter combinedwith a notch filter tuned to 60 Hz. The series combination ofboth filters passes the second harmonic and rejects the funda-mental component and remaining harmonics of the operatingcurrent. As a result, the polarized relay compares an operatingsignal formed by the fundamental component, plus the third andhigher order harmonics of the operating current, with a restraintsignal that is proportional to the second harmonic of the oper-ating current. The operating condition of the harmonic blockingunit, HBU, can be expressed as follows:

(10)

Typically, digital transformer differential relays use second-and fifth-harmonic blocking logic. Fig. 5(a) shows a logicdiagram of a differential element having second- and fifth-harmonic blocking. A tripping signal requires fulfillment of(5), without fulfillment of the following blocking conditions:

(11)

(12)


Fig. 5. Two approaches to a differential element.

Fig. 6. Three-phase differential relay with independent harmonic blocking orrestraint.

Fig. 5(b) depicts the logic diagram of a differential elementusing second- and fifth-harmonic restraint.

Fig. 6 shows the three-phase versions of the transformer dif-ferential relay with independent harmonic blocking or restraint.The relay is composed of three differential elements of the typesshown in Fig. 5. In both cases a tripping signal results when anyone of the relay elements asserts.

Note that in the harmonic restraint element [see Fig. 5(b)],the operating current, , should overcome the combined ef-fects of the restraining current, , and the harmonics of theoperating current. On the other hand, in the harmonic blockingelement the operating current is independently compared withthe restraint current and the harmonics. Table II summarizesthe results of a qualitative comparison of the harmonic restraint(using all harmonics) and blocking methods for transformer dif-ferential protection.

The comparison results given in Table II suggest the use of theblocking method, if security for inrush can be guaranteed. How-ever, it is not always possible to guarantee security for inrush,as Part II of this paper explains. Therefore, harmonic restraintis an alternative method for providing relay security for inrushcurrents having low harmonic content.

Another alternative is to use common harmonic restraint orblocking. This method is simple to implement in a blocking

scheme and is the preferred alternative in present-day digital re-lays. Fig. 7 shows a logic diagram of the common harmonicblocking method.

A method that provides a compromise in reliability betweenthe independent and common harmonic blocking methodsdescribed earlier forms a composite signal that containsinformation on the harmonics of the operating currents of allrelay elements. Comparison of this composite signal with theoperating current determines relay operation.

The composite signal, , may be of the following form:

(13)

may contain all or only part of the harmonics of the op-erating current. Another possibility is to calculate the harmonicsRMS value for each relay element, :

(14)

The composite signal, , may then be calculated as sometype of an average value, using (15) or (16).

(15)

(16)

The relay blocking condition is the following:

(17)

Common harmonic blocking logic provides high security butsacrifices some dependability. Energization of a faulted trans-former could result in harmonics from the inrush currents ofthe nonfaulted phases, and these harmonics could delay relayoperation.

B. Wave Shape Recognition Methods

Other methods for discriminating internal faults from inrushconditions are based on direct recognition of the wave shapedistortion of the differential current.

Identification of the separation of differential current peaksrepresents a major group of wave shape recognition methods.Bertula [25] designed an early percentage differential relay inwhich the contacts vibrated for inrush current (because of thelow current intervals) and remained firmly closed for symmet-rical currents corresponding to internal faults. Rockefeller [13]proposed blocking relay operation if successive peaks of the dif-ferential current fail to occur at about 7.5–10 ms.

A well-known principle [11], [26] recognizes the length ofthe time intervals during which the differential current is nearzero. Fig. 8 depicts the basic concept behind this low currentdetection method.

The differential current is compared with positive and nega-tive thresholds having equal magnitudes. This comparison helpsto determine the duration of the intervals during which the ab-solute value of the current is less than the absolute value of the


TABLE IICOMPARISON OFINDEPENDENTHARMONIC RESTRAINT AND INDEPENDENTBLOCKING METHODS

Fig. 7. Common harmonic blocking method.

Fig. 8. Differential relay blocking based on recognizing the duration time oflow current intervals.

threshold. The time intervals are then electronically comparedwith a threshold value equal to one-quarter cycle. For inrushcurrents [Fig. 8(a)], the low current intervals,, are greaterthan one-quarter cycle, and the relay is blocked. For internalfaults [Fig. 8(b)], the low current intervals, , are less thanone-quarter cycle, and the relay operates.

Use of rectified differential current components provides anindirect way to identify the presence of low current intervals.Hegazy [27] proposed comparing the second harmonic of therectified differential current with a given threshold to generatea tripping signal. Dmitrenko [28] proposed issuing a trippingsignal if the polarity of a summing signal remains unchanged.

This signal is the sum of the dc and amplified fundamental com-ponents of the rectified differential current.

Another group of methods makes use of the recognition ofdc offset or asymmetry in the differential current. Some earlyrelays [12], [29], [30] used the saturation of an intermediatetransformer by the dc offset of the differential current as ablocking method. A transient additional restraint based onthe dc component was an enhancement to a well-knownharmonic-restraint transformer differential relay [8]. Michelson[31] proposed comparing the amplitudes of the positive andnegative semicycles of the differential current with giventhresholds in two different polarized elements. Both elementsmust pick up to produce a trip. Rockefeller [13] suggestedextension of this idea to a digital relay. Another alternative [32]is to use the difference of the absolute values of the positive andnegative semicycles of the differential current for restraint. Theamplitude of the negative semicycle of the differential currentmay also be used as the relay operating quantity [32]. Thenegative semicycle is that semicycle having opposite polaritywith respect to the dc component. More recently, Wilkinson[14] proposed making separate percentage-differential compar-isons on both semicycles of the differential current. Trippingoccurs if an operation condition similar to (7) is true for bothsemicycles.

V. CONCLUSION

1) Most transformer differential relays use the harmonics ofthe operating current to distinguish internal faults frommagnetizing inrush or overexcitation conditions. The har-monics can be used to restrain or to block relay operation.Harmonic restraint and blocking methods ensure relay se-curity for a very high percentage of inrush and overexci-tation cases. However, these methods fail for cases withvery low harmonic content in the operating current.

2) Common harmonic restraint or blocking increases differ-ential relay security, but could delay relay operation forinternal faults combined with inrush currents in the non-faulted phases.


3) Wave shape recognition techniques represent anotheralternative for discriminating internal faults from inrushconditions. However, these techniques fail to identifytransformer overexcitation conditions.

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[8] C. A. Mathews, “An improved transformer differential relay,”AIEETransactions, pt. III, vol. 73, pp. 645–650, June 1954.

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[16] J. Berdy, W. Kaufman, and K. Winick, “A dissertation on power trans-former excitation and inrush characteristics,” inSymposium on Trans-former Excitation and Inrush Characteristics and Their Relationship toTransformer Protective Relaying, Houston, TX, Aug. 5, 1976.

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[24] K. Inagaki, M. Higaki, Y. Matsui, K. Kurita, M. Suzuki, K. Yoshida,and T. Maeda, “Digital protection method for power transformers basedon an equivalent circuit composed of inverse inductance,”IEEE Trans.Power Delivery, vol. 3, no. 4, pp. 1501–1510, Oct. 1998.

[25] G. Bertula, “Enhanced transformer protection through inrush-proof ratiodifferential relays,”Brown Boveri Review, vol. 32, pp. 129–133, 1945.

[26] A. Giuliante and G. Clough, “Advances in the design of differential pro-tection for power transformers,” in1991 Georgia Tech. Protective Re-laying Conference, Atlanta, GA, May 1–3, 1991, pp. 1–12.

[27] M. Hegazy, “New principle for using full-wave rectifiers in differentialprotection of transformers,”IEE Proceedings, vol. 116, pp. 425–428,Mar. 1969.

[28] A. M. Dmitrenko, “The use of currentless pauses for detuning differ-ential protection from transient imbalance currents” (in Russian),Elek-trichestvo, no. 1, pp. 55–58, Jan. 1979.

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[32] E. V. Podgornyi and E. M. Ulianitskii, “A comparison of principles fordetuning differential relays from transformer inrush currents” (in Rus-sian),Elektrichestvo, no. 10, pp. 26–32, Oct. 1969.

Armando Guzmán received the B.S.E.E. degree with honors from Guadala-jara Autonomous University (UAG), Mexico, in 1979. He received a diplomain fiber-optics engineering from Monterrey Institute of Technology and Ad-vanced Studies (ITESM), Mexico, in 1990. He served as regional supervisor ofthe Protection Department in the Western Transmission Region of the FederalElectricity Commission (the electrical utility company of Mexico) for 13 years.He lectured at UAG in power system protection. Since 1993, he has been withSchweitzer Engineering Laboratories, Pullman, WA, where he is presently a re-search engineer. He holds several patents in power system protection. He is aMember of IEEE and has authored and coauthored several technical papers.

Stanley (Stan) Zochollreceived the B.S. and M.S. degrees in electrical engi-neering from Drexel University. He is an IEEE Life Fellow and a member of thePower Engineering Society and the Industrial Application Society. He is also amember of the Power System Relaying Committee and past chair of the RelayInput Sources Subcommittee. He joined Schweitzer Engineering Laboratoriesin 1991 in the position of Distinguished Engineer. He was with ABB PowerT&D Company Allentown (formerly ITE, Gould, BBC) since 1947, where heheld various engineering positions including Director of Protection Technology.His biography appears inWho’s Who in America. He holds over a dozen patentsassociated with power system protection using solid state and microprocessortechnology and is the author of numerous IEEE and protective relay conferencepapers. He received the Best Paper Award of the 1988 Petroleum and Chem-ical Industry Conference and the Power System Relaying Committee’s Distin-guished Service Award in 1991.

Gabriel Benmouyal received the B.A.Sc. degree in electrical engineering andthe M.A.Sc. degree in control engineering from Ecole Polytechnique, Univer-sité de Montréal, Canada in 1968 and 1970, respectively. In 1969, he joinedHydro-Québec as an instrumentation and control specialist. He worked on dif-ferent projects in the field of substation control systems and dispatching centers.In 1978, he joined IREQ, where his main field of activity was the applicationof microprocessors and digital techniques to substation and generating-stationcontrol and protection systems. In 1997, he joined Schweitzer Engineering Lab-oratories in the position of Research Engineer. He is a registered professionalengineer in the Province of Québec, is an IEEE Member, and has served on thePower System Relaying Committee since May 1989.

Héctor J. Altuve received the B.S.E.E. degree from Central University of LasVillas (UCLV), Cuba, in 1969 and the Ph.D. degree from Kiev Polytechnic In-stitute, USSR, in 1981. He served as a professor in the School of ElectricalEngineering at UCLV from 1969 to 1993. Since 1993, he has been a professorin the Ph.D. program of the Mechanical and Electrical Engineering School atAutonomous University of Nuevo Leon, in Monterrey, Mexico. He is a memberof the Mexican National Research System, a Senior Member of IEEE, and aPES Distinguished Lecturer. He has authored and coauthored many technicalpapers. He is presently the Schweitzer visiting professor at Washington StateUniversity.

A Current-Based Solution for Transformer Differential Protection—Part I Problem Statement

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