IEEE Transactions on Power Apparatus and Systems, Vol.PAS-98, No.2 March/April 1979

TURBINE-GENERATOR IMPACT TORQUES INROUTINE AND FAULT OPERATIONS

J. M. Undrill, Senior Member, IEEE L. N. Hannett, Member, IEEE

Power Technologies, Inc.Schenectady, New York

Abstract - This paper reviews the shaft impactloadings created in turbine-generator shafts by bothnormal and fault initiated switching sequences. Itsobjectives are to clarify the significance of shaft im-pact torque simulations in relation to shaft fatiguelife data and to indicate the practicality of handlingimpact loading questions in the course of normal tran-sient stability calculations. Examples presented inthis paper compare shaft impacts produced by unit trip-ping, single and three-phase faults, high-speed reclos-ing, and manually timed switching sequences.

INTRODUCTION

Any elastic structure may experience impact load-ings in its internal members that exceed the ratedsteady state loadings on these members. Impact load-ings usually result from the sudden application or re-moval of a normal steady loading and may be avoided bygradual application and removal of load.

The normal loading on a turbine-generator shaft isa steady torque whose variations are very slow in rela-tion to the shaft's torsional natural frequencies and,hence, impact free. Impact loadings may be createdduring both normal and abnormal operation, however, andthere is growing concern over the ability of largeturbine-generators to withstand these impacts. In theUSA concern over impact loadings arose first in connec-tion with series capacitor compensated transmission.Continuing investigations suggest that impact loadingsdeserve close attention in tightly interconnected EHVsystems without series capacitors, as well as in seriescompensated systems.

There is as yet relatively little data available,from either instrumented operation, material tests, orcalculation, to indicate the existing margin of safetybetween actual impact stresses and the maximum stressesthat shafts can withstand without damage. Continuedmaterial testing will undoubtedly improve the shaft im-pact withstand capability data that is available tosystem designers. The value of this data is enhancedby considering the levels of impact torque imposed onshafts by the disturbances normally accepted in theplanning process.

This paper reviews the shaft impact loadingscreated by several well-recognized system disturbances.Its objectives are to clarify the significance of shaftimpact strength data in relation to known operatingsituations, and to indicate the practicality of han-dling many impact loading questions in the course ofnormal transient stability calculations.

F 78 011-9. A paper recamnended and approved bythe IEEE Paoer System Engineering Comnittee of the

I:E: Power Engineering Society for presentation at theEEE PES Winter Meeting, New York, NY, January 29 -February 3, 1978. Manuscript submitted Augst 22,1977; made available for printing Noveiber 1, 1977.

IMPACT TORQUE MECHANISM

Shaft impact torques could, in principle, be pro-duced by sudden changes in either the turbine torque(induced by steam flow) or the generator electromagnet-ic torque. In practice the rate of change of turbinetorque is slow in relation to the rates at which elec-trical system upsets can change generator electromag-netic torque. Hence the two principal factors influ-encing impact torques are:

first, sudden changes in generator electricaltorque due to changes in the 60 Hz genera-tor armature current and

second, electrical torque due to transient compo-nents of generator current at frequenciesother than 60 Hz.

All major generating units are subjected to impacttorques through both of these mechanisms in the courseof a normal lifetime complement of tripouts, imperfectsynchronizations, and transmission faults.

The first of the two mechanisms is most readilyperceived in a full load trip, where the generatortorque is changed instantaneously from rated value tozero. The second mechanism is represented in normaltransmission configurations by the d.c. and negativesequence components of fault current. The electricaltorques created by these currents do not normally cre-ate significant shaft impact torques, and hence suddenchanges in 60 Hz current are the major contributor toimpact torques.

Series capacitors may give rise to transient com-ponents of armature current oscillating at subsynchro-nous frequency in the wake of transmission disturban-ces. Interaction between these currents and the rotormotions associated with shaft torsional vibrations canaggravate the impact loadings produced by the initialchange in 60 Hz current. The key point in dealingwith impact torques in both uncompensated and compen-sated systems, however, is recognition of the majorrole played by sudden changes in normal power frequencycurrent.

DATA FOR EXAMPLES

Illustrative examples have been run with the sam-ple system segment shown in Figure 1. This representsa large plant with two identical units connected intoa large power system by transmission whose effectivetransfer capacity may be represented for our presentillustrative purpose by a single transmission line.This single line is assumed to terminate at a majorsubstation at which transformers, lines and subtrans-mission circuits form a strong tie into the large sys-tem. Faults are assumed to occur at or near thissubstation and to be cleared by circuit breaker oper-ations that leave the main outgoing transmission ofthe plant intact.

The key generator data items are listed in TablesI and II. Shaft damping factors were selected as re-quired to give shaft modal damping factors of approxi-mately 0.002 to 0.005, which are representative of

0018-9510/79/0300-0618$00.75 1979 IEEE

618

values being observed in the field.1'2'3 The threetor-sional natural frequencies of the shaft and the corre-sponding mode shapes are shown in Figure 2.

Figure 1. Sample System- Power Plant WithTwo Identical Units

(Transmission Impedances in P.U.on 100 MVA Base)

23#7-4k,z

32.4/4

CZA' IP=f/ 2P "p5

Figure 2. Shaft Torsional Mode Shapes ofSample Units

TABLE I

Turbine-Generator Shaft Data,Values Relative to Generator-Base Torque

STIFFNESSLOCATION H-FACTOR P.U./ELEC.RAD.

HP TurbineLP2 TurbineLPl TurbineGenerator

.25

.86

.88

.89

305070

RATED TORQUE/GENERATOR BASE

TORQUE

.25

.6251.0

TABLE II

Principal Generator Data,Values in P.U. on Generator Base

LdLq

dLI'

L'q

LI

1.75

1.72

0.35

0.25

0.53

T'Ododo

T'tqoTqqo

4. 5

0.06

0.55

0.06

619

REPRESENTATIVE IMPACT SITUATIONS

Full Load Generator Trip

A common event involving impact torques is thetripping of the generator circuit breaker. For a unitoperating at full load, tripping produces an instanta-neous change in generator electrical torque of one perunit. This could result, according to classical impactloading theory, in an initial change of shaft torqueequal to twice the applied change, with an ensuing os-cillation of corresponding magnitude. That is, a sim-ple full load trip could cause shaft torque oscilla-tions with a peak-to-peak amplitude of twice the origi-nal loading.

Figure 3 shows the actual variations of the 3shaft torques in the sample generating unit followinga full load trip. The initial torques in the 3 shaftsections are equal to the individual normal rated load-ings of these sections. Table III shows the initialtorque, and peak-to-peak span of the impact torqueexcursion created in each shaft section. The generatortorque steps from one per unit to zero instantaneouslyat time zero in this simulation, while the turbinetorques are assumed to decay to zero with 0.5 secondtime constant.

Figure 3 does not show pure sinusoidal torqueoscillations because the three torsional natural modesare excited simultaneously by the generator trip,causing each shaft torque trace to show the "beating"effect associated with the summation of the threelightly damped modal components of the disturbance.Table III shows that two of the three shaft sectionsare exposed to alternating torques with magnitudes inexcess of their rated torque. The IP-HP shaft, forexample, is exposed to an impact torque oscillationwhose peak-to-peak span is 2.4 times rated torque forthat shaft section. This cyclic impact torque loadingcould be significant in terms of typical shaft loss-of-life data.

Figure 3. Shaft Torques in Response to FullLoad Trip

(Note: All Shaft Torques in Thisand Subsequent Figures are in PerUnit of Generator Rated Torque)

0.15

620

TABLE III

Shaft Impact Torques Created by Full Load Unit Trip

INITIAL TORQUE(P.U. OF GENERATOR

SHAFT RATED TORQUE)

1.00.6250.25

SPAN OFIMPACT (P.U.OF GENERATOR

RATED)PEAK-TO-PEAK

1.11.10.6

SPAN OFIMPACT (P.U.

OF SHAFTSECTIONRATED)

PEAK-TO-PEAK

1.11.752.4

Single Line-To-Ground Fault

The outgoing transmission of a major generatorwould normally be designed on the assumption that asingle phase-to-ground fault is a normal event, to bewithstood without loss of synchronism or equipment dam-age.

Figure 4a shows the generator electrical torquetransient produced by a L-G fault of 6-cycle durationat bus 103. The fault was initiated near a zero ofa-phase stator voltage and hence produced a signifi-cant d.c. offset component in both fault and statorcurrent. The electrical torque transient consists ofthree components superimposed on the steady torque of1.0 p.u.:

--A downward square impulse with magnitude of ap-proximately 0.3 p.u. and a width of 0.1 second.

example the fault was initiated at a voltage maximum.Table IV summarizes the spans of the shaft torque os-cillations produced by these two faults. It is appar-ent that the impact duty imposed by the L-G faults isno more severe than that associated with full load re-jection and, further, that the magnitude of the impacttorque oscillation is dependent on fault duration.

Xa

I6vr fM1M

--A 120 Hz oscillation with a peak-to-peak ampli-tude of approximately 0.7 p.u. during the fault.

--An exponentially decaying 60 Hz oscillationwhich is initiated with the fault and then re-

applied at fault clearance.

The 120 Hz torque component is associated with thenegative sequence component of stator current producedby the L-G fault. The 60 Hz torque components are theresult of d.c. offset components of stator current.Note that fault clearance removes the negative sequence

effect but produces a second d.c. offset in the gener-

ator stator because the generator current is not exact-ly in phase with the fault current and hence is notzero when the fault current is extinguished at its own

zero crossing.

Only the first of the three torque componentshas any significant effect on the shaft since the fre-quencies of the two oscillatory components are wellremoved from all shaft natural frequencies and henceare effectively filtered out by the generator inertia.

Figure 4. Response to 6-Cycle L-G Fault

a) Generator Electrical Torque

b) Shaft Torques

TABLE IV

Shaft Impact Torques Created By L-G Faultat Bus 103

SPAN OF IMPACT(P.U. OF SHAFT SECTION RATED TORQUE)

SHAFT 6-CYCLE FAULT

GEN-LP1LPl-LP2LP2-HP

0.81.22.0

2-CYCLE FAULT

0.41.01.0

Figure 4b shows the shaft torque transients pro-

duced by the 6-cycle L-G fault, and confirms that thesquare torque impulse does produce significant impacttorques. Figure 5 shows the shaft torque transientsproduced by a 2-cycle L-G fault at bus 103; in this

Figure 5. Shaft Torques in Response to 2-CycleL-G Fault

Three-Phase Fault in Outgoing Transmission

While three-phase faults are regarded as a severe

and infrequent disturbance, it is generally acceptedthat a generator must withstand a limited number ofthese faults in a normal lifetime's service.

Figure 6 shows the generator electrical torquetransient produced by a 6-cycle three-phase fault at

bus 103. This contains a nearly square downward im-

pulse and a decaying 60 Hz oscillatory component.

GEN-LP1LPl-LP2LP2-HP

Figure 6. Generator Electrical Torque Responseto 6-Cycle 3-Phase Fault

Figure 7 shows the shaft impact torque transientscaused by the 6-cycle fault and by a 4-cycle fault atthe same location. Table V summarizes the shafttorque impact magnitudes produced by these three-phasefaults. It is apparent that the three-phase fault canproduce shaft impact torques nearly twice as severe asthose produced by a full load generator trip.

621TIMING EFFECTS

Comparison of Figures 7a and 7b shows that theform and magnitude of the shaft torque impact arestrongly dependent on the duration of the fault. Thereason for this is best illustrated by the classicalexample situation given in Figure 8 in which a squareimpulse is applied to a simple system having a singlenatural mode of oscillation. The shaft torque responsein this situation is shown in Figure 9.

AAeMMXE0 i72feMI.4AWmOA>V

Figure 7. Shaft Torques in Response to 3-Phase

Fault

a) 6-Cycle Fault

b) 4-Cycle Fault

TABLE V

Shaft Impact Torques Produced ByThree-Phase Fault at Bus 103

SPAN OF IMPACT(P.U. OF SHAFT SECTION RATED TORQUE)

SHAFT 2-CY FAULT 4-CY FAULT 6-CY FAULT-

GEN-LPlLPl-LP2LP2-HP

0.80.552.0

1.83.04.0

7owaLofL

Figure 8. Single-ModeSubjected to

71f14/C

Oscillatory SystemSquare Torque InputPulse

Figure 9. Response of Single-Mode System toSquare Torque Input Pulse

The leading edge of the input torque impulse,whose amplitude is AT, produces a shaft torque responseconsisting of a change in steady state value plus anoscillatory component. Because the system is lightlydamped, the initial zero peak-to-peak amplitude of theoscillation is nearly twice the final steady valueassociated with a continuously applied torque of AT.The trailing edge of the impulse produces a similarovershooting response, but the initial amplitude of theoscillation is now determined by the sum of the appliedtorque change and the residual amplitude of the oscil-lation that is already present as a result of the lead-ing edge of the impulse. It is readily apparent thattwo sudden changes of applied torque will have an addi-tive effect on the shaft torque oscillation if:

--either, they are of opposite polarity and sepa-rated in time by an odd number of half-periods of the shaft's natural oscilla-tion

--or, they are of like polarity and separated

1.52.93.0

622

in time by an even number of half-periods of the shaft's natural oscilla-tion.

The converse timing rule applies for cancellationof oscillationsby successive changes in applied torque.

The shaft torque responses shown in Figure 7 aremore complicated than that in Figure 9 because thesample turbine shaft has four natural modes of oscilla-tion. The principle of additive or canceling impactsapplies nevertheless. One can get an indication ofthe extent to which each shaft natural mode will beexcited by dividing the time separating sudden torquechanges by the half-period of each natural frequency.For application and removal of a fault an odd numberresult indicates strong excitation of the correspond-ing natural mode, while an even number result indi-cates cancellation.

For example, the 6-cycle fault duration (0.1 sec-ond) is 3.17 times the half-period of the 15.85 Hz nat-ural mode, while the 4-cycle fault duration is 2.11times the same half-period. Figure 7 confirms, asexpected from this, that the 6-cycle fault excites astrong component of torque oscillation at 15.85 Hz,while the 4-cycle fault produces relatively little re-sponse at this natural frequency.

It is readily apparent from these examples that ashift in the timing of a switching event by as littleas one period of the 60-cycle wave can have a major ef-fect on impact torque magnitudes.

REPEATED IMPACTS

The torque augmentation effect produced by the co-incidence of a sudden electrical torque change with apeak of a shaft torque oscillation, as illustrated byFigure 9, can occur with any power system operatingprocedure that produces a sequence of sudden generatorload changes. Any sudden load change occurring beforethe shaft torque oscillations excited by previous im-pacts have died out offers the possibility of a torquemagnification. If the interval between events is shortin relation to the decay time constants of the torque os-cillations, each repetition of a given impact-producingevent can nearly double the stress oscillations in theshaft.

4One frequently cited operating' sequence involving

repeated shaft impacts is high speed circuit breakerreclosing. Figure 10 shows, as an example, the resultof reclosing a circuit breaker at bus 103 onto asingle line-to-ground fault. Because there is no 8ig-nificant decay of oscillations in the interval betweenthe initial trip and the reclosure, the second impactproduces a nearly perfect doubling of the shaft torqueoscillation amplitude.

The impact torque oscillation spans produced bythis reclosure, and by reclosing into a three-phasefault at the same location, are summarized in Table VI.Comparison with Tab'le V shows that reclosure onto theL-G fault is less severe in terms of impact stress thana single three-phase fault without reclosure. Reclo-sure onto the 3-phase fault is shown to impose an ex-tremely severe shaft impact duty.

Another example situation involving repeated im-oacts is the nearly, but not exactly, simultaneoustripping of generators in a major power plant. Suchtripping might originate in plant auxiliaries, boilercontrols, or with operator action, and would generally-be regarded as a normal operating event. Figure 11

shows the shaft torques produced in unit 2 of the exam-ple plant when this unit is tripped 1.35 seconds afterthe tripout of unit 1. No fault or other transmissiondisturbance is involved; it is assumed that the tripsignals originate within the plant. The impact torqueoscillation spans produced in unit 2 are summarized inTable VI. Comparison of these oscillation magnitudeswith those of Table V and the first column of TableVI shows this tripout sequence to be of comparable se-verity to a single 3-phase fault, and significantlymore severe than reclosing into the single phase fault.

Figure 10. Shaft Torques in Response to2-Cycle L-G Fault With Reclosureinto Fault and Second Clearance

in 2-Cycles

.IoI0

Figure 11. Shaft Torques in Unit 2 in Responseto Tripping of Unit 1 with Tripping

of Unit 2 1.35 Seconds Later

TABLE VI

Shaft Torques Produced by Repeated Torques

(TORQUE OSCILLATION SPAN IN P.U. OF SHAFTSECTION RATED TORQUE)

RECLOSE INTO RECLOSE INTOSINGLE-PHASE 3-PHASE FAULT TRIP UNITSFAULT AT BUS AT BUS 103, 1 AND 2 WITH103, 2-CYCLE 2-CYCLE 1.35 SECONr

SHAFT CLEARING CLEARING INTERVAL

GEN-LP1LPl-LP2LP2-HP

0.91.921.40

3.16.15.0

1.32.723.20

DAMPING EFFECTS

The period of exposure to shaft torque augmenta-tion after an initial impact is determined by the timetaken for the oscillations produced by an initial im-pact to decay to a small amplitude whose addition to anew impact is not harmful. The rates of decay observedin practice for shaft torque oscillations are, unfortu-nately, very much smaller than that used for illustra-tive purposes in Figure 9.

It is common to express the damping of a shaft1

natural mode in terms of logarithmic decrement, L. Thetime required for an oscillation at frequency, f, todecayto a fraction, K, of its initial value is given by

-loge KfL

While information on the damping available in theshafts of units now in service is far from complete,the available test data suggests that the representa-tive range of logarithmic decrement is from 0.001 to0.01. Figures 12 and 13 show the effect of damping

Figure 12. Reduction of Torque OscillationAmplitude with Time Due to Damping

Effects

a I I I I

0 .002 .00W 1e9o A>C O.0Figure 13. Time Needed for a Torque

Oscillation to Decayto 20 Percent of Its Initial

Amplitude

623on the residual amplitude of a single mode shaft torqueoscillation. It is apparent that the torque oscilla-tions, particularly those at lower frequencies, mayretain sufficient magnitude to give strong torque aug-mentation for many seconds after an initial impact.The implication of this is that manually executedswitching sequences, as well as high-speed relaying se-quences, could expose turbine shafts to significantaugmentation of impact torques.

IMPACT TORQUE CALCULATIONS

As impact torques become a matter of increasedconcern, it is desirable to examine the cost of calcu-lating them in system planning and design studies.Initial interest in impacts produced by transmissiondisturbances arose in connection with series capacitorinstallations. The key role of the subsynchronous ca-pacitor discharge oscillation in series compensatedsystems made it necessary to execute impact torque cal-culations with digital computer programs in which theelectric network is modeled at a level similar to thatused in transient network analyzers. One representa-tive programof this type is described in reference [5].

These programs using the "digital TNA" networkrepresentation are very much more expensive to operatethan are modern comprehensive transient stability pro-

grams '7 It is desirable, therefore, to execute impacttorque calculations with transient stability programswhenever series capacitors are not involved.

Two different programs were used in the examplecases shown above. Cases such as those of Figures 4and 6, where the transient generator torques associ-ated with d.c. and negative sequence currents areshown, were executed with a program similar to thatcovered by reference [53, in which each transmissionelement is represented by its differential equations onan individual phase bases. Cases such as those ofFigures 3, 10, and 11 were made with a transient sta-bility program using a power frequency positive se-quence network representation. With the exception ofthe stator "pi" terms, the generator, excitation sys-tem, shaft, and governor models of the two programs areidentical. The generator rotors are represented at thesubtransient level, with allowance for an unlimitednumber of branches in the equivalent circuit of eachaxis.

The use of the "transient stability" level of net-work representation in impact torque studies has beenjustified by running comparison cases on the two pro-grams.

As an example, consider the single L-G fault re-sponse displayed in Figure 4. The electrical torqueresponse shown in Figure 4a was obtained with thedifferential equation network treatment and is particu-larly rich in negative sequence and d.c. electricaltransient effects. Figure 14 compares electricaltorques and shaft torques of Figure 4 with those ob-tained by rerunning the study with the transient sta-bility program and with the L-G fault being modeled inthe conventional way by a shunt impedance of (Z2 + Z0)as seen at the fault point. The difference between the"exact" result as obtained with the differential equa-tion network treatment and the result obtained with thetransient stability program is insignificant.

Similarly good comparisons have been found for awide variety of transmission disturbances. The expenseof running impact torque calculations with a differen-tial equation level (TNA) network representation is,

624

therefore, justified only when series capacitors areinvolved or when a shaft has a natural frequency veryclose to 60 or 120 Hz.

/0Z,.' " 7'

0. //.IV

Figure 14. Comparison of Response to 6-CycleL-G Fault, as Calculated by Machine!

Networks Program (Dashed) and By(Solid) Transient Stability Program

a) Generator Electrical Torque

b) Shaft Torques

REVIEW AND CONCLUSION

The aim of this paper is to assist in the inter-pretation of the results of impact torque calculations.Since shaft impact strength data is not yet fully de-veloped, it is advisable to review impact torque levelscalculated for new operating situations in relation tothe torque levels calculated for routine situationsthat are known to have been experienced and survivedby many generators.

We have suggested single and sequenced full loadgenerator trips as a useful reference point for cali-brating impact torque calculations. The results shownhere for a representative two-unit turbine-generatorplant suggest that the impacts produced by the most com-

mon transmission disturbance, a single line-to-groundfault, are no more severe than those produced by veryplausible unit tripping situations,even when the possi-

bility of reclosure into the L-G fault is allowed. Re-closure into a 3-phase fault has, however, been shownto produce much more severe shaft impacts than would beexperienced in plausible normal operating sequences.

The augmentation of shaft impact torques by re-peated impacts is not a problem restricted to high-speed relaying applications. Because the damping ofshaft torque oscillations is low, significant torqueaugmentation can occur even when switching operationsare separated by intervals of several seconds.

Turbine-generator shafts have been withstandingsignificant torque impacts in many years of normal ser-vice. Problems may arise either because of a rise inthe level of applied torque impacts, or because of re-ductions in the strength margins of new generatingunits. Impact torque levels are generally increased byreductions of system impedances and by the use of se-ries capacitors, and hence must be expected to rise asthe power system becomes more strongly interconnected.

The examples presented here are specificallyapplicable only to the sample situations for which theywere calculated. They serve, however, to illustratethe type of event that may need to be considered in im-pact calculations, the timing and other factors thatare important, and the general relationship between theresults to be expected from different disturbances.

REFERENCES

[1] R. Quay and R. J. Placek, "Cyclic Fatigue ofTurbine-Generator Shafts", IEEE Symposium on Sub-synchronous Resonance, Publication No. 76-CH1066-O-PWR, 1976.

[2] D. N. Walker, C. E. J. Bowler, and R. L. Jackson,"Results of Subsynchronous Resonance Tests atMohave", IEEE Trans., Vol. PAS-94, pp. 1878-1889,1975.

[3] D. G. Ramey, et al, "Measurements of Torsional Dy-namic Characteristics of the San Juan No. 2 Tur-bine Generator", ASME Paper No. 76-JPGC-PWR-4,Joint Power Generation Conf., Sept., 1976.

[4] J. S. Joyce, et al, "Effect of Clearing Short Cir-cuits and Automatic Reclosing on Torsional Stressand Life Expenditure of Turbine-Generator Shafts",IEEE Trans., Vol. PAS-95, pp. 14-25, 1976.

[5] G. Gross and M. C. Hall, "Synchronous Machine andTorsional Dynamics Simulation in the Computationof Electromagnetic Transients", IEEE Power Engi-neering Society Paper No. F77-529-1, Summer PowerMeeting, 1977.

[6] D. G. Ramey and R. T. Byerly, "Dynamic Simulationof Interconnected Systems", IEEE PICA Conf. Proc.,pp. 31-40, 1967.

[7] J. M. Undrill, F. P. de Mello, R. J. Mills, andT. E. Kostyniak, "Interactive Computation in PowerSystem Analysis", IEEE Proc., Vol. 62, pp. 1009-1018, 1974.

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John M. Undrill (M'66, SM'74, F'78) received a

Bachelor of Engineering degree, with first classhonors, from the University of Canterbury,Christchurch, New Zealand, in 1963, and aPh.D. from the same University in 1965. Follow-ing a Post Doctoral Fellowship at the University

Toronto, he joined the General Electric Com-

pany's Electric Utility Engineering Operation in1966. He joined PTI in 1971.

Dr. Undrill's work has covered the areas ofelectric utility dynamic behavior analysis,

industrial process simulations, and electric power network simulationand security analysis. At General Electric, Dr. Undrill was responsiblefor research on the implementation of calculations for on-line com-puters in security analysis applications. Under the sponsorship of theElectric Research Council, he directed General Electric's research efforton power system equivalents for use in dynamic performance andstability studies. In dynamics engineering, Dr. Undrill has made con-tributions to the dynamic analysis methods available for large intercon-nections of synchronous machines, and has applied these methods on

problems ranging from electric utility power swings to torquemagnifications in industrial drive systems. His dynamic simulation con-tributions cover hydraulic and gas flow, hydro plant, steam boiler/fur-nace, and mechanical drive/gear sytems. He is presently responsible forthe development of interactive computing systems for electric powersystem simulation.

Dr. Undrill has given graduate courses at Universities in Canadaand New Zealand and is a lecturer in the PTI Power TechnologyCourse. He is a Registered Engineer in New York, Ontario and NewZealand.

Louis N. Hannett (M'74) received the degree of

KS. * Bachelor of Science in Electrical Engineeringwith honors from Clarkson College ofTechnology in 1971.

Upon graduation, Mr. Hannett joined

Power Technologies, Inc. as an analyticalengineer. He has been active in large systemstudies involving load flow and stability analyis.He has contributed in the development of powersystem simulation programs at PTI. He has beeninvolved with the development of MNT3,

Mechanical-Network Transient Analyzer for Three Phase Systems Pro-gram. His work has included economic dispatch, load rejection studies,development of a program for transmission line construction costs, gas

path dynamics of fossil plants, parametric study of machineparameters, and subsynchronous oscillation studies in both frequencydomain and time domain (simulation).

Discussion

C. E. J. Bowler (General Electric Company, Schenectady, NY): Thispaper makes two generalizations; one concerning turbinegenerator/system modeling, and a second on the acceptability of faulttorque duty.

Specifically, it is suggested (I) that survival, apparently withoutdistress of operating turbine-generators, is testimony to the safety ofpreviously accepted transmission operating practices, (2) that neglect ofthe system electrodynamics in the manner of a transient stability pro-gram is a sufficiently accurate model to study the turbine generatorshaft torques on the occasion of faults and reclosing.

Addressing, first, the safety of these "accepted" operating prac-tices, it must be said that operations such as high speed reclosing andunit tripping have, until the present, been practiced for the purpose ofraising stability margins with little regard to turbine-generator impactloading effects. While it is true that there have been relatively few casesof cracked or broken shafts attributable solely to transient duty, therehave been several incidents of the shaft system becoming misalignedand some cases where shrunk on components have cocked on their fitsresulting in kinking of shafts. These conditions frequently result in

625outages that require rebalancing, realignment, and remachining ofcoupling faces, etc. The transmission system therefore should be design-ed and operated to avoid these previously "accepted" transmissionsystem conditions.

Additional perspective is obtained by considering that about 50%of the operating capacity in turbine-generators has yet to see more thanabout 15 years of service out of a planned service life of 30 to 40 years.The absence of fatigue cracks on these relatively few large ratingturbine-generators cannot be considered to indicate a fatigue resistanceequal to the planned duty cycles of high speed reclosing and line restora-tion at large reclosing angles. The nature of fatigue is such that noevidence of its occurence appears until a crack is produced. Since it isnot appropriate to wait and see if the fatigue resistance is in fact equalto these demands, the industry is developing models and methods toestimate cumulative fatigue life consumption based on analysis ofsystem switching practices. It has been deduced that there may besignificant risk associated with these practices as planned. (1)

Based on the above observations, we suggest that there is littlesignificance between routine situations of impact known to have beensurvived by many generators and the calculated value of torque in a newsituation. The approach to determine significance requires an in-depthlook at the service experience and the calculated fatigue life consump-tion; not the torque level per se.

With respect to the omission of system electrodynamics in model-ing, this paper does not in any way produce proof that impact torquescan be calculated with reasonable accuracy using only transient stabilitylevel in modeling. What is shown is that in a particular circumstance ofa remote fault application the calculated torques appear to be valid.

The theory of neglecting the so called stator transient term "pW" isrelatively well established. However, from the standpoint of turbine-generator impact torque calculation, the pip modeling introduces, ingeneral, significant additional response. The modeling of the pip term in-troduces the well known dc offset or unidirectional component of ar-mature fault current. This offset is dependent upon the point on thevoltage wave at which the fault is applied. The corresponding compo-nent of stator flux induces 60 hz components of rotor body current. Thesignificant 60 hz rotor body resistance to the flow of this current pro-duces losses that appear as unidirectional torque components andsignificantly changes the amplitude of shaft impact torque response.

The effective rotor body resistance is a function of the reactance upto the point of fault since the open circuit and short circuit subtransienttime constants approach one another, reducing effective resistance, asreactance increases. This appears to be the reason for the apparent goodagreement between the two calculation approaches for the case cited inthe paper. In the case of multi-parallel lines with faults between the sen-ding and receiving system, the pip term must not be neglected. There isalso a second unidirectional torque significant to impact torqueresponse associated with the offset 60 hz stator current produced bystator l'R loss. This component is only partially in evidence when theptp term is neglected. The only time that it seems permissible to neglectthe pw term is on sufficiently remote faults and upon load rejection.

The question of load rejection must not be treated lightly in rela-tion to fatigue consumption. Generation dropping is another plannedoperational measure to maintain system integrity. The data presented inthis paper would appear to raise some question on this practice.

REFERENCE

I. P. G. Brown, R. Quay, "Transmission Line Reclosing-TurbineGenerator Duties and Stability Consideration," Protective RelayEngineers Conference, Texas A&M University, April 20, 1976.

Manuscript received April 26, 1978.

John S. Joyce (Allis-Chalmers Power Systems, Inc., West Allis, WI)and Dietrich Lambrecht (Kraftwerk Union AG, Muelheim/Ruhr, WestGermany): The authors are to be highly commended for so clearlypresenting how system faults and switching operations impact on thetorsional stressing of turbine-generator shafts. Back at the 1975 PESSummer Meeting, we presented a paper, which the authors kindly list astheir Reference [41, in which we explained how turbine-generator shaftsreact to the three involved types of electrical disturbing torques, namelyunidirectional, system-frequency and double-frequency torques, andwhat a decisive role the timing of such torque shocks plays in determin-ing the resulting mechanical oscillations and thus shaft torsional

626fatigue. We are pleased that the authors have seen it fit to explain againthis all important basic mechanism of the phenomenon of torsionalstresses being induced in turbine-generator shafts as a result of systemfaults and switching operations.

In our paper [41 we showed how individual shaft sections of largesteam turbine-generators react differently to unidirectional, 60 Hz and120 Hz electrical torques. This critical difference in response was handl-ed by calculating for each shaft section a sensitivity factor which wasdefined as the ratio of the maximum mechanical torque to the ap-propriate electrical torque stimulus. These sensitivity factors dependlargely on the ratio of the moments of inertia of the masses on eitherside of the shaft section under consideration. Would the authors pleaseconfirm whether either of the two sets of unusually low values listedunder "span of impact" in their Table III are indeed the sensitivity orresponse factors defined by us.

The use of a simple transient stability program to investigate shafttorsional stressing and fatigue due to electrical transients, as advocatedby the authors, only allows the effect of unidirectional electrical torquesto be considered since such programs cannot treat any alternating tor-ques. Such an approach is perfectly adequate in studying themechanical torques arising from a generator load rejection when theelectrical torque is entirely unidirectional without any 60 or 120 Hzcomponents. However, it could not be applied to the case of a generatorno-load short circuit when the electrical torque is made up of onlysystem and double-frequency alternating components without offset orunidirectional component. Since all other faults and switching condi-tions lie between these two extremes of load rejection and no-load shortcircuit, i.e. they all give rise to more or less 60 and 120 Hz electrical tor-ques, the simplification of using a transient stability program incurs acommensurately large or small error in calculating the resultingmechanical torques and consequently shaft torsional fatigue.

We agree that for many system faults and switching operations, atransient stability program yields sufficient accuracy for practicalsystem planning purposes. However, it is advisable that the errorassociated with using a transient stability program be first estimated bymultiplying the expected magnitude of the 60 and 120 Hz electrical tor-ques by the appropriate shaft sensitivity factors in order to ensure thatthe results fall within the desired band of accuracy. It is our practice toemploy a sophisticated transient analysis representation program for allshaft torsional stress and fatigue calculations so as to make sure that thecontributions of the 60 and 120 Hz electrical torques be always correctlytaken into account.

Manuscript received February 22, 1978.

Timothy L. Skvarenina (U.S. Air Force, W. Lafayette, IN), Paul C.Krause and David M. Triezenberg (Purdue University, W. Lafayette,IN): The authors point out in the Abstract that the objectives of theirpaper are "...to clarify the significance of shaft impact torque simula-tions in relation to shaft fatigue life data and to indicate the practicalityof handling impact load questions in the course of normal transientstability calculations." They conclude from Fig. 14 that "The dif-ference between the exact result as obtained from the differential equa-tion network treatment and the result obtained with a transient stabilityprogram is insignificant." They continue by saying "Similarly goodcomparisons have been found for a wide variety of transmission distur-bances. The expense of running impact torque calculations with a dif-ferential equation level (TNA) network representation is, therefore,justified only when series capacitors are involved or when a shaft has anatural frequency very close to 60 or 120 Hz." This conclusion, whichappears to be the main thrust of this paper, is not true in general.

The authors state in the section entitled "Impact TorqueMechanisms" that the 60 and 120 Hz components of electrical torquearising from the DC and negative sequence components of fault cur-rent, "...do not normally create significant shaft impact torques." In[4], Abolins et al. defined sensitivity factors relating the response ofeach shaft to the different components of electrical torque. These werecalculated for the mechanical system given in Table I and are shown inTable A below. While it is true that the shafts are less sensitive to theoscillatory components of electrical torque than to step changes, theamplitude of each component must be considered. While the step dropin torque is normally less than 1.0 p.u. the amplitude of the 60 Hz com-ponent may be several per unit, depending upon the subtransient reac-tance of the machine and the reactance between the machine and thefault. To obtain an indication of the relative effect of each component

Table A

Sensitivity Factors for Mechanical System

SHAFT

LPI-G LP2-LP1 HP-LP2

R0 1.25 1.0 0.4

RFN 0.4 0.25 o.l8

R2FN 0.14 0.10 0.07

of the electrical torque upon the shafts, each sensitivity factor should bemultiplied by the amplitude of its respective component.

On the other hand, the authors may have been misled by the systemconfiguration and fault location which they selected. The line im-pedance of the system shown in Fig. 1 is .025 + j.25 on a 1,000 MVAbase, representative of a line of over 150 miles in length. Clearly, thepresence of this long transmission line between the machine and thefault markedly attenuates the amplitude of the 60 Hz component ofelectrical torque. Also it appears that the curves in Figs. 5 and 7b werecalculated with a transient stability program although this not not clearfrom the text.

TLP2-HP TLP2-HP [

2.525-LP2- -

GLPI TGLPI 2

-1.5-1

2 2

isec

Fig. A. Electromagnetic and shaft torques for a three-phase fault athigh side of generator step-up transformers of system shown in Fig. 1.Left traces for "exact or TNA" solution, right traces for transientstability program solution.

To illustrate the influence of the 60 Hz and 120 Hz torque pulsa-tions on the shaft, the authors' system was simulated on the hybridcomputer at Purdue and extensive studies were performed. Figure Ashows the electromagnetic and shaft torques for a 6 cycle, three-phasefault at the high side of the generator step-up transformers. The traceson the left are for the "exact or TNA" solution; the traces on the rightare obtained from the type of simulation used in a standard transientstability program. The difference in shaft torques is very significant.This difference is depicted in Fig. B where the maximum peak-to-peakshaft torque is plotted as the fault distance is decreased from Bus 103 tothe high side of the generator step-up transformers, for the shaft be-tween the low pressure turbine and the generator. Machine 1 is themachine used in the paper. Machine 2 is also a 1,000 MVA unit and wassimulated using electrical parameters supplied by the manufacturer andwith the same mechanical system as Machine 1. Other machines wereconsidered and it was found that the peak-to-peak torques fell betweenthose shown for Machine 1 and Machine 2. The curves denoted as"detailed" are for the "exact or TNA" representation wherein the dif-ferential equations are represented completely. The curves denoted as"simplified" are for the simulation used in a standard transient stabilityprogram.

Shaft torques during a single line-to-ground fault were alsostudied. Figure C shows the shaft torques for a single line-to-ground

------- MACHINE 1____MACHINE. 2

0 DETAILED& SIMPLIFIED

.2 .4 .6 .8 1.0FAULT DISTANCE

Fig. B. Maximum peak-to-peak shaft torques between low pressureturbine and generator as the location of the three-phase fault is movedfrom Bus 103 to the high side of the generator step-up transformers.Distance to Bus 103 = 1.0. Detailed is the "exact or TNA" solution;Simplified is the transient stability program solution.

627fault with a transmission line 1/6 the length of the line given in thepaper. The zero sequence was assumed to be 2.5 times the positive se-quence impedance of the line, and the generator step-up transformerswere assumed to be connected A-Y grounded. The traces on the left arethe "exact or TNA" solution while the traces on the right were obtainedfrom a transient stability program type simulation. Again, the dif-ferences in the instaneous shaft torques are significant. This is shown inFig. D wherein the maximum peak-to-peak shaft torques are given forthe shaft between the low pressure turbine and the generator forMachines 1 and 2 and for the detailed and simplified simulations. Inthis case the line length was varied from that given in the paper down to1/6 of its original length.

Clearly, the validity of conclusion set forth by the authors is depen-dent upon the machine parameters and fault location. A method ofmodifying a standard transient stability program for the purposes ofapproximating shaft torques is given in [A].

REFERENCE

[A] "Effects of Neglecting Electrical Transients on Shaft Torques,"T. L. Skvarenina, D. M. Triezenberg and P. C. Krause, IEEEConference Paper, A78 233-9, 1978 Winter Power Meeting.

Manuscript received February 16, 1978.

D. G. Ramey, R. H. Daugherty, and M. S. Baldwin (WestinghouseElectric Corporation, East Pittsburgh, PA): This paper is of benefit to

0.5 _ o s[ the industry as a clearly written reference which explains the factors thatTrl2-e o must be considered in performing a study to determine turbine shaft

torques. It also highlights the importance of obtaining more meaningfuldata for both the damping factors for large amplitude mechanical

1.5 shocks and a design criterion related to shaft torque that will providesafe operation with an acceptable level of reliability over the design life

,a1sec,0 of the turbine-generator. Since it is not desirable to deliberately stagetests of sufficient severity to obtain this data, it is important thatmonitoring systems be applied to a number of machines to record the

1 [ shaft response to naturally occurring shocks. Such records would great-TLP1.LP2 L ly improve the industry's understanding of the shaft torque profile thatis to be expected for a modern turbine-generator.

Although it is very useful to have generalized rules concerning both.TE the type of system most susceptible to high shaft torques and the re-

o quired complexity of the analysis program, these rules should be ap-plied carefully to avoid overlooking important factors. The paper states

ctromagnetic and shaft torques for a line-to-ground fault that impact loadings would be expected to be most severe in strongly in-ith the line impedance reduced to one-sixth the value given terconnected systems. Quite often, strongly connected systems implyttraces for "exact or TNA" solution, right traces for tran- multiple transmission paths and generators to share the sudden change

program solution.in power frequency current so that the impact on each machine is small.

rprogram solution. Our studies have shown the impact loadings to be more related to thechange in effective impedance between the generator and load centerthat results from the switching operation than the absolute level of theshort-circuit impedance. Thus, remotely located generating plants con-nected to the load centers with a minimum number of transmission lines

O DETAIL. often experience the largest shocks resulting from breaker operations.O IWHLIFI The general statement that 60 Hz and 120 Hz torques are not very

--- MAE1ImE 1 significant unless there are shaft natural frequencies near 60 or 120 Hz isMACHUE 2 not always correct. While it is true that the shaft response is much less

for these components than for equal magnitude step changes, themagnitudes of the various torque components are not equal, especiallyfor short circuits close to the generator. In such cases the sudden changein electrical current can be much greater than one per unit, while thestep change in electrical power is limited by internal losses in themachine. When the various components of electrical torque are applied

.------- --- .3 separately to the shaft system model, the shaft torques resulting fromhigher frequency components of electrical torque can exceed thoseresulting from the step change and ensuing exponential decay of steadytorque.

Figure 11 and Table VI indicate the severity of sequential tripping0.2z 0. 4z 0. 6z 0. 3z z of two generating units within the same plant. In the case studied for the

paper the units were of identical rating. The torques could be even moreLINE IMPEDANCE severe if one unit is significantly larger than the other, and the larger

aximum peak-to-peak shaft torques between low pressure *unit is tripped first.,enerator during a line-to-ground fault for various line im- A full consideration of the effects of the 60 and 120 Hz com-= .025 + j.25). Detailed is the "exact or TNA" solution; ponents of electrical torque requires much more complex models of thethe transient stability solution. shaft system than those presented in this paper. The very large turbine-

TgU.pOP.U. OF

TG-LP1 .|

0

1.5

TUP1 LP2 .-'

O ff

TE 21

Fig. C. Eleat Bus 103 wiin Fig. 1. Leftsient stability

2 -

Tg_lp1P.U. OFSHAFTRATING

Fig. D. Mzturbine and gpedances. (zSimplified is

.75TLp2--w

0 I-IJ

628generators in use today can have as many as 30 modes of rotor oscilla-tion with resonant frequencies below 130 Hz. In addition, considerationmust be given to possible damage of stationary components of thegenerator such as stator end-turns. New modeling techniques havegreatly advanced the industry's understanding of these interactions inrecent years. However, much work remains to be done.

Manuscript received February 10, 1978.

D. L. Hackett (Consumers Power Company, Jackson, Michigan): Thispaper is an interesting and informative discussion of the study of shaftimpact torques. The shaft torques presented here were obtained fromtwo digital computer programs. In one, the stator and network elec-trical transients were represented. In the other, these transients wereneglected as is normally done in a conventional transient stability pro-gram. The results from both for a particular example compare well asshown in Figure 14.

In another paper (1] similar comparisons are made. There theresults from neglecting stator and electrical transients are significantlydifferent from those where the transients are represented.

Would the authors comment on possible reasons for the dif-ferences in results?

REFERENCE

[1] T. L. Skvarenina, D. M. Triezenberg, P. C. Krause, "Effects ofNeglecting Electrical Transients on Shaft Torques," IEEE PaperA78 233-9, Winter Power Meeting, Jan-Feb 1978.

Manuscript received January 30, 1978.

J. M . Undrill and L. N. Hannett: We thank the discussors for theircomments. Their breadth indicates quite general agreement, at least tothe extent that the impact implications of virtually all switching eventsneed increased recognition in both planning and operations.

Messrs. Bowler and Ramey, Dougherty and Baldwin point out thatsurvival of impacts in the past by many units does not indicate that im-pacts are not a problem, and that monitoring of actual shaft duty isneeded to accumulate a fund of data on a wide range of naturally occur-ring events. Contrary to Mr. Bowler's implication, we did not state thatsurvival of impacts is testimonial to the safety of past practices; we

simply observed that many impacts have been survived by units in awide variety of situations. In fact a principal objective of our paper wasto point out the wide variety of events, other than transmission faultsand reclosures, that can cause significant impacts. We agree, in par-ticular, that generator dropping as a means of enhancing transientstability can have serious impact torque implications.

In response to Messrs. Joyce and Lambrecht, the span-of-impactgiven in Table III is not equal to their sensitivity factor, r,, because wedefine span as the greatest difference between successive maxima andminima of shaft torque, while their sensitivity is based on maximum ab-solute stress. Examination of our Figure 3 and of Figure 1 of reference 4shows that our "span", measured after a unit trip, could be eithergreater or lesser than the discussors' r. sensitivity factor, dependingupon the shafts modal properties.

All the discussors comment on and debate our remarks regardingthe use of conventional transient stability programs to handle impacttorque calculations. We certainly agree with them that a full "networktransients" simulation is needed in critical cases or where the adequacyof a solution without network transients cannot be judged. We do,naturally, use full network transient modelling in many of our impacttorque simulations.

As several discussors point out, and as Messrs. Skvarenina, Krauseand Triezenberg quantify at length, the very close correspondence inFig. 14 is due, in large part, to our choice of fault location. We wouldcaution, in relation to the discussion by Messrs. Skvarenina, et al., thattheir figures seem to indicate the use of lower generator stator andtransformer resistances than we used and that the decay time constantof the d.c. offset component of stator current can be a factor in deter-mining the effect of the alternating components of generator torque.

Our main point in replying to the discussions remains, as in thepaper, that the high cost of simulating large transmission systems withnetwork transients included discourages the study of events that cannotbe handled in small network equivalents. This tends to limit considera-tion to events at sites close to generators, even though switching se-quences at points many buses removed from any plant can cause signifi-cant impacts. We, therefore, retain the view that the use of a conven-tional transient stability program, at least as an explanatory and screen-ing measure, is a desirable way of broadening the range of events con-sidered in a study. To this end we have pursued a number of ways of im-proving estimates of the alternating torque components without resort-ing to full network transient solutions, and will be reporting on these ina paper in the near future.

Manuscript received June 23, 1978.