A New Approach for Transformer Ground Differential Protection

Dr. Tevfik SeziSiemens Power Transmission and Distribution, LLC

Distribution Automation DivisionP.O. Box 29503

Raleigh, NC 27626-0503 USA

ABSTRACT: Existing electromechanical ground differentialprotection relays are impaired in the event of CT saturation.They might trip when the fault is external (or not trip whenthe fault is internal) unless the configuration and settings aredesigned very carefully. In addition, inrush effects can alsocause wrong protection behavior. Simulations and fieldobservations have revealed that the phase angle differencebetween the ground current and zero sequence current, incombination with the ratio of their magnitudes, can be used toidentify precisely a transformer ground fault. Theseobservations were used for the development of a newnumerical transformer differential protective relay.Simulations and test results have shown that the new solutioncorrectly detects a wider range of phenomena that wouldindicate an internal fault, while remaining able to not trip inthe event of an external fault.

KEYWORDS: Power distribution protection, power systemprotection, power transformer protection, power transmissionprotection, protection, protective relaying.

I. INTRODUCTION

This paper describes a new approach for transformerground differential protection, also known as restrictedground fault protection. The algorithm described has beenimplemented in a new numerical transformer differentialrelay to obtain better protection coverage for transformersand shunt reactors than the classical solutions. Extensivesimulations and field tests have proven the reliability of theimplemented algorithms. The new solution does notrequire any external auxiliary CTs, and the settings arevery simple.

II. CLASSICAL SOLUTIONS

Phase-current differential protection schemes fortransformers are not sensitive enough to detect an internalphase-to-ground fault if the fault is located near the neutralpoint of the transformer. Also, it is difficult to detect aground fault if the transformer is resistance- or reactance-grounded, since the ground current will be limited.

One classical solution for detecting an internal groundfault is to use a high-impedance differential-current relay(Fig. 1). This solution is also often used as a compromisesolution for providing differential protection to a groundeddelta-wye transformer bank when no delta-side CTs areavailable (or convenient). This is a common situation fordistribution and industrial ties with the delta as the high-voltage side and protected by fuses.

An alternative classical solution is to use a directionalovercurrent relay or a product relay. This is often done if

87N

52

51N

IG

ICIBIA

A B C

Optional Resistoror Reactor

iG

3i0iOPERclassical

Fig. 1. Conventional Ground Differential Protection SchemeUsing a High-Impedance Differential Relay.

the characteristics or CT ratios of the CTs are not suitablefor using a high-impedance differential relay. This solutionis particularly applicable when the ground current islimited or when a sensitive ground CT is used. Fig. 2shows two different operating principles that use adirectional overcurrent relay. In one case, an auxiliarycurrent balancing autotransformer is used, in the other casean auxiliary 1:N current transformer.

If the directional overcurrent relay solution is used, therelay has a directional unit that operates as a product unit.The overcurrent unit itself is non-directional and operatesonly in response to the amplitude of the current. In Fig. 2,it is shown as the coil without an indicated polarity. Thisnon-directional unit has an inverse time characteristic, butoperates only if the directional unit operates.

In any classical solution, the relay operates if theproduct of the amplitude of the ground current, theamplitude of the zero sequence current, and the cosine ofthe phase angle between the two currents exceeds a certainlimit. For any particular current amplitudes, the maximumoperating torque occurs if the phase angle between the twocurrents is 0, while the maximum restraining torqueoccurs if the phase angle is 180. Zero torque occurs at 90. With the classical protection scheme, detailedconsideration must be given to ensuring that the relay willoperate correctly even if no zero sequence current ispresent [1].

III. THE NEW ALGORITHM

The new, low-impedance ground differential protectionalgorithm is based on Kirchoffs law. The informationprovided to the algorithm is sampled values of the phasecurrents and the ground current.

Using the known phase and ground CT ratio information(specified as relay settings), the sampled current values arenormalized relative to the nominal current of the protectedtransformer winding, In. This simply means that the unit ofmeasure for all currents is In, not amperes. Then, thequantities used by the algorithm are calculated:

A. Calculated Quantities

The restraining current, IR, is the scalar sum of theseparate amplitudes of the measured phase and groundcurrents. It is a measure of the total amount of currentflowing through the transformer, regardless of whether thecurrents are balanced. It is calculated according toequations (1) and (2):

)()()()()( kikikikiki GCBAR +++= (1)

-

=-=

1

0)(

1)(

N

kRR kniN

nI (2)

87N

52

51N

IG

ICIBIA

Optional Resistoror Reactor

iG

3i0

iOPERclassical

+

+

87N

iG

3i0

iOPERclassical

+

+

Directional Overcurrent Relay withCurrent-Balancing Autotransformer

Directional Overcurrent Relay withAuxiliary Current Transformer

A B C

Fig. 2. Ground Differential Protection Scheme Using a Directional Overcurrent Relay with Either anAuxiliary CT (left dashed-line box) or an Autotransformer (right dashed-line box).

where N is the number of samples taken during each powersystem cycle, while iA(k), iB(k), iC(k), and iG(k) are thesampled and normalized values of the phase and groundcurrents.

The fundamental vector of the ground current, IG, iscalculated using Fourier analysis:

( )[ ] ( )[ ]22 )(Im)(Re)( nInInI GGG += (3)

( ) )2cos()(2)(Re1

0 Nk

kniN

nIN

kGG p

-

=-= (4)

( ) )2sin()(2)(Im1

0 Nk

kniN

nIN

kGG p

-

=-= (5)

Two calculated current vectors, *0Ir

and **0Ir

, are themajor components of the new algorithm:

GIIrr

=*0 (6)

0**

0 3IIIII CBArrrrr

=++= (7)

Both quantities are calculated using the Fourier-analysisalgorithm described in equations (3), (4), and (5).

The differential current, ID, is by definition theamplitude of the vector-difference of the measured groundcurrent and the calculated zero sequence current. Byconvention, any current flowing into the protectedequipment is considered to have a positive magnitude; soID is calculated using the following equation:

**0

*0 III D

rr+= (8)

B. Fault Detection

The new algorithm detects that a fault has occurred ifthe differential current, ID, exceeds a relay setting(indicating that the ground current and zero sequencecurrent differ too much), or if the restraining current, IR,exceeds another relay setting (indicating that the totalamount of current flowing through the transformer is toohigh). Once a fault has been detected, further analysisoccurs. As with the classical solution, the question to beanswered is whether the fault is internal (requiring a trip)or external (not requiring a trip).

C. Trip Decision

In theory, an external fault can be easily recognizedsince the calculated quantities *0I

r and **0I

r will have equal

magnitudes and a phase angle difference of j = 90. Inreality, inrush effects or CT-saturation may distort themeasured currents. CT-saturation can affect both theperceived amplitudes of the fundamental current vectorsand the phase angle between them.

Classical Trip Area: The algorithm calculates a valuecalled the stabilization current, ISTAB:

IIIIrrr

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 30 60 90 120 150 180

1/ **0*0 =II

4.0

6

*0I

IOP

j (degrees)

k0 =

1.0

3

CLASSICALTRIP AREA

EXTENDED TRIP AREA

BLOCKAREA

Fig. 3. Trip area for 1/ **0*0 =II

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 30 60 90 120 150 180

2/ **0*0 =II

4.0

6

2.0

4

*0I

IOP

j (degrees)

k0 =

1.03

1.37

EXTENDED TRIP AREA

CLASSICALTRIP AREA

BLOCKAREA

Fig. 4. Trip area for 2/ **0*0 =II .

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 30 60 90 120 150 180

2.04

1.37

4/ **0*0 =II

*0I

IOP

j (degrees)

k0 = 1.03

4.0

6

CLASSICALTRIP AREA

EXTENDED TRIP AREA

BLOCKAREA

Fig. 5. Trip area for 4/ **0*0 =II .

Vector analysis can show that the amplitude of thestabilization current, ISTAB, will be negative if the phaseangle j between *0I

r and **0I

r is in the range

-90 j 90. In this case, the fault is internal, so a trip isappropriate if the amplitude of a calculated operatingcurrent, IOP, is above a minimum level (a relay setting):

*0IIOP = (if -90 j 90) (10)

Trip if SETTripOP II _ (if -90 j 90) (11)

Extended Trip Area: The new algorithm extends thetrip area to recognize internal faults that the classicalsolution will fail to respond to, while still avoiding animproper trip if the fault is external.

If the phase angle j is in the range 90 j 270(outside the classical trip area), the magnitude of ISTAB willbe positive. In this case, the new algorithm still bases thetrip decision on the amplitude of the operating current, IOP,but calculates IOP differently:

STABOP IkII 0*0 -= (if 90 j 270) (12)

Trip if SETTripOP II _ (if 90 j 270) (13)

where k0, the stabilization factor, is a relay setting usedto adjust the sensitivity of the protection when90 j 270. Note that when j is in that range, IOP is afunction of four quantities: the amplitudes of the currents

*0Ir

and **0Ir

, the phase angle between them, and thestabilization factor, k0:

( )**0*00 ,,, IIkfIOP j= (14)Since only the ratio of *0I to

**0I is of interest, one can

imagine graphing IOP as a three-dimensional surface wherethe dimensions correspond to IOP/

*0I (the normalized

value of IOP), j, and *0I /

**0I . Different values of k0 would

correspond to different plotted surfaces. Figures 3, 4, and 5show as graphs three cross-sections of such a plot. Eachgraph corresponds to one value of *0I /

**0I , with the

vertical axis corresponding to IOP/*0I and the horizontal

axis corresponding to j. (Only the range 0 j 180needs to be shown because of phase-angle symmetry). Thedifferent curves plotted correspond to different values of k0(a setting).

The interpretation of these graphs will now beexplained.

For any particular combination of *0I , **

0I and k0values, the value of the operating current, IOP, is affectedby j (the phase angle between *0I

r and **0I

r) in the

following way. If j is 90, the amplitude of thestabilization current, ISTAB, will be zero, and equation (12)will yield the same value as equation (10), the classicalsolution. However, as the phase angle j increases into therange 90 j 270, the stabilization current ISTAB willbecome larger, and so the operating current IOP willbecome smaller (equation 12).

If j is in the range -90 j 90, then IOP is equal to*0Ir

(by definition). This is the same behavior as for theclassical protection solution, so the area is labeled theClassical Trip Area.

The new algorithm extends the area in which a trip willbe allowed. Unlike the classical solution, a trip can stilloccur even if j is greater than 90 (further to the right onthe graph). It is very important to realize that the curvedboundary of the extended trip area moves while the relay isoperating. At all times, the instantaneous values of thenormalized operating current value, IOP/

*0I , and the phase

angle, j, will plot to a point somewhere on the curvecorresponding to the value of the stabilization factor, k0.In Figures 3, 4, and 5, the curved boundary of the extendedtrip area is plotted for several values of k0.

Compare Figures 3, 4, and 5 to see how as the ratio of*0I to

**0I increases the extended trip area becomes larger.

This is appropriate since a larger ratio means that themeasured ground current is becoming much larger than thecalculated zero sequence current. Hence, it is more likelythat the fault is internal than that it is external, even if CTsaturation is distorting the value of the perceived phaseangle between the currents.

For any given combination of the stabilization factor,0k , and ratio of the current amplitudes,

*0I /

**0I , there

exists a maximum phase angle jMAX at which theoperating current IOP reaches the value zero. If the phaseangle j is greater than jMAX, the operating current IOPwould be negative. To handle this, the algorithm changesany negative value for IOP to zero, so no trip occurs.

Table 1 lists the corresponding value of jMAX for valuesof k0 when 1/

**0

*0 =II :

Table 1.Values of the maximum phase angle, jMAX,corresponding to different values of thestabilization factor, k0, when 1/

**0

*0 =II .

k0 jjMAX 90

4.05657 100

2.03603 1101.36603 120

1.03372 130

D. Second Harmonic Restraint

The amplitude of the second harmonic of the differentialcurrent, ID (equation 8), is calculated to detect the effect ofinrush. If this amplitude exceeds a corresponding setting(typically 15% of the fundamental value of ID), the tripsignal will be blocked. But, if an internal fault with CT-saturation occurs during inrush, the trip signal must not beblocked. This situation is handled by disabling second-

harmonic blocking if the magnitude of the fundamentalcomponent of the differential current ID exceeds a separatesetting (typically ten-times the nominal current of thetransformer winding that the ground differential algorithmis protecting).

Evolving Faults

The algorithm is able to track the dynamic motion of theoperating point during power cycles. If an external faultwith CT saturation occurs, the algorithm will correctly nottrip. However, if the motion of the operating pointindicates that an internal fault is evolving (specifically, ifthe operating point moves from the blocking area into thetripping area and remains there for two power cycles), thealgorithm will issue a trip signal.

IV. TESTING AND AN EXAMPLE

The new ground differential algorithm has beenimplemented in a new numerical transformer differentialrelay. EMTP simulation tests and field experience havedemonstrated the high reliability of the algorithm.External, internal, and evolving fault test cases wereconducted. Both single-phase and multiple-phase faultswere considered. Simulations have shown high stability ofthe algorithm in the case of transformer inrush.

Figures 6, 7, and 8 show results for a simulated faultwith saturation of phase CTs. Thus, the zero sequencecurrent is distorted. The ground current CT is notsaturated.

Fig. 6, shows the calculated values of the normalizedcurrents *0I and

**0I ; Fig. 7 shows the normalized values

of the stabilization current ISTAB and the operating currentIOP; and Fig. 8 shows the calculated value of the phaseangle j.

Shortly after the start of the transformer inrush, thedistortion of the calculated zero sequence current is sosevere that the phase opposition of the two currents *0Iand **0I gets lost. Thus, a positive stabilization currentoccurs. Since the stabilization current is positive (in thetrip area), the absolute value of the phase angle betweenthe two phasors is less than 90, so a transition from theblock area to the trip area occurs. The algorithmrecognizes that CT saturation is present if the stabilizationcurrent is positive for a short time, then becomes negativefor a longer time. In other cases, there may be severaltransitions between the block area and the trip area. Forthis reason, the trip signal is delayed if a transition fromthe block area to the trip area is detected. The timer is resetafter each block-to-trip area transition. A trip signal is onlypossible if the stabilization current is positive for aspecified delay time and the operating current remainsabove the threshold value. The delay time is adjustable,with the default value being 2 cycles. Thus, no trip occursin the example shown.

V. CONCLUSION

The presented algorithm is highly sensitive, regardlessof the phase angle between the currents *0I

r and **0I

r. As

explained earlier in this paper, with increasing phase angleclassical product relay will require higher currentamplitudes to generate the necessary torque for a trip.Thus, the sensitivity of a classical relay decreases as thephase angle grows. In typical applications, no trip ispossible for phase angles greater than 85. With the

0

-1

-2

1

0.0 2.5cycles

5.0 7.5

*0I

**0I

Fig. 6. Normalized Currents *0I and**

0I During a Fault

2.5 5.0 7.5

1.0

0.5

0.0

-0.5

cycles

STABI

OPI

Fig. 7. Stabilization Current, ISTAB, and Operating Current, IOP.

200

150

50

100

0.0 2.5cycles

5.0 7.5

j

Fig. 8. Phase Angle j During a Fault

extended trip area, internal faults causing heavy CTsaturation problems will be detected. In addition, manytime consuming commissioning tests and fine adjustmentsnecessary for the classical ground-differential solutionsusing directional overcurrent relays are avoided.

VI. REFERENCES

[1] J.L. Blackburn, Protective Relaying: Principles andApplications, 2nd Edition. New York: Marcel Dekker,1998.

[2] C.H. Einvall and J.R. Linders, A Three-Phase DifferentialRelay for Transformer Protection, IEEE Transactions onPAS, Vol. PAS-94, No. 6, Nov/Dec 1975.

[3] W.A. Elmore, editor, Protective Relaying Theory andApplications. New York: Marcel Dekker, 1994.

[4] L.F. Kennedy and C.D. Hayward, Harmonic-Current-Restrained Relays for Differential Protection, AIEETransactions, Vol. 57, pp. 262-266, 1938.

[5] O.P. Malik, P.K. Dash, and G.S. Hope, Digital Protectionof Power Transformer, Paper No. A76 191-7 IEEE PES1976 Winter Power Meeting, New York.

[6] C.A. Mathews, An Improved Transformer DifferentialRelay, AIEE Transactions, Vol. 73, Part III, pp. 645-650,1954.

[7] J.A. Sykes, A New Technique for High-SpeedTransformer Fault Protection Suitable for Digital ComputerImplementation, IEEE paper No. C72 429-9, SummerPower Meeting of PES, 1972.

[8] J.A. Sykes and I.F. Morrison, A Proposed Method forHarmonic-Restraint Differential Protection for PowerTransformers, IEEE Transactions on PAS, Vol. PAS-91,No. 3, pp. 1260-1272, 1972.

VII. BIOGRAPHY

Dr. Tevfik Sezi (M 1997) wasborn in 1953 in Adana, Turkey. Hestudied power electronics at theTechnical University of Berlin(Germany), obtaining his Ph.D.(Dr.-Ing.) in 1985 after being anassistant professor there from 1980to 1985. His research areas haveincluded frequency variable drives,protection algorithms, andoptimized software structures for

protective relays. He has been with Siemens since 1985,working as a development engineer for protective relaysfrom 1985 to 1996, and was responsible for the relaydevelopment department between 1993 and 1996. Heholds several patents on protection algorithms. SinceAugust 1996 he has been in the United States as ProductManager for Protective Relays.