a study of lossofexcitation relaying and stability of a 595mva generator on the detroit edison

7/29/2019 A Study of LossOfexcitation Relaying and Stability of a 595MVA Generator on the Detroit Edison

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IEEE T r a n s a c t i o n s on Pow e r A ppa ra tu sa n dS y s t e m s , vo l . PAS-94, no. 5 ,S e p t e m b e r I O c t o b e r1 9 7 5A STUDY OF OSS-OF-EXCITATIONR E L A Y I N G A N D S T A B I L I T YOF A WS-MVA GENERATOR ON T H EDET ROIT EDISON SYSTEM

Charles R.rndt McCIennonogersTH E DETROIT EDISON COMPANYDetroit, Michigan

ABSTRACTT hi s ap er describes the investigation andvaluation ofrelationships etweenoss-ofexcitation/fieldLOF) relaying andstabilityofa 595-MVA generator on th eDetroit Edisonsystem.Need for the formulation of a plan of action to promote a reliableapplication of LOF relays is made evident. Operating guidelines aresuggested which will safeguard the enera tor nd system fromd a m a g eu r i n gns ta bl e swings while avoiding inadvertentgenerator tripping during stable swings. In addition, a n examinationof operatingcharacteristicsofa loss-of-field relay in response tochanges in voltage and frequency is presented.

INTRODUCTIONAt the present ime,electricpowerutilities do no t agree that

LOF relay application to automatically ripmachines is desirable.While Detroit Edison uses them to trip the generator, several othercompanies donot. t is felt by some companies hat these relayshave trippedmachines in past blackouts when the machines hadnot reached thepoin t of instability.They, herefore, believe thatthese machines were removed from heir systems unnecessarily andcon trib ute d o he blackout. Several relay manufacturers favor theuse of hese relays for machine protec tion and some have madestudies f relay oper ation s during the Northeast lackout. Onestudy indicates th at units which were tripped probably had alreadybecome unstablewith swings which caused the ystem appa rentimpedance rajectory to ente r he relay operating mpedance zone.Ano ther tudy indicates that of seventeen relay operations, tenwere correct, five were undetermined, and two were incorrect.

From the above, it is appa rent that there is need for a clear andconvincing solut ion which will lead to a reliable application fLOF relays, thus protectinggenerators from damage andye tno tinitiating trip s during stable swings.

To helpmeet hisneed, the following course of ction wasunder taken o gain the knowledge anddata necessary to evaluateth eha ra c t e r i s t i c s a ndperation of anOF relay andsync hron ous generator during system disturbances:1 ) A mathematicalmodel was developed which simulates oneof Detroit Edisons major units which is protected by a LO F relay.The model uses machine and regu lator constan ts supplied by themanufacturer. Studies have been conducte d using analog and digitalcomp uters to determine the apparent impedance trajectories of thegenerator following system disturbances.2) An investigation of the generators LOF relay characteristics

has been c ond ucted which relates relay response to voltage andfrequency.3 ) F i e l de s t sr ee n t a t i v e l yl a n n e do determine,experimentally, ransfer func tions describing the dynamic behaviorof hegenerator. The performance of these tests would provide amore realistic mathematical representation of the machine.

ternRelaying Committee of the IEEE Power Engineering Society for presenta-Paper T 73318-3, recommended and approved by the IEEE Power Sys-

tion at the IEEEPES Summer Meeting & EHV/UHV Conference, Vancouver,B.C., Canada, July 15-20, 1973. Manuscript submitted February 20, 1973 ; madearailable for printing April 19, 1973.

SUMMARY OF RESULTSThe studies conducted to date have been performedwith onemachine working through a transformer and system impedance intoan infinite bus as shown in Figure 1.

P+ J Q- t 30 FAULTLOCATiON ESTRANSFORMERREACTANCEx * 9.5 %

SYSTEMREACTANCEx L =8.8 yoV I

Figure 1. Simplified system studied (constants on plants MVA base)Th e load seen by the m achine at its terminals is represented onan R-X diagram, a typical example of which is shown as Figure 2.The results of the resent stud y will be summarized using thisfigure as a guide. Point A corresponds to the load seen by themachine underormalteady-stateperating conditionsunitypower factor for this example). Point B represents the condition ofa three-phase fault at he high-voltage terminalsof hemachinet ransformer .o in t Corresponds to the instantaneous loadimmediately af ter he fault is cleared, and the trajectoryCDEF

represents he ransient load impedance following the clearing ofthe ault. The circle of center G anddiameter HI is the 6GHztrippingcharacteristic of the oss~of-excitation relay, where pointH corresponds to he relay characteristic offset and poin t I to themaximum ohmic reach.T h e R - X trajectory was determined forifferent initialoperating conditionsund er three-phase faults nd unde r loss ofexcitation. The following results were obtained:1) Under three-phase faults, with clearing times close to critical,th e R- X trajectory, in certain cases, pe netra ted the relay rippingcircle while the machine was still stable. In several cases, thetripping circle was crossed in the vicinity of the maximum ohmicreach point I and ,in a few cases, in the vicinity of the offset pointH. The maximum timeduring which the rajectorystayedwithinthe relay operating circle was 0.21 econds (1 2. 6 cycles) for the

crossings at I and 0.10 seconds (6 cycles) for the crossing at H.Had these cases occurred in reality, he machine would have beentripped unnecessarily.2) On three-phase faults when the clearing time was decreased,the dwelling time of he rajectory inside the relay operating circlealso decreased so that below acertain clearing time the trajectoryno longer crossed the circle. For he model used in this study, twas determined, for instance, th at for 0.9 per unit (P.u.) power atunitypower facto r (full load), the critical clearing time was 0.18seconds (10.8 cycles), and the corresponding trajectory remained inthe circle for about 0.10 seconds (6 cycles). For a clearing time of0.15 seconds (9 cycles), the trajectory no onger crossed the circle.As a esult of previous multimachine tability tudies based on196 8 system impedance dat a, the breakers are normally set to clearsuch faults in 4 t o 5 cycles with backup relaying set to clear the

fault in 1 1 to 12 cycles. Itappears, therefore, that if abreakerope ra t e srope r ly ,he R-X trajectoryoes not have the1449


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opportunity of crossing the operating circle of theLOF relay.However, should a breaker fail to oper ate properly, the LO F relaymay trip the machine unnecessarily.3) On loss of exc itatio n, the R-X trajectory always crossed therelay operating circle and ntersected he X-axis within 0.35 t o0.90 seconds (21 o 54 cycles) after he crossing occurred. As thetrajectory ntersects he X-axis, the machine star ts slipping a poleas aprelude to instability, and tripping may be indicated at hatpoint.Therefore, hould delay of approxim ately 0.25 seconds( 1 5 cycles) be inserted in the operationof the relay, harmlessexcursions of the R-X trajectory into he relay operating circlewould not cause unnecessary trippings of the machine, and yet,loss of excitation would be duly detected and protected against.4) Terminal voltage variations o f t 25 percent had no effect o nthe relay perform ance; however, frequency variations affected bot htheohmic reach (measured by distance 01) and the torque angle(angle between the positive R-axis and 01). At 60 Hz, the ohmicreach was 25 ohms at an angle of 270 0; at 58 Hz and 62 Hz thesevalues became respectively 23 o hm s at 264O and 29 ohm s at 276O(Figure 2). At no time during the test on he generator model didthe requencyvariations exceed ? 2 Hz while experiencing stabletransients. Under a hree- phase fault condition, the portion CD ofthe trajectory is covered while A f is positive ( A f is the variationof frequency from 6 0 Hz), and the portion DE, while A f isnegative. Thus, the possibility of excursions intohe relayoperating circle is increased atpoint Hand decreased atpoin t I.However, if the relay is provided with delay of 15 cycles asalready suggested, stable ystem swings which result in app aren timpedan ce trajectories entering the circle will no t trip the mach ine,while actual conditions of excitation loss will trip it.5) This study was performed on the basis of one machineworking against an nfinite bus and with the use of a simplifiedregulator-exciter modelurnished by themanufacturer. Twomethods, one analog and one digital, were employed to obtai n thedynam ic behavior of the system und er the most severe three-phasefault onditions and bothme thod s yielded comparab le results.Although the conclusions to be drawn are meaningful anduseful,the ext ent of their validity still remains to be proven on he basisof a more realisticmultimachine system. Furtherm ore,hemathematical epresentation of the regulatorexciter system mustb experimenta l ly de te rminedhroughctualynamicests

performed on the actual enerator nd xcitationystem.Thisshould: a) yield a more accu rateepresentation of the ystem,b ) x p l i c i t l y h o wh e i f f e r e n t o m p o n e n t s of th eregulatorexciter system so that possible contingencies in thesecomp onents can be readily simulated, and c) allow the tudy ofperiodic swings inhe rent o the system aswellas those caused byexternal disturbances.DESCRIPTION AND PERFORMANCE OF R E L A Y

LOF relaying is provided on all hydrogen-cooled unitson heDetroit Edison system. T h e primary fu nction of his relaying is tosense the loss of excitation on a unit and remove the unit from thesystem.Lossfxc i ta t ion on a unit may cause the following

undesirable consequences:1 ) System voltage reduction caused by excessive reactivepower-flow into the unit.2) Loss of synchronism resulting in theunit operating s aninduction generator.3) Possible thermal damage to the otor due to induced eddycurrentsT h e relay in this study is aingle-phase, singleelement,high-speed m ho distance-type relay. T he opera ting characteristic ofthe relay is shown in Figure 2 where the offset OH and hemaximum reach 01 are adjustable. Since the relay is energized bymachine voltage and current, he origin of the R-X diagram is atthe machine terminals. Normal relay settings re OH equal to

X RELAY OPERATING CIRCLEAT 60 H zAT 62 HZ----- AT 58 Hz__- - - -

270'

Figure 2 . Typical R - X diagram f or a 3-phase fault at the machinetransformer terminal

X'd/2trans ient reactance) and 01 equal to (direct-axissynchronous reactance) of the machine being protected. Anauxiliary relay withdelayedpickup (4 o 5 cycles) is provided tointerlock tripping from the distance element. This prevents trippingof the unit ue to momen tary ontact closure resulting fromvibration or ther transient cond itions ot related to machineoperation.

Laboratory ests were cond ucted o determine the performancecharacteristics of the relay described above. From these tests hefollowing general conclusions were made:1) A voltage variationof 2 2'5 percent of rated voltage hasanegligible effect on the impedance characteristic of he relay. Thistest was performed at 5 5 and 65 Hz as well as at he rated 6GHzfrequency.2) In general, an nderfrequency con ditio n will result in alower relay maximum torque angle and a shorter relay ohmicreach. An overfrequen cy con ditio n will give an increased maxim umtorq ue angle and longer ohmic reach.a) Maximum Torque Angle - With zero ohms offsetand the6@Hz relay maximum torque angle set at 2700 the orque anglea t 55 Hzs 2520, and at65 Hz is 84O. Maximum torqu e isdeveloped at these angles atbot h the minimum andmaximumrelay ohmiceach. As the impedance circle is offset from heorigin of the R-X diagram, the maximum torque angle at bot h 5 5and 65 Hz will tend to shift toward the 6GH z setting.b) Ohmic Reach -With zero ohms offset, the 5 5 Hz maximumohmic reach is 78 percentof the60 Hz maximumohmic each.

T h e 6 5 Hz maximumohmic each is 138percent of th e60 Hzmaximum ohmic reach.Figure 3 , shows the laboratoryesults obtained rom aes tconductedon the elay. Fo r this test he relay's offsetand reachwere adjusted to correspond to the pecifications of the ystemunder study.

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Based o n these assumptions, and with reference to Figure 4, th e6 0 HERTZALIBRATION system under study can be mathematicallyepresented by theDIAMETER-23 OHMS 0 - N L 2 7 0 ' D I A . - 5 - 5 0 OHMS PHASE-TO- following equations:REACH-250HMS 0- N L 270 ' NEUTRAL.OFFSET- 2 O H M S 0-p.~ 2700 O FFS E T-0 -4 OHMS PHASE-TO-NEUTRAL. Equation of Motion90' p28=-2 (Pm - P)

Power Output..

P = Eq Iq (active)Q =Eq Id - 2Xq (reactive at machine erminal)

340 Components ofnfinite Bus VoltageE s ~ ES COS 8 =E'q - x' d + xt +XL) IdEsd = Es sin 8 = (X t + XL +$1 Iq

Com pone nts of machine erminal voltageVq = E1 - Xd IdVd = Xq Iq

Field EffectsE1 = E'q + (X d - X'd) IdpE'q =2 Efd - EIS )Td'oEI S = E1 + AEI

2500 270 2009 0 300 = A eB(E'q-0.8)Figure 3. Impedance characteristic fo r the LOF relay

ANA LYTICAL STUDY PROCEDURE

E, = E1 - (X d - Xq) IdWhere: A BMachine 0.03 6.4047Exciter 0.001 22 1.211

1) Onlyundamentalrequency curren ts and voltages wererepresented in the tator ndhe connected system. This wa saccomplished by setting the rates of change of flux linkage termsof the direct and quadrature axes equal to zero.

2 ) The effect of machine speed variations upon thegeneratedvoltage was neglected.3 ) Amortisseur damping and the shielding effect of theamortisseuresbetween he field and stator were neglected duringtransients.4) During the period of interest, the action of the prime movergovernor was assumed to be not sufficiently fast to change themechanical power input following a small change in speed, so thatthe mechanical power input was constant.5 ) Machine and system resistances along with all other factorswhich could cause damping, such as mechanical friction, windage,

etc., were neglected.

Figure 4 . Phasor diagram generator-transformer-infinite bus

Analog SolutionThe model consisted of t hree parts: )heegulator-exciter

analog, 2 ) the analog of thegenerator-transformer-transmission tothe nfinite bus, and 3 ) the analog used to comp ute he resistance(R) and he eactance (X) seen by the machine at ts terminals.The block diagram of theegulator-exciter ystem is shown sFigure 5 . This is an IEEE Type I representation for a continuouslyacting regulator and exciter fo r which the manufa cturer providesd a t a . h e n a l o g m p l e m e n t a t i o n f h emachine-transformer-transmission line is show n as Figure 6 . Themathematical equations developed in the preceding paragraph wereused to implement his model. The third part of the model wasprogrammed to calculate R and X.1 I II I 1I I II II I EXCITER II REGULATOR / II I SATURATION ~' V R E F VR MA XII I FUNCTION

$ EF o .

TE=0.52F=0.08TF =0.963

Figure 5 . IEEE Type Iexcitation ystem epresentationfor continuously acting regulator and exciter.1451


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Figure 6. Equivalent analog of the basic system.The analog studies were conducted as follows: The voltage (Es)of the infinitebu sand the nput power Pm) were chosen suchtha t he steady-state real power (P) and the reactive p ower Q)were fixed t o predetermined values. Fo r each set of (P,Q) values, ath ree -phase fau l t a the transformerecondary (high-voltageterminals) was simulated.Underault onditions, the quation sdescribing the system were modified as follows:

E t = P = I q = OEq = (Xd +Xt) Id

All other equatio ns were unchanged. In each case, the fault wascleared after a imeand the transformer was reconnected to heinfiniteushrough the prefault im edance. Fo r each faultcondition, R vsX, R vst, X vs.t, andd s.t were disp laye d on anX-Y plotter. d tDigital Solut ion

The digital solution was performed on an on-line time-sharingdigital computer. T he exciter-regulator imulated was identical toth eone shown on Figure 5 , and the system equations were thosedescribed in the previous section.A ibrary program was used todigitally solve the anal-og representation shown in Figure 6.

I n t h i s t u d y ,h e econdorde r Runge-Kut tantegrationtechnique is employed since low oscillation frequencies inherent inpowerystem work make the sec on da de r rout inemore thanacceptable as a solution technique for the differential equations.Finally, R-X tabulations were obtained fo r three-phase faults atdifferent values of P and Q in a similar fashion as for he analogsimulation. The R-X values thus obtained were plotted on a R-Xdiagram.

DISCUSSION OF D A T AThe test results from the model for a three-phase fault and LOFcond itions are summaried in Tables I and 11.Table I contains data obtained following a three-phase fault at

the high-voltage terminals of the main unit transformer and isorganized intoour groupsccording to real powernd lineimpedance. Within each group,ower factor was varied todetermine the effect of different levels of excitation. Prefault ineimpedance was the same as the postfault impedance.A group of figures representative of data tabulated in Table Ihave been ncluded in this report. These figures are analog anddigital plo ts of machin e mpeda nce following a three-phase fault,and indicate the relationship to he60 Hz LOF relay operatingcharacteristic. The effect of power factor is shown in Figures 7, 8an d 9. They demonstrate hat reducedexcitation educes critical

clearing timendesults in an pparen t impedancerajectorywhich mo re closely approaches o r ente rs the relay operating circlefor a given clearing time. Figures 8 and 10 reflect he educedtendency t o enter he operating circle andan increase of criticalclearing time at reduced ower levels. Figure 11llustrates thetendency of the trajectory to stay within the circle for longerperiods of time with reduced excitatio n levels.Data obtained using a transmission impedance of 0.176 p.u.ohms, which is twice th at of the the r tests, indicate riticalclearing times are reduced and impedance rajectories are moreremoved from the operating circle f or stable conditions.Table I1 is asummaryof LOF data obtained rom the modelsfor various conditions. In each case, the loss of excitation w as du e toa simulated short-circuitedield.ypicalxamplefOFtrajectory is shown in Figure 12.Unstableransientswithheir xcursion into he negative Rregion are typified by the curve in Figure 13. The trajectory of theapparentmpedance in Figure 13 does ot reverse but insteadcontinues toward the negative R region and crosses the Requalszero axis, an d. the machine slips a pole.F igure 14 i s a p lo t o f a v s , R vs t, and X vs t.dt

This type of plot was made for all tests cond ucted on the analogsolution to helpelate the model response to the frequencycharacteristics of the relay.Another approachdemonstrating the stability or instabilityofthe machine response to the transient isturbance is shpwn inFigure 15. This phase plane rajectory is a plot of (&a ) for astable and an unstable conditio n. The curve A B C D and back to

A illustrates a stable machin e swing following a disturbanc e appliedwhen the machine was operating at oint A. During the .18second fault ,(& 8 ) followed curve AB. At B, the fault cleared andthe ensuing spiral back to the steady-state cond ition occurred.When the fault ime was increased to0.20 seconds, curve AEFresulted,with never reversing polaritynd the machine wasunstable.CONCLUSIONS

1. Loss of excitation nd the specific unstable swings whichwere observed invariably operated the relay, as desired.2. Underparticularoperatingconditions,certain table swingsalso resulted in relay operation, which is undesirable.3. Insertion of a ime delay of 0.25 seconds (15 cycles) in th e

relay operating equence will prevent undesirable relay ope ratio n.RECOMMENDATIONS

1. Amultimachinesimulation study should be made to verifythe results of this basic model study.2. Actualdynamic estsshould be made on th eunit tested toverify the accuracy of the model and constan ts used in this study.

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+ X , 1.0P U

i=.I8\ . 2 10 PU. +R

7'\Figure 7. Impeda nce trajectory flagging PF ) or

PIC =0.9, QIC = 0.252, t c = 0.19,X, =0.088

Figure 8. Impedance trajectory fPF nem Un ity) forPIC 0.9,QI C = 0.05, tc = 0.18,X , = 0.088

+R

Figure 9. Impedance trajectory (leading PF ) orPIC =0.9, QIC = -0.13, t c = 0.17,XL = 0.088

+ X .Q .U.

IFigure 11 . Impedance trajectow (reduced power levelandleading PF) for PIC = 0.75, QIC = -0.25t c = 0.18, x, = 0.088+I oP.U.

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TABLE I Transient After ThreephaseFault

TestN0.1234567891011

- Ini t ial Condit ionsRealeactivempedance LineFigureowerower zNo .- 0.9 0.49 0.088- 0.9 0.28 0.0887.9 0.25 0.088- 0.9 0.25 0.088- 0.9 0.09 0.0888.9 0.05 0.088- 0.9 0.005.08814 0.9 -0.04 0.088- 0.9 -0.12 0.088- 0.9 -0.12 0.088- 0.9 -0.24 0.088

- -D.U.)D.U.)P.U.)

12 -131415 -16 -17 1118 -19 -20 -2122 -23 -

-

-

0.75 0.470.75 0.270.75 0.070.75 -0.040.75 -0.060.75 -0.250.9.45 0.9.45 0.9.38 0.9.36 0.90.02 0.90.20

0.0880.0880.0880.0880.0880.0880.1760.1760.1760.1760.1760.176

Durationof Faul t(5 )

0.180.180.190.210.180.180.180.180.170.180.150.180.180.180.180.180.180.170.180.170.180.150.14

Timeof FirstIntersection(SI

NoneNoneNone0.540.570.430.190.680.250.52

NoneNoneNone0.450.4 10.43NoneNoneNoneNoneNoneNone

24 - 0.75 0.37 0.176 0.18 None25 - 0.75 -0.08 0.176 0.18 0.5726 - 0.75 -0.12 0.176 0.18 0.6627 - 0.75 -0.25 0.176 0.16 0.2528 - 0.75 -0.25 0.176 0.18 0.25*No t Ava i lab leTrajectory above circle on f i r s t swing

Table I headings are defined as follows:1) Duration of Fault is defined as the length of time duringwhich the short circuit was applied, and any value shownless than 0.18 seconds ndicates,within 0.01 seconds, thecritical clearing time fo r ha t set f onditions. Criticalclearing time is defined s the maximum fault du rationtime which does not cause instability.2) Time of Firstntersection is theim e between fault

Time InCircleANoneNoneNone0.120.100.100.290.090.10

NoneNoneNone0.100.190.21NoneNoneNoneNoneNoneNone

+

+

None0.120.100.100.1ot

+*I I0 .U.

Point o fIntersectionNoneNoneNone

BottomBottomTOPTOPBottomTOPBottomNoneNoneNoneBottomBottomBottomNoneNoneNoneNoneNoneNoneNoneBottomBottomTO PTOP

StableorUnstableSSSU++SSSUSUSSSSSSSSU * *SU *+SS

clearance and the f m t intersection of the mho circle. , I o P.U.3) Time in Circle is the time th at the rajectory remains int h em ho c i rc leor stableransients.hi sime wasdetermin ed by using R-X, R-t, and X-t plotswithheanalog model and from graphing and interpolatinghedigital data.

% R

4 ) Point of Intersection ndicates the general area in whichthe trajectory intersects the mho circle.5 ) In the Stable or Unstable olumn, S indicates that hetransient was stablean dU ndicates that the ransient wasunstable.

Figure 13. Impedance trajectory - nstable fo rP I c = O . 9 , Q 1 ~ = - 0 . 0 4 ,C = 0 . 1 8 ,x, =0.088

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TABLE I IResults- oss of Field

Init ial Condit ionsReal ReactivempedancePowerower Z

Line-P.U.)P.U.)0.9 0.43 0.0880.9 0.03 0.0880.9 00 0.0880.90.13 0.0880.9 -0.25 0.0880.75 0.48 0.0880.75 0.44 0.0880.75 0.09 0.0880.750.126 0.0880.750.26 0.0880.90.02 0.1760.75 -0.08 0.1 760.750.12 0.176

Timeof FirstIntersection(SI

1.91.51.31. 11.052.101.51.51.31.41.3

2.851.8

Time InCircle ToR EqualsZero(SI

0.350.60-0.650.60--0.80-0.900.350.650.55

TotalObservedTime InCircle(SI0.500.750.700.700.750.700.950.901.100.55

0.80

0. o0.80

Column headings are defined as follows:1) Time of First Intersection is the tim e betwe en loss-of-field voltage and trajectory ntersection of the operating circle.2) Time in Circle to R Equals Zero is the time between entering the circle and crossing the R equals zero axis.3) Total Observed Time in Circle is the time between entr y into the circle and exit from the circle or the end of the test, whicheveroccurred first (the functio n generator used in the analog model was valid for plus or minus 1800 ).

E

I200 4 0 0 6 0 0 8 0 0 1000

Figure 15. Phase plane trajectory fo r PIC =0.9, QI C =0. 17 ,t c =0.18 & 0.20, XL =0.088

ACKNOWLEDGMENTThe material presented in this paper resulted from the efforts ofthe Gen erator System Dynamics Task Force of which the autho rsare members. Th e remaining members who contrib uted directly are

M. S. Mashikian, J . R. Mather, and C. E. Ojanen.Figure 14 . Frequency deviation and mpedance as a function Futher more , he autho rs acknowledge the valuable contrib utionof T. A. Laichalk who conducted the aboratory tests on the LOF

relay.f t i me f or P IC =0.9, tc = 0.18, XL =0.0881455


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Ef dE1

EIS

EtfHIId, q

KaKE

NOMENCLATUREterminal voltage of the machine fieldstator voltage induced by the field currentneglecting saturationstator voltage induced by the field currentincluding saturationvoltage behind the quadratu re axis reactancexqquadrature axis component of the voltagebehind ransient eactance xdinfinite bus voltagethe direct and quadrature a x i s componentsof the infinite bus voltagetransformer voltagefrequency 60 Hzmachine inertiamachine phase currentthe direct and quadratu re axis compo nentof Iregulator gainexciter constant related to self-excitedfieldregulator stabilizing circuit gainreal electrical power outputmechanical power inputreactive power outputresistance (at machine erminal) per un itregulator amplifier ime constantfault clearing time seconds)exciter ime constantregulator stabilizing circuit ime cons tant

Tdo openircuit field time con stant of thegeneratorV machine output voltage at terminalsvd9 vq directxis anduadrature axis componentsof the machine erminal voltageXeactance (at machineerminal)er unitdq direct and quadrature-axis synchronousreactancesXd direct-axis transi enteactanceXL per unit systemeactancext per unit transformereactances angle between the q-axis andhe infvlitebus voltagePifferential operator 6subscript IC indicates the steady-state value of the variable at anoperating point

REFERENCES( 1 ) I E E EW o r k i n gG r o u p fh e x c i t a t i o n S ys te mSubcommittee of the IEEEPower GenerationCommittee,ComputerRepresentation ofExcitation Systems, IEEETransaction Paper No. 3 1TP67-424.(2 ) Ewort, D.., and F. P. dehlello. FACE-A DigitalDynamic Analysis Program, Power IndustryComputer

Applications Conference, May 15-17, 196 7.(3 ) Fitzgerald, # E., and C. Kingsley, Jr. Electric Machinery,2nd ed, McGraw-Hill, New York, 1961.(4 ) DetroitEdison,GeneratorSystems Dynamics Task Forc eReport, May, 197 1.(5) IEEE Power System Relay Committee, Loss-Of-FieldRelay Operation During SystemDistrubances, February,1970.(6 ) Mason ,. R. Thert and Science ofrotectiveRelaying, Wiley & Sons, New Yor k, 1956.(7 ) General Electric, NotesFrom Power Systems EngineeringCourse, 1968- 1969.

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a study of lossofexcitation relaying and stability of a 595mva generator on the detroit edison

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