IEEE Transactions on Power Apparatus and Systems, Vol. PAS-101, No. 8 August 1982

INVESTIGATION OF TRANSIENT STABILIZING CONTROLEFFECTS ON TURBINE-GENERATOR SHAFT TORQUES

U. 0. Aliyu, Member, IEEE A. U. Chuku, Member, IEEE

Electrical Engineering DepartmentAhmadu Bello University

Zaria, Nigeria.

ABSTRACT

In this paper, the implementations of somespecific transient stabilizing control means,exemplified by dynamic braking resistor,forced excitation and fast turbine valving,are investigated from the vi'ew-point of theirpotential effects on the torsional stresses ina turbine generator shaft system. For thepurpose of this study, a state space digitalsimulation model of one machine infinite bussystem is employed whereupon.the interactionsbetween the transient stabilizing controlschemes,electrical and mechanical subsystemsare well represented. The results of thephenomenon under investigation are presentedand some pertinent conclusion drawn. In addi-tion, the relative effects of thecontrol meansimplementations on the turbine generator shafttorques are compared and their benefits fromthe standpoint of power system stability arediscussed.

INTRODUCTION

The adverse effects on the power systemstransient stability margins due to the designtrends of modern generating units and increasedsystem network complexities are well known.Several transient stabilizing control schemesare available that can be effectively utilizedto extend power system transient stabilitymargin in an event of a severe system dis-turbance. The various control means whichinclude dynamic braking resistors, forcedexcitation and fast turbine valving have beenfairly well studied in many investigations[1 - 5] from the viewpoint of their suitablecontrol strategies to achieve maximum potentialstability margin benefits. Their practicalutilizations are, therefore, being pursued bysome utility companies [6 - 7] in addition tothe adoption of faster system protectionphilosophies.

In other studies [8 - 101, also relatedto system operational conditions, it has beenestablished that network faults, compounded byseveral other influencing factors, can exciteabnormal torsional stresses in the electri-cally nearby turbine-generator shaft system.In particular, after fault network switchingoperations associated with the well esta-blished technique of automatic high speed

circuit breaker reclosing and also single poleswitching, have been identified to produceexcessive transient shaft torques under un-favourable conditions. In view of the possibleturbine-generator shaft system failure thatcould arise from such repetitive torsionalstresses, a substantial number of shaft fatiguerelated studies have emerged for various cate-gories of faults and out-of-phase synchroniza-tion [11]. Although a significant progress isevident from the scope covered by the.se studies,no totally satisfactory attempt is yet made tocharacterize the potential effects on theturbine-generator transient torques due to theimplementations of some keytransient stabili-zing control means dedicated to power systemtransient stability margin improvement. Fur-thermore, the concern for the.potential effectsbecomes very relevant when suchcontrol schemesare located within or electrically nearby to agenerating unit and their modes of controlinvolve discrete switching operations.

The main objective of this paper is toinvestigate such potential effects associatedwith the specific implementations of dynamicbraking resistor, forced excitation and fastturbine valving and on the basis of the studyto establish their relative effects on thephenomenon of interest as compared with theirtransient stability enhancement capabilities.In addition, the system model used for thisinvestigation is described and special para-metric study with ample computer simulationresults for each transient stabilizing controlmeans considered are presented. The pertinentconclusions drawn from this investigationshould be of special interest to the turbine-generator and the allied control designers andshould form also the basis for further refinedstudies.

STUDY SYSTEM DESCRIPTION

For the purpose of this investigation, adetailed state space model of one machine in-finite bus system of Fig. 1 is employed. The

Goyer Synchronousnor Machine Transformer B

P Q~G V

Stea4m M

urbine

81 JPGC 918-2 A paper recommended and approw-vtc by i-l:IEEE Power Generation Committee of the 'IEEE Power Engi- RB Dynapmic Brak ing Resistor

neering Society for presentation at the IEEE/ASME/ASCE UFE Supplementary Excitation Control

1981., Joint Power Generation Conference, October 4-8, UFV Fast Valving Control Signal

1981, St. Lpotis, Missouri. Manuscript submitted

August 13, 1981; made available for printing September 10,Fig. 1: System Investigated With Various1981. Transient Stabilizing Control Means.

0018-9510/82/0800-2619$00.75 1982 IEEE

2619

2620

Transborrmtion

Fig.2: Complete Structure of the DynamicSimulation Mbdel

Turbine StagesGenerator

T45 T 34 T23 T12

Fig. 3: Turbine Generator MbchanicalSystem Model

Fig. 4: Static Exciter and VoltageRegulator Model

Fig. 5: Governor Turbine Model

complete parameters of the system are set forthin the Appendix. The nonlinear simulation modeldevelopment is essentially an extension of thedigital simulation approach described in[121 toincorporate, fairly accurately, the electricalinteractions between the various transientstabilizing control schemes and the torsionallyvibrating shaft system of the turbine-generatorunder investigation. With this modification, inaddition to the models chosen for the varioussub-systems and the simulation techniqueadopted, the overall dynamic simulation modelis sufficiently detailed for the objectives ofthis study and possibly other studies relatedto turbine-generator shaft torques. The overalldynamic simulation model structure is-shown inFig. 2 and, in the subsequent subsections, themodels for the various subsystems are brieflydescribed. Table 1 summarizes the order of statevariables used for the mathematical simulationof the various subsystems.

Table 1: Various Dynamics Represented in theSystem Investigated

No. of StateDynamic Components Variables

Generator ElectricalRepresentation 6

Turbine-Generator Shaft System 10Exciter and AVR Model 4Turbine and Governor Model 6

Network Electrical Representation 6

Overall System Dynamic Model 32

Synchronous Machine and Network Model

The electrical representation of the syn-chronous machine in d-q-0 variables includesthe stator winding transients, and two damperwindings with the series r-L circuit model forthe transformer also simulated in the rotorreference frame. However, the performance equa-tions for the medium length transmission linecircuit, modelled as a transposed-lumped-para-meter system using pye section representation,are expressed in a-b-c ordirect phase variableswith suitable provision for the implementationof discretely switchable dynamic braking resis-tor. Such digital simulation model necessitatesimplementation of Park's transformation to re-late machine d-q-0 variables to network a-b-cvariables at their interface. Other relevantdetails such as the development of system equa-tions, machine and network equivalent circuits,not given here, can be found in [121. It isworthwhile to note, however, that this phase ofthe overall model development allows a unifiedapproach to be adopted in the study of bothsymmetrical and assymmetrical faults, andfurther facilitates easy realization of sequen-tial fault clearing pertinent toaccurate resultpredictions in the turbine-generator shafttorque related studies.

Turbine-Generator Mechanical System

As previously mentioned, turbine drivengenerators can develop unacceptably high shafttorsional stresses due to the torsional stiff-ness of the shafts coupling several rotatinginertias which are forced to oscillate against

one another through various interactive effectsof system electrical shocks. To incorporatethe shaft dynamics into the overall systemdynamic model, the mechanical system isassumed to be comprised five concentratedmasses (four turbine stages and generatorrotor masses) coupled by shafts of known tor-sional stiffness values (see Fig. 3). Exceptfor the various mechanical dampings neglectedin its mathematical simulation, this mechanicalsystem representation is similar to that ofreference [13].

Excitation System

A block diagram representation for a highgain static excitation system, as adopted forthis study, is given in Fig. 4. A number ofother studies [4,5,7] have shown that such highinitial response excitation with high voltageceiling yields a substantial improvement in thesystem transient stability margin when activatedby speed derived signals fed through appro-priately designed compensating network circuits[141. A somewhat pragmatic approach is followedin the choice of the excitation forcing signalsfor satisfactory post-disturbance system tran-sient performance whilst its effects on theshaft dynamics are then studied.

Governor-Turbine System

The possible effects of the fast turbinevalving on the turbine generator shaft dynamicsare investigated via the block diagram repre-sentation for the governor-steam turbine systemof Fig. 5, incorporated into the overall systemsimulation model. The model includes four tur-bine stages with a reheat and agoverning systemwith linear operating characteristics assumed.In addition, linear characteristics are assumedfor the control valve (CV) and the interceptvalve (IV); the latter being available, inpractice, for the fast turbine valving imple-mentation. Further details on this model may beobtained from [15].

System Operating Conditions

The initial loading conditions and thecomputed bus voltage profiles of the systeminvestigated are given in Table 2. On the basisof the system loading conditions, the initial

values of all the state variables and otherpertinent non-state variables, for the completedynamic simulation model, are then completelydetermined.

With the system assumed operating undermaximum loading and steady-state quiescent con-ditions, a symmetrical three-phase to groundfault is applied at the high voltage side ofthe generator-transformer, near bus 2 of Fig.l,and is subsequently cleared torestore immedi-ately the pre-disturbance system configuration.For fault duration periods of .18 sec , .195sec and .21 sec , the transient behaviour ofthe system under the effective implementationof each transient stabilizing control meansconsidered is parametrically evaluated toidentify the main effects on the turbine-generator shaft torques. The fault clearingtimes were chosen to include both systemunstable and marginally stable transientoperating conditions.

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Table 2: Initial System Loading Conditions

Parameter Value (pu)

pG + jQG: Generator Complex Power .90 +j.05

VT: Generator Terminal Voltage 1.14L22.10VM: Transformer High Tension

Voltage 1.08L13.710VB: Infinite Bus Voltage 1.0/006 : Synchronous Machine Rotor

Angle 60.3 deg

COMPUTER SIMULATION RESULTS

In this section, the main computer simu-lation results are presented that illustratethe influence of each implemented transientstabilizing control means on the turbine-generator shaft torques. Although the faultinduced peak torques in the various shaftsections of the turbine-generator shaft systemwere investigated, only the characteristics ofthe most severe peak torques in the generator-turbine shaft section are depicted as a func-tion of a specific control variable with systemfault clearing time as a parameter. Theresultsof the parametric studies provide the basisfor uniform comparison between the relativeeffects of the transient stabilizing controlmeans on the turbine-generator shaft torsionalstresses versus their system transient stabi-lity enhancement capabilities.

Effect of Forced Excitation Control

The effect of high gain static excitationsystem on the torsional dynamics of a turbine-generator shaft system have been studied on thebasis of system dynamic stability analysis [16]and also within the framework of subsynchronousresonance phenomenon[IT]. A natural extensionof these studies into the power system tran-tsient state would be to characterize the effectof forced excitation control on the turbine-generator shaft torques.

The effect is so studied here under thescheme of high gain static excitation systemwith the dominant stabilizing signals derivedfrom weighted shaft speed. The concept of theweighted shaft speed signal derivation is~shownclearly in Fig.6 and is found to provide thedesired forced excitation action. With thestatic exciter field voltage limits set at + 8pu, an extensive characterization of the tran-sient behaviour of the system investigated hasbeen made for the postulated system transientdisturbance.

Figure 7 shows some typical time res-ponses of the torques in the various shaftsections of the turbine-generator shaftassembly for a three phase fault duration of.18 sec. It can be seen that the torques inthe various shaft sections pulsate and thevarious natural frequencies present are deter-mined by the inertias and the stiffness of theturbine-generator shaft system. It is worth-while to mention that the shaft dampings notaccounted for in its simulation, is partlyresponsible for the long sustained pulsationsin the shaft torques. For the sake of compari-son, Table 3 summarizes the peak torques inthevarious shaft sections, with and withoutforcedexcitation control.

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'nAw 1 ( t) a

g4 AW2 (t) Q 2c~~~~~~~~~

Z Aw 3 (t)_ e04

u) AW4 tt)

InAw5(t)*a =H / H. j 1,2.. .5

Fig. 6: Stabilizing Signal DerivationfBllockDiagram Representation

Some other selected system variable timeresponses for the same fault condition areshown in Fig.8. In this figure, the variable,VTM denotes machine terminal voltage whilst therotor angle and electromagnetic torque time res-ponses are illustrated as well for the uncon-trolled system to facilitate common basis forcomparison. Although the system is marginallystable without static excitation control, it isclear from Fig.8 that its inclusion has sub-stantially improved the transient performanceof the overall system.

Table 3: Peak Torques in Various ShAft Sections

aa.

.1I-%wa

0. I

gI-

I

01

:3

.-4

Io

J- 411

aI1a"

c .

Maximum Pea r Torques (pu)Sh&ft Without Static With StaticSections Excitation Excitation In-

Control* Control** crease

GEN-LP2 3.135 3.580 14.2LP2-LP1 2.803 3.053 8.9

LP1-IP 1.45 1.526 5.24

IP - HP .805 .848 5.34

* Constant Excitation Voltage = 2.127 pu

** Field Ceiling Voltage Limits = + 8.0 pu

Figure 9 depicts the main results of theparametric study characterizing the main in-fluence of the forced excitation control on thegenerator shaft torques. Data plotted corres-pond to various maximum peak torques in thegenerator-turbine shaft section which weretaken from 27 system simulation time responses.Note that the field ceiling voltage is varieddiscretely between its fixed excitation valueand a maximum positive value of + 10 pu. Thedashed line portions for some curves in Fig. 9indicate loss of system transient stability,for the corresponding fault clearing time andfield ceiling voltage.,It is worthwhile to notealso that the peak torque values plotted for.the.system transient instability cases were takenas those that occured before machine poleslippage.

A number of interesting observations canbe made with regard to the influence of theforced excitation control on the peak shafttorques. It is quite clear from Fig. 9 that thepeak shaft torques, for a given fault clearingtime, showed substantial increase with higherfield ceiling voltages and of course, theactualpeak shaft torque values depend on the faultclearing time which cannot be systematicallycharacterized. It can be concluded that while

LP2-GEN SHAFT

LP1 - LP2 SHAFT

IP-LD1 9E-TAFT

HP-IP SHAFT

t.O0 3.0o 4.00TIM1ECSEC)

Fig. 7: Transient Torques in Various ShaftSections With Forced Excitation Con-trol ±8 pu; Fault Clearing Time of.18 sec.

t,J

la0

CC

-With Static Exciter-- Without Static Exciter

C4

ZL o- ° W- FAULT OFF

v °v°O 2°oo 2.00 3.00 4.W0 5.00 6.0TIMI(SEC)

Fig. 8: Selected System Variable TransientResponses Corresponding to Control/-Fault Conditions of Fig. 7.

5.00 0.00

3.6

3.t

3.2

0

4&2. 0

X2 6

>2.

2.2

2.0

I t= .18s

I t .21sII /

I /

II

Fixed ExcitationI Voltage _I 0 t - .1958

II a

t-.. La aL0 5.0 10

Exciter Ceiling Voltage (pu)

Fig. 9: Variation of Maximum Peak Torques inLP2-GEN Shaft With Forced ExcitationCbntrol and Fault Clearing Time.

high field ceiling voltages are advantageousfrom transient stability margin enhancementstandpoint, they tend also to boost the tor-sional stresses in the various shaft sectionsof the associated turbine-generator shaftassembly.

Other sentitivity tests made, involvedvariation of static exciter transient gain,and inclusion of supplementary discontinuouscontrol signals as suggested in 14]. Except forminor changes in the system transient perfor-mances and transient stability margin gain, itwas noted, however, that the sensitivity testsyielded insignificant effects on the turbineshaft torques when compared with the observedinfluence of field ceiling voltage.

Effect of Fast Turbine Valving Control

Modern steam-turbine generators are beingequipped with the capabilities of fast actua-tions of control and/or intercept valves insome prescribed close-open cycles, in order toeffect pronounced temporary reductions inprime-mover powers. Although such control philosophyhas been documented in several investigations[15, 18, 191 as an effective option for systemstability preservation during a severe tran-sient disturbance, there is need also to in-vestigate the influence of the resultingmechanical braking forces on the turbine-generator shaft torques in view of the concernfor severe shaft fatigue. In this subsection,the detailed representation of the governor-turbine described in the preceding sectionpermits, evaluation of the system transientperformance and parametric study to be performedon the system investigated with the objectiveof establishing relationship between faultclearing time, fast turbine valving and thetransient peak torques in the turbine-generatorshaft section.

In keeping with the accepted practice, itis assumed that only the intercept valve (IV)is available for control manipulation withactuating delay time of .1 sec, valve closingtime of .15 sec and valve reopening of .5 secas suggested in [5]. The approach employed inthe implementation of the first swing fastvalving control, is essentially a modifiedversion of the time-based control decisionsset forth [15], whereupon valve reopening isinitiated at maximum weighted shaft angular

2623

deviation. However, the actuating logic forsubsequent fast valving reapplications con-stitutes a simple relay control on weightedshaft speed deviation Aw0 (t) as follows:

Ufv =O.; if Aw0(t) Aw (Reclose IV)

ufv = 1.; if Aw0(t) 0.0 (Reopen IV)

where UfN7 denotes intercept valve controlsignal; Aw is the allowable shaft speed de-viation threshold limit determined approxima-tely, from the simplified single-mass model ofthe system investigated under the worst faultcondition, using the familiar equal area ana-lysis. A value of 4.8 rad/sec for aX is usedthroughout this investigation in order tominimize repetitive reapplications of the fastturbine valving. Note further that theeffectiveness of the fast turbine valving isrestricted to the positive swings.

Figures 10 and 11 illustrate, again, thetypical transient torques in the various shaftsections and some selected system time res-ponses, respectively, for the faulted systemwith fast valving incorporated. Note thatthese results are valid for a fault durationperiod of .18 sec and a full intercept valveclose-open cycle. The induced transienttorques in the various turbine-generator shaftsections for this case study exhibit similarfeatures as described in the preceding sub-section. However, more important is the factthat the peak torques with fast valving arelower than in the case of forced excitation

0,q.

0.

N0c

aC

0

0

0.1' -

cm

1-

o1

_C's

)ol

I-

:3

I-

:3

1-cxa* _

LP2-GEN SHAFT

LP1-LP2 SHAFT

TP-LP1 SHA.YT

HP-IP SHAFT

0.00I- -------I - I * I I

1.00 2.00 3.00 4.00TInE(SEC)

5.0o *,.0a

Fiq. 10: Transient Torques in Various ShaftSections With 100% IV Fast Valving;Fault Clearing Time = .18 sec.

. . I II-----,T-

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g Xa. Su W

,o-oL0 0

~0 Br .

~~2

1 FU O----FAULT OFF'

- -FAULT ON

,J 00 1.0O 2.00 3.00 5.00 0 (OQTIME[SEC3

Fig. 11: Selected System Variable TransientReGponses Corresponding to Control/-Fault Conditions of Fig. 10.

3.2

3.0

i,2.6

2.6

2.4V1

i 2.o

1.a

t = .18s

g _ 4- -_. 4--_ -_ _ _ -' -

t = .21s

t = .195s

0 20 /0 60 s0 10 0

Percentage Fast Valving

Fig. 12: Variation of Maximum Peak Torques inLP2-GEN Shaft With Fast Turbine Valv-and Fault Clearing Time.

control. rhe improved transient performance ofthe system with single application of fullintercept fast valving is clearly manifestfrom Fig.11.

Figure 12 depicts the results of the para-metric study that offers an insight into theinfluence of fast turbine valving on the peaktorques induced in the turbine-generator shaftsection. Here again, the peak torques plottedwere obtained from several simulation resultswith system fault clearing time as parameterand percentage of intercept valving asvariable.It is clearly seen that the effect of fast tur-bine valving is rather mild on the peak shafttorques whether or not system transient stabi-lity is insured by its implementation. Infact,the peak shaft torques slightly decreased withhigher percentage of fast turbine valving,thereby, indicating weak positive dampingeffect on the turbine-generator fhaft torques.Variation in the parameters such asvalve delay,opening and closure times, which affected thesystem stability margin gain [15] , did not

render void the aforementioned influence offast turbine valving implementation on theturbine-generator shaft torques.

Effect of Dynamic Braking Resistor Control

The concept of dynamic braking for power systemstability enhancement is not altogether new, butit is onlyof recent that attention has beenfocused on its practical application to largepower systems 16,7]. However, in all the con-trol strategies that have evolved for effectiveutilization of the dynamic braking concept, theturbine-generator shaft system has been assumedto be infinitely stiff. In this subsection,however, such assumption is relaxed in order toinvestigate the implemental effect of the dyna-mic braking on the turbine-generator tran-sient shaft torques in relation to its corres-ponding stability margin gain. The dynamicbraking scheme is incorporated into the overalldynamic simulation model as a bank of switch-able shunt resistive load, electrically sitedto interact with the turbine-generator mechani-cal system.

The control strategy developed in [203forclosed-loop application of dynamic braking resresistor in bang-bang mode is utilized herein.The geometric interpretation of the firstswing transient stabilizing control law, forswitching on and off the dynamic braking re-sistor, is depicted in Fig. 13. The deter-mination of the approximate switching, requir-es crude system model with an assumption ofworst fault condition as outlined in 120].The pertinent parameters used to synthesizethe first swing closed-loop control law, forthis case study, are specified in Fig. 13.Furthermore, the criterion for the dynamicbraking resistor control during subsequentswings is exactly the same as in the case offast turbine valving.

The main results of this case study de-picted in Figs. 14-16, were obtained under thesame fault conditions and test procedures asdescribed in the preceding subsections. Theclosed-loop bang-bang application of an opti-mum dynamic braking resistor of 1.0 pu on thetransiently perturbed study system yielded thetypical transient torques in the various shaftsections and the transient responses of someselected system variables shown in Figs. 14and 15, respectively. Comparisons of Figs. 10and 14 reveal that the maximum transient peaktorques in the various shaft sections forboth case studies are of the same order of

8-BRAKIt G ZONE -i - '

A 3

If

wl ,NA%%%

0

A-A-AB-B-BFig.

Parameter

_A = 4.8r/sASu= 80 degAS = 50 deg

' An =65 degs Atm = 1 r/s

B

-tn~~~~~~~~~~~~~~~~~~.

-_~~~~~ I'00 Il

Brakc Switch-on lineBrake Switch-off linc

13: First Swing Dynamic Braking Control

itw--w-T v _ ---Fw-- 11,-%a.0tu -

Q-.0U-3 1 . . % I I

9 %vit ..

Es %- With Fast Valving- -- Without Fast ValvincTga

1---mM0:

0%, % ., % % k %, I % % %

A6-F-I

2625

g!, LP2-CEN SHAFT

LPl-LP2 SHAFT

1~~~~~~~~~~~~~~~.

IP-LP1 SHAFT

%.4.9Inc-8

HP-IP SHAFT

0.00 1.0X 2.0O 3.09 4.o0 5S. .6.TJIME(S)

Fig. 14: Transient Torques in Various ShaftSections With 1.0 pu Dynamic BrakingResistor; Fault Clearing Time =.18sec.

With Dynamic BrakingWithout Dynamic Braking

.. o FAULT OFF

za FALT ON

Fic^. 15: Selected System \Tariable Tran.sientResponses Corresponding to Control/-

* Fault Conditions of Fig. 14.

3.2

3.0

j 2X

X 2.6

2.4i

t = . 18s

_ _ _ _ *-x*x -* - 4 t . 21 s

2.2

o 1.0 2.0Dynamic Resistor Conductance (pu)

Fig. 16: Variation of Maximum Peak Torques inLP2-GEN Shaft With Dynamic Brakingand Fault Clearinq Time.

magnitude. Note that even thoucrh the effecti-veness of the dynamic braking resistor imple-mentation is restricted to the post-fault in-terval because of the three-phase fault loca-tion relative to it, substantial improvementin the system transient performance is evidentfrom Fia. 15 with two successive dynamic bra-king resistor applications.

Fig.-16 depicts similar parametric studycharacterizing the effect of the dynamic bra-king resistor control. Here, the.dynamic bra-king resistance is varied discretely between.5 pu to 1.5 pu.for each fault clearing timeconsidered to generate the data plotted inFig. 16. Note that the corresponding conduc-tance of the dynamic braking resistor is pre-ferred as the independent variable instead,in order to include zero dynamic braking con-trol condition. It is quite clear from thisstudy that as in the case ot fast turbinevalving, the dynamic braking resistor controlhas relatively weak effect on the transient.sbaft torques compared with that of the forcedexcitation control.

Comparison of.Results

A comparison between the system stabilitymargin gain realized from each of the transie-nt stability control considered is'given inTable 4. It is.quite clear from the Tablethat high gain excitation system static withhigh ceiling voltage limits of +8 pu is moreeffective than either a full intercept fastvalving or 1.0 pu dynamic braking resistorcontrol from the standpoint of the transientstability margin enhancement of the system in-

Table 4: Comparison of System StabilityMargin Gains

Stabilizing Max. Fault Cleaxing % In-Control S5chnes Times (Sec) crease

No Control .184

Forced ExcitationControl (+8 pu) .216 17.4

Fast Valving(100% IV Valving) .204 11.9

Dynamic Braking(1.0 pu) .198 7.6

.A.-L- I 11

2626

vestigated. However, on the adverse side, thesubstantial increase in the transient shafttorques due to the forced excitation controlcould cause unacceptably higher torsional str-esses than without it.

CONCLUSIONS

A digital computer investigation of thepotential effects on the turbine generatorshaft torques due to the implementations ofsome specific transient stabilizing controlschemes has been performed using a detailedbenchmark model of one machine infinite bussystem. The isolated effects of each of thetransient stabilizing control means consideredon the phenomenon of interest, have been demo-nstrated and compared with their respectivetransient stability enhancement capability,through extensive parametric studies supportedby ample simulation results.

More specifically, the results of thisstudy indicate that among the transient stabi-lizing control means explored, high gain sta-tic exciter with high ceiling voltage limitsexhibited the most adverse effect on the tran-sient peak shaft torques, but performed most sa-tisfactorily from the system stability marginimprovement standpoint. The extent of suchadverse effect on the cumulative shaft fatigueand consequently its life expenditure, wouldrequire more elaborate study than presentedherein.

ACKNOWLEDGEMENTS

The authors wish to thank the authoritiesand staff, particularly Messrs N.S. Khandpurand I.R. Udofia, of the Computer Centre, A.B.-U., Zaria, for the excellent computing faci-lities/assistance provided for this work.

REFERENCES

1. E.W. Kimbark, "Improvement of Power SystemStability by Changes in the Network", IEEETrans. Power Apparatus and Systems, Vol.PAS-88, 1969, pp. 773-781.

2. W.A. Mittelstadt and J.L. Sauger, "AMethod of Improving Power System TransientStability Using Controllable Parameters",IEEE Trans. Power Apparatus and Systems,Vol. PAS-90, 1971, pp. 2149-2157.

3. J.L. Diney, C. Preece and A.J. Morris,"Optimized Transient Stability from Exci-tation Control of Synchronous Generation,IEEE Trans. Power Apparatus and Systems,Vol. PAS-87, 1968, pp. 1696-1705.

4. J.P. Bayne, P. Kundur and W. Watson, "Sta-tic Exciter Control to Improve TransientStability", IEEE Trans. Power Apparatusand Systems, Vol. PAS-94, 1975, pp. 1141-1146.

5. J.H. Sawada and Y.N. Yu, "Transient PowerSystem Stability Control With Braking-Re-sistance, Forced-Excitation and/or FastValving", IEEE Conference Paper A-75-584-3,Winter Power Meeting, New York, January,1975.

6. M.L. Shelton, W.A. Mittelstadt, P.F. Win-klenon and W.L. Bellerby, "BonnevillePower Administration 1400-MW Braking Re-sistor", IEEE Trans. Power Apparatus andSystems, Vol. PAS-94, 1975, pp. 602-611.

7. H.M. Ellis, J.E. Hardy, A.K. Blythe andJ.W. Skkoglnng, "Dynamic Stability of thePeace River Transmission System", IEEETrans. Power Apparatus and Systems, Vol.PAS-85, 1966, pp. 602-609.

8. A. Abolins, D. Lambrecht, J.S. Joyce andL.T. Rosenberg, "Effect of Clearing ShortCircuits and Automatic Reclosing on Tor-sional Stress and Life Expenditure of Tur-bine-Generator Shafts", IEEE Trans. PowerApparatus and Systems, Vol. PAS-95, 1976,pp. 14-25.

9. T. Fujikura, T. Komukai and M. Udo, "Sta-tistical Approach to Analysis of Turbine-Generator Shaft Torques at High Speed Re-closing", IEEE Conference Paper A 77-051-6,Winter Power Meeting, New York, January,1977.

10. J.S. Joyce, T. Kulig and D. Hambrecht,"Torsional Fatigue of Turbine-GeneratorShafts Caused by Different Electrical Sy-stem Faults and Switching Operations",IEEE Trans. Power Apparatus and Systems,Vol. PAS-97, 1978, pp. 1965-1977.

11. P.C. Krause, W.C. Hollopeter and P.C. Rus-he, "Shaft Torques During Out-of-PhaseSynchronization", IEEE Trans. Power Appar-ttus and Systems, Vol. PAS-96, 1977, pp.1318-1323.

12. U.O. Aliyu, "Digital Simulation of PowerS stem for Unbalanced Fault Studies", Pro-ceedings of the 1980 International Confe-rence on Cybernetics and Societyr pp. 76-83.

13. R.T.H. Alden and P.J. Nolan, "EvaluatingAlternative Models for Power System Dyna-mic Stability Studies", IEEE Trans. PowerApparatus and Systems, Vol. PAS-95, 1976,pp. 433-440.

14. V.M. Raina, J.H. Anderson, W.J. Wilson andV.H. Quintana, "Optimal Output FeedbackControl of Power Systems With High-SpeedExcitation Systems", IEEE Trans. PowerApparatus and Systems, Vol. PAS-95, 1976,pp. 677-686.

15. M.E. Martin, D.M. Triezenberg and P.C.Krause, "A Study of Fast Turbine Valving",IEEE Conference Paper C 73-080-9, WinterPower Meeting, New York, January 1973.

16. W. Watson and M.E. Coultes, "Static Exci-ter Stabilizing Signals on Large Genera-tors-Mechanical Problems", IEEE Trans.Power Apparatus and Systems, Vol. PAS-92,1973, pp. 204-211.

17. M.A. Badr and A.M. El-Serafi, "Effect ofSynchronous Generator Regulation on theSubsynchronous Resonance Phenomenon inPower Systems", IEEE Trans. Power Appara-tus and Systems, Vol. PAS-95, pp. 461-468.

Ex=it-ation Suvster Par=meters

,S.ymbol/D.e.scr.Ipt.ion Value

KA :Excite'r Gain 200

TA :Exciter Time Constant .05 sec.

VRMAX:Exciter Maximum VoltageLimit +(3. 0 - 10.0)pu

VMI :Exciter Minimum VoltageRMNLim.it -(3.0 '_ 10.0)pu:RF Base Excitation 1.151 pu

Tv :Transducer Time Constant .01 sec

T1 :Compensation Lead TimeConstant .154 sec

T2 :Compensation Lag TimeConstant .015 sec

Ks :Compensation CGain .04

Tw :Washout Time Constant 1.6 sec

Go'vernor'-7urbine' Parameters

S.ymbo.l./Des.cription Value

R :Speed Regulation 0.05

T1 :Controller Lag TimeConstant .10 sec

T2 :Controller Lead TimeConstant ..20 sec

T3 :Governor Time Constant .03 sec

T4 :Steaim Chest TimeConstant .2 sec

T5 :Reheater Time Constant 10.0 sec

T :Cross-Over Tfime Constant*6 (IV/IP) .20 sec

T7 :Cross-Over Time Constant-(IP/LP) .4 sec

KI :Fractional Power1 Developed by HP .4

K2 :Fractional Power2 Developed by IP .3

K. :Fractional Power-3 Developed by LP2 .2

K4 :Fractional Power4 Developed by IP2 .2

P :Base Power .933 pu0

pmax:Upper Power Limit 6.0 pu

Pmin :Lower P.ower Limit 0.0 pu

18. R.H. Park,, "Fast Turbine Valving", IEEETrans. on Power Apparatus and Systems, VoLPAS-92,'1973, pp.'1065-1073.

19. P. Kundur and J.P. Bayne., "IA Study ofEarly Valve Actuation Using Detailed PrimeMver and Power System Simulation"', IEEETrans.' on Power Apparatus and Systems, VoLPAS-96,, 1975,, pp. 1275-1287.

20. U.0. Aliyu, "Corrective Control forTransient Emergency State of Power Syst-ems"g, TR 78-51, Purdue University, WestLafayette, Indiana, May, 1978.

- ~~~APPENDIX

The parameter values of the system stud-ied are given below and unless otherwise sta-ted, they are expressed on 100 MVA and S00 KV(Line-Line) base quantities.

Generator and Transformer Parameters

Symbol/Des.c.ri.p.t.i.o.n . .Value(pu)

rs :Armature Resistance .0032

Xl zArmature Leakage Reactance .093

rfd :Field Resistance .001

rk :D-Axis Damper Resistance '.011

Xlkd:D-Axis Damper Leakage Reactance .0478

rkq. :Q-Axis Damper Resistance .0140

Xlkq:Q-Axis Damper Leakage Reactance .0320

Xm :D-Axis Magnetizing Reactance 1.56

Xm :Q-Axis Magnetizing Reactance 1.47

rT :Transformer Resistance .02

XT:Transformer Leakage Reactance .2

Turbine-Generator Shaft 'Sysitem Parameters

Ms -Shaft Iniertia Spring Constantass~~~.aH (s:e.c) .K (.pu Torque/rad)

HP .185794

HP-IP 19.303

IP .311178

IP-LPI 34.929

LP1 1.71734

LP1-LP2 52.038

LP2 1.76843

LP2-GEN 70.858

GEN 1.73699

2627

2628

Discussion

T. J. Hammons (Glasgow University, Glasgow G12 8QQ, U.K.): TheAuthors have provided much-needed information on the effect highgain static excitation systems with high ceiling voltages have on tran-sient peak shaft torques following worst-case system disturbances. Theyhave also given data on the effectiveness of fast turbine valving anddynamic braking resistors in reducing peak shaft torques so as to reducefatigue impact to the shaft following severe disturbances on the gridsupply.

In Table 3, peak torques are stated which depict maximum peak shafttorque following worst-case 3-phase fault clearance occurs at the tur-bine/generator coupling and peak torques reduce progressively asdistance of the shaft section from the generator increases. The discuss-or's investigations(A, B) confirm that this, in general, is true, but insome machines maximum peak torque will occur at a shaft section otherthan the turbine/generator coupling. The discussor's investigations(A, B) have also shown that torque at the exciter coupling (if a rotatingexciter is used) may, following certain disturbances, become inconve-niently large. The discussor also confirms that excitation control, whilstenhancing system stability, can give rise to significantly higher shaft tor-ques following worst-case fault clearance particularly if high ceilingvoltages are employed.Although fast turbine valving can be an effective mechanism in

reducing peak shaft torque, it is believed its application is more effec-tive in reducing accumulative fatigue life expenditure of the shaft pro-vided non-linear steam valve stoking is employed. This is particularlytrue for the turbine/generator coupling since shaft torsional vibrationswill cause the HP control and/or intercept valves to partially close, thusreducing mean shaft torque and accumulative fatigue life expenditureof the shaft. The effect non-linear steam valve stroking has on meanturbine torque following clearance of worst-case 3-phase faults isdiscussed in Reference C.Another observation which should be made is that accumulative

fatigue life expenditure of machine shafts depends not only on peakstress (torque), but also on torsional vibration modes and the time cons-tant at which each frequency of vibration decays.Damping of shaft torsional vibrations is dependent on material,

steam and electrical damping. Material damping is due to the energyloss each strain cycle and is greatly dependent on stress of the outerfibres of the turbine shaft, and includes the effect of micro-slippage atcouplings and blade fixings and movement of lacing wires which stiffenLP blades. It is very non-linear being dependent very much on peakstress. It is the effective mechanism for damping shaft torsional vibra-tions when stress approaches the endurance limit of the shaft. Steamdamping is due to the hyperbolic nature of the turbine/speedcharacteristic.

Electrical damping depends very much on frequency of the torsionalvibration, on the electrical constants of the machine and on the im-pedence of the system to which the machine is connected. For example,the time constant for decay of the predominant low frequency torsionalvibration (12 Hz) of a large 3000 rpm turbine-generator at the tur-bine/generator coupling due to steam and electrical damping followingworst-case three-phase fault clearance is 4 - 5 seconds, whereas follow-ing worst-case malsynchronisation where there is negligible steamdamping it is 2 - 3 seconds. The increased damping of the lower fre-quency modes of torsional vibration following worst-case malsyn-chronisation is due to increased electrical damping on the direct axis ofthe synchronous-generator. The next predominant torsional vibr ion(22 Hz) has a time constant for decay of 9 - 11 seconds following wbst-case fault clearance, and 15 - 17 seconds following worst-case m',-synchronisation. The higher torsional modes of vibration havelong rdecay time constants, damping being almost negligible for some hig h-frequency vibrations.Doubling the resistance of the damper circuits reduces the time cons-

tant for decay of the predominant (12 Hz) torsional vibration by almostone half while its effect on the time constant for decay of the higher fre-quency torsional vibrations is very small. Doubling impedance betweenthe stator and infinite busbar, while reducing peak shaft torque by asignificant value, almost doubles the time constant for decay of the 12Hz torsional vibration while having little effect on the time constant fordecay of the 22 Hz vibration. Loss of fatigue life in this case however,on account of significant reduction in peak shaft torque, would be verysmall.

It should be emphasised that more fatigue life may be expendedfollowing a severe system disturbance at a shaft section along the tur-bine shaft than at the turbine/generator coupling although the highesttorque may occur at the turbine/generator coupling. This is on account

of the predominant frequency of vibration being different at couplingsalong the turbine shaft and because the lower frequency modes of tor-sional vibration decay faster due to electrical damping. This discussor isof the opinion that all couplings should be considered in estimating ac-cumulative fatigue life expenditure of machine shafts following severesystem disturbances. Accumulative fatigue life expenditure of turbine-generator shafts following worst-case switching disturbances where theeffect of electrical and steam damping is analysed is discussed inReference D. Electrical damping is shown experimentally to be muchmore significant than material damping following severe system distur-bances in Reference E.

Concerning the effect of dynamic braking resistor control illustratedby the Authors in Figures 13 - 16, the discussor's investigations (A, B)have indicated that peak shaft torque at a given shaft location varies ina cyclic manner with fault clearing time of period corresponding to thatof grid supply. Fault clearing time corresponding to maximum peak tor-que may be dependent to a small extent on conductance of the breakingresistor. It may therefore be necessary to tune-in the fault clearing timeto give maximum peak shaft torque for each value of breaking resistorconductance depicted in Figure 16.

This discussor believes that controlling dynamic braking resistors todamp the predominant low frequency torsional vibration of the tur-bine/generator shaft should be investigated in addition to investigatingthe damping of load angle oscillations. In this case, a control systembased on measured change in generator speed would be applied with aspeed transducer capable of detecting at least a 0. W% change ingenerator speed (F). Controlling the resistor bank to damp only thelower frequency torsional vibrations might appear more practical, andis effective in damping those modes which contribute more significantlyto shaft fatigue. The Authors' comments on these points is welcome.

REFERENCES

A. T. J. Hammons, "Stressing of large turbine-generators at shaft cou-plings and LP turbine final-stage blade roots following clearance ofgrid system faults and faulty synchronisation", IEEE Trans(PAS),Vol 99, (4), 1980, pp. 1652-1662.

B. T. J. Hammons, "Generator shaft torsional phenomena - stressingof large turbines at shaft couplings and LP blade roots and govern-ing following electrical system disturbances", Trans. Aust. Inst.Engrs. Vol ME6, (2) 1981, pp. 104-117.

C. T. J. Hammons, "Shaft torsional phenomena in governing largeturbine-generators with nonlinear steam valve strokingconstraints", IEEE Trans. (PAS), Vol 100, (3), 1981, pp.1013-1022.

D. T. J. Hammons, "Accumulative fatigue life expenditure of turbine-generator shafts following worst-case system disturbances",IEEE/ASME/ASCE 1981 Joint Power Generation Conference,October 4-8, 1981, St. Louis, MO, paper 81 JPGC 927-3.

E. J. F. Goossens, A. J. Calvaer, and L. J. Soenen, "Full-scale short-circuit and other tests on the dynamic torsional response ofRodenhuize No. 4, 300 MW, 3000 rpm turgogenerator, Parts I andII", IEEE Trans. (PAS), Vol 100, (9), 1981, pp. 4166-4185.

F. 0. Wasynczuk, "Damping shaft torsional oscillations using adynamically controlled resistor bank", IEEE Trans. (PAS), Vol100, (7), 1981, pp. 3340-3449.

Manuscript received November 20, 1981.

U. 0. Aliyu and A. U. Chuku: We would like to thank Professor Ham-mons for his good grasp of the main thrust of the paper as clearlymanifested by his invaluable comments. We are also pleased that hisown investigations confirm some of the major findings of our paperespecially the adverse effect of high gain excitation systems with highceiling voltages on transient peak shaft torques. We agree that thepossibility exists for the maximum peak torque to occur at a shaft sec-tion other than the turbine-generator coupling in-some machines de-pending on their design parameters, the nature of the primary controlsand the adequacy of the mechanical system modeling. Further, we alsobelieve that the inclusion of rotating exciter instead of static excitationsystem assumed in our paper, could give rise to adnormally large tran-sient peak torques at the exciter-generator coupling as confirmed by thediscussor's investigation.We welcome the comments on the fast turbine valving as the

discussor has clarified and expended on a pertinent point which is strict-ly not within the scope of our paper, but centainly add value to our in-

vestigation. This concerns the discussor's experience with, and/or hisbelief that, fast turbine valving is more effective in reducing the ac-cumulative fatigue life expenditure provided that non-linear steam valveis utilized. Although our investigation has shown that fast turbine valv-ing, employed as a transient stabilizing control means, exhibits addi-tional positive damping effect on turbine-generator transient peak tor-ques, this should be considered as a preliminary work leading to a moreelaborate study of this important aspect of the problem. We are cur-rently investigating it and we hope that such natural extension of our

study will complement investigations already made by the discussor andpossibly offer insights into other related problems. We are also of theopinion that any meaningful estimation of the accumulative fatigue lifeexpenditure should involve all shaft couplings because of the variousfrequency modes present in the torsional vibrations along the shaft andthe varying influences of material and electrical damping on them. Itshould be pointed out, however, that no single unified approach to thestudy of accumulative fatigue life expenditure of turbine-generatorshafts is possible in view of the uncertainties about the systemparameters and disturbances.With regard to the discussion on the dynamic braking resistor, we

wish to draw the attention of the discussor to the statement made in ourpaper that the control facility is utilized for system transient stabilityenhancement purpose whilst its implemental effect is then studied on

2629

the turbine-generator shaft torques. It is clear that the power absorbingcapability of the dynamic braking resistor, at any given instant, isdependent on its conductance value and the voltage across it, and thisdetermines its transient stability enhancement ability, depending, ofcourse, on its control strategy for a specific fault condition. Therefore,the use of dynamic braking conductance as the independent variable inFig. 16 of the paper is most appropriate for the objective of our study,although we are not certain whether any additional information wouldhave been offered if the fault clearing time was tuned-in to give peakshaft torque for each braking resistor conductance. We share the view-point that the control of dynamic braking resistor for dampingpredominant low frequency torsional vibrations deserves further in-vestigation. However, it should be emphasized that the choice of thedynamic braking resistor size, its electrical location and, more impor-tantly, its control methodology ultimately determine its effectivenessfrom the standpoint of damping either lower frequency torsional vibra-tions or the rotor transient oscilations after a major system disturbance.The authors, once again, express their appreciation to Professor

Hammons for his timely comments on our paper which would be of im-mense assistance in our future investigations.

Manuscript received December 4, 1981.