A Transformer Protective Relaying Algorithm

8/6/2019 A Transformer Protective Relaying Algorithm

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Paper accepted for presentationat 2003 IEEE Bologna PowerTech Conference, Jun e 23-26, Bologna, Italy

. . .I.*. lk, ,R,, Rk, ,Lhb,LTk,Lha5, ,L

A Transformer Protective Relaying AlgorithmUsing the Ratio of the Flux LinkagesY. C. Kang, S . H. Kang, . Crossley and S . J. Lee, M embers , IEEE, B. E. Lee, Student M ember, IEEE

Secondary winding currents (34)Secondary winding resistances (34)Secondary leakage inductances (34)Secondary flux linkages (34)

Abstrad-The ratio of the increments of the primary andsecondaly winding flux linkages (RIFL) is the same as the turnsratio during normal operating eonditions such as magneticinrush, overexcitation and external faults. For an internal fault,the RIFL is not equal to the turns ratio. This paper proposes atransformer protective relaying algorithm using the RIFL. For asingle-phaseor a three-phase Y-Y transformer, the increments ofthe flux linkages are calculated. For a three-phase Y-Atransformer, the differences between the two phases of theincrements of the flux linkages are calculated to use the linecurrents, because the delta winding current is unavailable. TheR l FL is compared against the turns ra tio; if they are different, itis an internal fault. Test results indicate that the proposedalgorithm successfully discriminates between internal windingfaults and magnetic inrush. This paper also describes the resultsof implemen tation of the algorithm into B digital signal processorbased prototype relay.Index Term- Magnetic Inrush, Remanent Flux, FluxLinkages

I. NOMENCLATURE

vr, va. vcI", Is, IC,i., ia ,,RA,RB ,RcL,, La , Lea,, b,VOb, Vk, v,

. . .

Symbols I DefinitionVI, v2 IVoltages

Primary voltages (34)Primary currents (34)Secondary line currents (34)Primary winding resistances (34)Primary leakage inductances (34)Primary flux linkages (34)Secondary voltages (34)

~~ I Currents.I . ~,al,A I Flux linkagesR I ,R> I Winding resistancesL,,.1." 1 Leakaee inductancesw I Mutual fluxNI,N2 I Number of twn s

This work WBS sponsored by Korea Minishy of Science and Technologyand Korea Science and Engineering Foundation through the ERC progra"!(Next-Generation PowerTechnologyCenter, NYTC).Y. C. Kang and B. E. Lee are with " T C an d Division of Electronics andInformation Engineenng, Chonbuk National Univ., Chonju, 561-756, Korea(e-mail:yckang@m oak.chonbuk ac.kr and mpec@dream x.net).S. H. Kang and S. . Lee are with NPTC and Department of ElectridEngineering, Myongji Univ., Yongin, 449-728, Korea (e-mail:shkang@mju .adz and [email protected]).P. Crossley is with School of Electrical and E l e m l l l e Engineering, theQueen's Univenity ofBelfm, N. Ireland (email: p.crosrley@?ee.qub.ac.uk).

0-7803-7967-5/03/$17.00 02003 IEEE

Authorized licensed use limited to: Iran Univ of Science and Tech. Downloaded on June 27, 2009 at 06:32 from IEEE Xplore. Restrictions apply.


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has four terms containing the circulating components and theycannot be obtained analytically. The fault detection procedurefor a wye-delta transformer is composed as follows. TheReference Phase out of thre e phases is first chosen. Secondly,the four terms for the Reference Phase are calculated usingthe remainder of the equation. Thirdly, they are substitutedinto the other equations for the other two phases after beingmultiplied by factors; these include the parameters of theReference Phase and the other phases. Finally, the algorithmdetects an internal fault if the multiplied and substituted termsdo not satisfy any other equations. The procedure assum es theXiR ratios of the delta winding are large. The faulted phasecan be identified based on the results when all the three phasesare used as the Reference Phase [SI. n addition, for a delta-delta transformer, each equation has eight term s containing thecirculating currents, because primary and secondary windingshave their winding currents. Thus, the conversion factors thatshould contain the parameters of the Reference and the otherphases of both windings, will be in a more complicated form.The basic principle oftransformer protection using the ratioof the induced voltages of the primary and secondarywindings was proposed in [9]. The internal fault is detectedbased on comparing induced voltages or induced voltagedifferences with turns ratio. It approximates the differentialterms using the backward Euler method and may cause someerrors if it is implemented in a digital relay. This paperdescribes a transformer protective relaying algorithm that usesthe ratio of the increment of the primary and secondarywinding flux linkages (RIFL). It is the integral version of thealgorithm in [9]. For magnetic inrush and over-excitation, theRIFL is equal to the turns ratio, while for an internal fault, it isnot. The algorithm estimates the increments of flux linkagesfor a single phase and a three-phase wye-wye transformer. Onthe contrary, for a wye-delta transformer, it estimates thedifferences of the increments of the flux linkages between thetwo phases to use the line currents. Then, the matchingincrements or differences ofth e increments are compared withthe turns ratio. The a lgorithm was tested for magnetic inrushand internal faults. The paper also describes the results ofimplementation of the algorithm on a digital signal processorbased prototype relay.

111. A m N S F O R M E R PROTECTIVE RELAYING ALGORITHMUSING THE RATIO OF FLUX LINKAGES

A . A single-ph ase transformerthere is no internal fault, v , an d vi can be given by:Fig. 1 shows a two winding single-phase transformer. If

dil dA,v , = R , i , + L , , - + -dt dt

Rearranging (1) an d (2) yields:di ,-= v I- Rlil- ,,-dt dt

di zdt dt-=4 v 2 + R Z i 2 + & -

(3)(4)

The increm ents of the flux linkages,M,,AA, are estimatedby integrating (3) an d (4). The ratio of the increment of theprimary and secondary winding flux linkages (RIFL) is thendefined as:

A4A 4RIFL =-

In the steady state, the RIFL is the same as the turns ratio(NJN,) except when AA, = 0 or AA = 0. For magnetic inrushand overexcitation, the RIFL is also equal to NJN,, althoughM, and AA are non-sinusoidal and distorted. For internalfaults, the RIFL is not the same asN,/N,.From this point, the RTFL can be directly used fordiscriminating internal faults from magnetizing inrush andoverexcitation. Howe ver eve n for norm al operating conditions,the RIFL is not always equal to NJN, because AA t an d AA ar einstantaneous values and consequently pass through zero. Inorder to overcome the problem, the D etector described by (6)is used to detect a fault in this paper. The Detector measuresthe percentage difference between the two estimatedincrements of the flux linkages. If (6) is less than a threshold,the transformer is not faulted; ifgreater, it is.

where, T is the sam pling intervalB. A three-phase Y- A transformertransformer. Voltages are represented in (7) - 12).Fig. 2 shows the connections of a three-phase Y-A

......4.c J . . . . . . . &,,,,+Fig. 2 A hvo winding three-phase ye-deltatr ansfor mer.: . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 1 A twowinding singlephrse h-ansforma



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diA dAAv A= R A i A+L, -+-dt dtdi, dA8vH= RBiH+Lm +-dt dt

(9)(10)(1 1)

diC dAcvc =R&+L,-+- dt dtdi dAabvab= RJab + LlabA+-dt dtdik dAkvb, = R a j k +L,bc- -t dtdi, dA,v , = R,i, +Ll,- -t dt

If there is no internal fault, (13) is valid.(13)hnH = N t =_AAzb N , ' AAk N,' AA, N ,

If Ad,,,&, A&, AAd, A&, an d A% can be calculated from(7 ) - (U),he three Detectors can he derived directly from(13). AAA,A&, A&, can he calculated, but AAb,A&, an d A&cannot from (10) - 12 ) because i,, i,, and i, are unavailable.In [7] and [8], j o b , i, an d i, were decomposed into the non-circulating and circulating currents. The non-circulatingcurrent could be derived from the line current. However, theterms relating the circulating currents could not be obtainedanalytically and thus an alternative was used to detect aninternal fault as mentioned in Introduction.In this paper, to use the line currents, the followingrelationship between the line and winding currents on th esecondary winding is used.

(14). . . . . . . .I , - #* = , , la b - b< = b , bC I , = I,In addition, if there is no internal fault, the assumption in(15) is valid.R, " R , = R , = R , L,d zz L, =Lb = L, (15)Subtracting (IO) from (U),11) from (IO) and (12) from

( 1 1) yields:

divaa-v , -Rib -L,4dt dt dtdaab dAk -dievac- ea- Ri, -L,-

dt dt dtd n , -

Therefore, whilst AAb,A&, an d A% cannot he calculated,their differences between the two phases can he calculated byintegrating (16) - (IS). The corresponding equations to (16),(17)'and (1 8) can be derived from (7 ) - 9):

On the other hand, the relationship between the differencesof the increments of the flux linkages can be derived by:A 4 A AA - N , MAA& - N, An, -A 4 - N ,AA,-AA, N I A & - A L k N 2 M,-M, N 2

Equation (22) is a nece ssary and sufficient conditio n for(13). Its proof is shown in Appendix. In this paper, (22) isused for fault detection for a Y-A transformer.

--, -- , -- (22)

Thus, the three D etectors are given by:NA(& - A A ) - A A ( A , -Anb)

A V c A TA(AA -AB)-%A(Aaa -Abc )AVmT

xlOO(%) (23)2Detector 1 =

x 100 (%) (24)2Detector 2 =

A( a B A c ) - z A ( a k -a,)xIOO(%) (25)2AVBcTDetector 3 =

rV. CASE TUDIESFig. 3shows a single-diagram of the simulated system andthe power frequency is 60 Hz.A two-winding three-phase Y-

A transformer (154kV/14.7kV, 55 MVA) is used to generatefault and inrush data using EMTP. The hysteresischaracteristics of the transformer core are modeled using atype-96 element; the saturation point of (40 A, 334 Vs) isselected to use HYSDA T, a subroutine of EMTP. The internalwinding fault modeling techniques in [ IO] are used torepresent turn-to-ground and turn-to-turn faults.The sampling rate is 32 samples/cycle and the voltages andcurrents are passed through the Butteworth Znd order filterswith a stop-band cut-off frequency of 960 Hz (half thesampling frequency).Th e performance o f the proposed algorithm was verified onthe various conditions such as magnetic inrush and internalwinding faults.A . Magnetic inrush

The magnitude of the inrush current depends on th eenergization angle, the remanent flux at the instant ofenergization and load. Thus, different inrush currents aregenerated by varying the ab ove parameters and used for test.

Fig. The model system shldied



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Case I : energization angle of 0 eg , 80% remanentflux, noloadFig. 4 shows the currents and voltages for Case 1. Thecurrent and voltages are severely distorted, Fig. 5 shows thetwo components of Detector 1 i.e. A(&- AA ) an d N,/N2A(&-Ab). he results show that the two estimated differences of theincrements of the flux linkages are nearly the same even if thecurrents and voltages are distorted.If the Detector output is greater than 5% , a counter isincreased by one; otherwise it is decreased by one. If thecounter is less than zero, it is reset to zero. If a counterexceeds four, the final trip signal is issued. Fig. 6 shows thethree Detectors and the trip signal. The output of from each o fthe three Detectors are less than 5%, consequently the tripsignal is not activated.Case 2: energization angle of 0 deg, 80 % remanenfflwr,fir11 oa dFig. 7 shows the operating response of the three Detectorsfo r Case 2; this is identical to Case 1, except a full load ( 5 5MVA) is connected to the transformer secondary.The primaryand secondary voltages are also severely distorted. All threedetectors remain below 5% , consequently the trip signal is notactivated.The two results indicate that the algorithm accuratelyestimates the differences of the increments of the flux linkages,even though the currents and voltages are severely distortedby the high remanen t flux and the load current.

20 40 60 80 lm 120 140Time (ms)(a) Primary cments

- :,---,- I :108 0 ~ -B -102 10e 0 ; . , --.ill-d ~10p 10

8 10- 10 ~ 70 ~-

20 4C 60 ED 100 120 140I1-20 40 M m tm ID 140:

20 40 60 to io0 120 140

m I : . :-----XI------I---

120 40 60 80 100 120 14010

Time (mr)(cj Secondary voltages (v, vbi vJFig. 4 --phase currents and voltages

2 10

d -1010

IB-IIIB o

$ 0

-d -102 10

d -10C O

I-- 10a.r -l o

---*-----+--020 40 60 Bo IM 120 140

I I I 1 ,20 40 50 m 100 120 14020 4C 60 33 lm lW 140

iZb A $0 A ld 0 lb li0



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B. Internal windingfaultsThe fault data for various faults on the pha se B of primarywinding are generated and used to test the algorithm. The testresults for two of the fault scenarios are described in Ca ses 3and 4.Case 3: A turn-to-ground ault, located 60 % f r o m theneutral winding end and at 0 deg inception angle.Case 4: A turn-to-turn ault, located between 20% and 30%and at 0 deg inception angleFig. 8 an d Fig. 9 describe the operating response of thethree Detectors for Cases 3 and 4, respectively. As th edifferences of the increments of the flux linkages are not thesame and thus Detectors 2 an d 3 exceed the 5% operatingthreshold. The signals in Detector 1 remain sm all, because itnot affected by a fault on phase B. In Case 3, the trip signal isactivated 2.6 rns after fault occurrence. In Case 4, this delay isincreased to 5.2 ms.

V.HARDWARE IMPLEMENTATIONFig. 10 show s the configura tion of the prototyp e system.

The relay was implemented on the TMS320C6701 digitalsignal processor. The sam pling rate is 3 2 sampledcycle. Thecurrents and voltages are passed through Butterworth 2d orderfilters Y-, = 96 0 E), hich are Sallen & Key active filters, tothe 14-bitA/D converter.

PCL-727 D IA Board(DiA Conversion11 l 2 Analog2nd Order Low-Pass Filter(Sailen 8 Key Active Filter1Spe c : Stop-band cutoff l r e ~ .GOHz.Gain 0.1

x 12 Filteredlmola Quad. IP PCI Carrier BoardAJD Module(lP341)12 CH. SimullaneOuS AID ConversionSpec: ReSOiulion : 14bits. I6CH's

Time ("7s)Fig. 9 Detectorsand IheWip si@ for Case 4

l n p ~ t

AnalogInout

QuantizedDayIonaTMS320C6701 PCI Dual Board

Code-Camaser Studio (Debwain0 TooilCPU: IGFLOPS. 167MHz

Fig. IO Thewnfguration ofhardware implementation



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e 102 08 10a)cE -10QEId -10% U- 10m

E-10

V1. CONCLUSIONThis paper describes a transformer protective relayingalgorithm using the ratio of the increment of the primary andsecondary flux linkages. The algorithm estimates theincrements o f the flux linkages for a wye-wye transformer orthe differences of the increments of th e flux linkages for atransformer including a delta winding to use the line currentsinstead of the winding currents. It compares them with theturns ratio to discriminate internal faults from magnetic inrush.The test results clearly demonstrate that the proposedalgorithm remains stable for magnetic inrush. In addition, thealgorithm detects internal fa ults within on e cycle. A prototype

relay successfully discriminates between internal faults andmagnetic inrush.The algorithm does not need to h o w the h ys te resi scharacteristics of the transformer core and the use of timedomain signals ensures the operating time is less than aconventional relay.

i~~.~~~i~ ~~~&.&~&&U&I I I I I I0 20 40 E 80 100 120 140.L-4.--

I , I I I I I0 20 40 60 80 100 120 140I I I I I I

VII. APPENDIXSufficient condition can be proved trivially in substituting(13) into (22). Thus, only necessary condition will be proved.Let three FUFLs be as ollows.

40208 00 -20d -40c

-E 40

Substituting (AI) into (22) yields:(4,N ,YLU,-dab- A ( & -nab )

da b - bc =$ (aab - ) (A3)&Ik - y M M = % A ( A ~ - A = ) (A4)N2In (M ) , f AA - # O , M n b = 0 , then y = N I N , . Similar, in

(A3), if AAsb tO,M, = 0 , then a = N , / N 2 ; in (A4),AAbe# O , A & = 0, he n p = N , / N , .In order for ( A l ) - (A3) to be valid for all A&, AA,,

M, , the condition of a = p = y = N , N , should be

................... ......~. . i...... ~ . ;.......

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A Transformer Protective Relaying Algorithm