Influence of governors on power-systemtransient stabilityJ. L. Dineley, M.Sc.Tech., Associate Member, and M. W. Kennedy, B.Sc, Graduate

Synopsis

The paper describes an investigation into the contribution that a conventional velocity governor controllingthe input power to a synchronous generator makes to the transient stability of a typical power-systemconfiguration. It seeks to ascertain the corresponding transient-stability effect using an alternative operatingsignal, derived from rotor acceleration, for the control of input power. A governor actuated from acompound of velocity and acceleration signals is described, and its effect on transient stability is compared.The effects on this stability of varying some of the parameters of the system, the machine and the governorare described. The paper concludes with a brief study of the effect of various governors on the transientstability of a synchronous generator connected to a large system by a single faulted transmission line thatis fitted with autoreclosing circuit breakers.

List of symbols8 = rotor angle, electrical deg/ = system frequency, c/s

H = inertia constant, kWs/kVAM = H/l80f

Pe0 = initial electrical output, p.u.Pe = electrical output, p.u.Pj = mechanical power input, p.u.Kd = damping torque coefficientGg = velocity governor gain

Gag = acceleration governor gainT| = servomechanism time constant, secT2 — governor-valve time constant, secT3 = turbine time constant, sec

t = time, sectc = clearing time, secTc = critical clearing time, secXd — machine direct-axis synchronous reactance,

p.u.X'd = machine direct-axis transient reactance, p.u.Xq = machine quadrature-axis synchronous reac-

tance, p.u.rd0 = field time constant, secX, = transmission-line reactance, p.u.Rt — transmission-line resistance, p.u.Xc — transmission-line shunt reactance, p.u.

Xti, Xt2 = transformer reactances, p.u.oi = angular velocity, p.u.p — d/dt

Ku K2 — voltage gains associated with constituentparts of automatic-voltage-regulator mainloop

AT3, K4, K5 = voltage gains associated with automatic-voltage-regulator stabilising loops

T4, T5, T6, T7 = time constants associated with magneticamplifier and control exciter

T8 = main-exciter time constantT9> Tio> Tn = iimQ constants associated with stabilising

loopsV = comparator error voltage

Vc = control-exciter open-circuit voltageVf = main-exciter output voltage$ = angular separation between machine terminal

voltage and currentPaper 4346 P, first received 21st March and in revised form 6th August1963Mr. Dineley and Mr. Kennedy are with the Department of ElectricalEngineering, University of Newcastle upon Tyne98

1 IntroductionFor many years it has been realised that more

sophisticated control of the input power to synchronousgenerators would materially contribute to the stability oflarge electric power systems.1 In more recent years theintroduction of fast-acting automatic voltage regulators hasincreased the transient-stability capabilities of synchronousgenerators, and has thereby made a longer time availableafter a disturbance, during which the mechanical powerregulator or governor may adjust the prime-mover inputpower. This has given the governor a more significant rolein synchronous-power-system transient stability.

Since the stability of power systems ultimately depends onthe rapid and accurate matching of the input and outputpowers of each individual machine in all conditions ofoperation, it is important that the input power to a machineshould be made to respond to the difference between inputand output powers to reduce the difference to zero as soon aspossible.

The contribution that is made to transient stability by thecontrol of input power has not been widely recognised, andforms the subject matter of the paper. Initially the study wasdesigned to investigate the contribution that conventionalvelocity governors make to synchronous-machine stability,but on the results, the work was extended to the explorationof those aspects of governor design that can be modified toimprove performance. The paper therefore seeks to indicatelikely trends in power-system performance when various feed-back signals are used in input-power control to improvetransient stability. Attention was directed in the first instanceto the governor rather than the automatic voltage regulator,since the effects of the governor on transient stability appearto be less well known.

The studies were carried out on a combined analoguecomputer and network analyser that has been describedelsewhere.2

2 Velocity governor2.1 General

The governor that responds to changes in velocity isbelieved to have been invented by James Watt for use onearly reciprocating steam engines; a schematic of a modernvelocity-sensitive governor for use on steam turboalternatorsis shown in Fig. 1.

Governors fitted to synchronous generators must usuallymeet an empirical requirement. The appropriate British

PROC. IEE, Vol. Ill, No. 1, JANUARY 1964

Standard3 defines a governor gain of 25, since a speed changeof 004p.u. must produce an input-power change of 1 Op.u.at full load. A general definition of velocity governor gainis thus

This specified sensitivity has been found necessary in orderto protect turboalternators from dangerous overspeed whenall the electrical load is suddenly removed. As shown inFig. 1, the actuating device usually operates an oil servo-

double-circuit transmission line, as shown in Fig. 2. Asalient-pole generator is represented in view of the generalnature of the paper. This Figure shows the position at whichthe faults were applied whilst studying their effects on thetransient stability of the controlled generator. Fault clearanceis effected by the simultaneous 3-phase tripping of the circuitbreakers at each end of the faulted line, without theirsubsequent reclosure, except as described in Section 7.

In order to present in a concise form the large number ofswing curves that were computed to establish stability trends,a stability boundary is defined9 such that, when a fault occurs

Fig. 1Schematic of velocity governor

mechanism, which in turn operates the steam valve or valvesthat actually control the input to the turbine.

In some published works dealing with the transient stabilityof synchronous generators^5 it has been assumed, in solvingthe equation of disturbed motion of the generator's rotatingsystem, that the mechanical power input to the generatorremains unchanged during the transient disturbance beinginvestigated, i.e. in the equation

and is disconnected by circuit-breaker operation, a longerclearing time or a higher initial or prefault load on thegenerator would cause instability and loss of synchronism,whilst shorter clearance time or lower initial load would

transformer

synchronousmachine

p. - pe = Mp2h (2)

Pi remains constant.Other authors,6"8 however, have assumed a variable input

power, and described a transfer function to represent theturbine and the governor. The same method has been adoptedhere, since a separate investigation has verified it and ledto the conclusions that the transfer function used (seeAppendix 11.2) is valid for power-system transient-stabilitystudies. The point is referred to again in Section 6.

Many large steam turboalternators now include reheatingof steam during the turbine cycle. If this reheated steam isnot governed, a very long time delay is introduced into thecontrol of power to the generator. Therefore, for this studyit has been necessary to assume that there is no reheat cycleor that the reheat cycle is governed exactly as the inputpower. The time delay in the input-power response togovernor movement introduced by an ungoverned reheatcycle must render the governor contribution to transientstability almost negligible.

2.2 Study detailsThe system chosen for study is that of a synchronous

generator connected to an infinite power system through aPROC. 1EE, Vol. Ill, No. J, JANUARY 1964

i

X. R.t "tX i KSWU—v/WV i X

- X | /vflflft; y/WV I X -

transformerTo

rinfinitesystem

Fig. 2System studied

enable the generator to remain in ultimate synchronism withthe system. Fig. 3 shows such stability boundaries for thegenerator and system tested, without automatic voltageregulator or governor, with automatic voltage regulator andgovernor separately, and with both together, on the occur-rence of a 3-phase-to-earth fault. For these curves the rotatingsystem has been assumed to have an inertia constant of5kWs/kVA rating, and the governor has been taken asvelocity-actuated with a gain of 20.. These curves demonstrate that the automatic voltageregulator and governor both together and separately increasethe generator stability above that for the ungoverned,unregulated machine. The automatic voltage regulator andexcitation system considered is described in Appendix 11.3,

99

and, in order to compare different governor characteristics,this same representation of voltage regulator has beenemployed in all the studies described in the paper.

Figs. 4 and 5 have been prepared to show the effect onstability of different machine inertia constants and different

velocity governor has a significant effect up to a value ofabout 30, higher gain producing little improvement. Thesecurves suggest that, when inertia constants are below about4kWs/kVA, the velocity governor becomes less satisfactory,so far as its contribution to first-swing stability is concerned.

1-5-

10

O-3r

025 05 0-75critical clearing time, sec

10

Fig. 3Effect of automatic voltage regulator and governor on stabilityboundaries3-phase-to-earth fault. H = 5kWs/kVAa With governor and automatic voltage regulatorb With governor, without automatic voltage regulatorc Without governor, with automatic voltage regulatord Without governor or automatic voltage regulator

0-5

4 6 8inertia constant, kWs/kVA

10

Fig. 4Effect of inertia on critical clearing time, for various velocity governorgains3-phase-to-earth fault. Pe0 = 1 -09 p.u.a Gg = 40b Gg - 20c Gg - 10d Gg-A

velocity governor gains. Fig. 4 relates the governor gain,critical clearing time and inertia constant for a prefaultpower level of 1-09 p.u. (see Appendix 11.4 for details ofinitial conditions), whilst Fig. 5 relates these quantities in adifferent presentation for a prefault power level of 1 -23 p.u.It will be seen from these figures that, when the machineinertia is low, the governor gain tends to be less significantthan at higher values. With an inertia constant of between 3and 4kWs/kVA, increase of governor gain makes only amarginal contribution to stability as long as the gain exceedsabout 6, although Fig. 3 shows that the improvement overan ungoverned machine is much more apparent. If the inertiaconstant is higher than about 4kWs/kVA, the gain of a100

' 0 - 2

10-1

8 12 16 20velocity governor gain

24 28

Fig. 5Effect of velocity governor gain on critical clearing time for two valuesof inertia3-phase-to-earth fault. Peo = 1 - 2 3 p.u.a H = 5-0kWs/kVAb H = 3-0kWs/kVA

At fast clearing times of less than about 200ms, only alimited contribution to first-swing stability can be expected,even over a wide range of inertia constants and governorgains.

The influence of inertia and governor gain can also bedemonstrated by their effects on rotor transients. Fig. 6relates the acceleration of the rotor from an initial loadangle, the prime-mover input power, and the rotor anglewhen 2-phase-to-earth faults are applied to machines ofdiffering inertias, differing governor gains and differing faultclearance times being used.

The reduced governor gain permits larger rotor-angleexcursions and longer periods of oscillation, whilst lowerinertia gives greater initial rotor acceleration. The initialrotor acceleration, of course, corresponds to the loss of loadcaused by fault application, and the point at which the faultis cleared gives a similarly clearly defined rotor deceleration.

In Fig. 6, curve d has been prepared for comparison withcurves a, b and c to show the effect of a less severe 2-phase-to-earth disturbance occurring on a machine with an initial loadof 0-73p.u. The longer permissible clearance time of 0-6secenables the governor to make a more significant contributionto first-swing stability.

Fig. 6 also indicates that the velocity governor makes acontribution to the positive damping of the rotor oscillations,and from these curves and Fig. 3 it is evident that, at lowerinitial power levels and in less severe disturbance conditions,the extended clearing times then possible would permit thevelocity governor to make a more significant contribution totransient stability.

The most important contribution of a velocity governorto stability seems to lie in its ability to add to the positivedamping of the rotor oscillations, rather than in the reduction

PROC. 1EE, Vol. Ill, No. 1, JANUARY 1964

of energy to the rotating system during the first quarter of asecond or so of a disturbance. Stability after heavy faultsseems to be decided in this first short period, and a sufficientlysensitive velocity governor gives a significant contribution to

disappears, so that a gain of 50 at usual values of inertiaconstant will probably render a governor susceptible to selfinduced oscillation unless special preventive measures aretaken. Such special measures are suggested later in the paper.

2 0 3 0

Fig. 6Rotor swing, input power and rotor acceleration with velocity governor2-phase-to-earth fault

Initialloadp.u.1-231-231-230-73

Clearancetimesec

0-20 1 50 1 50-6

Governorgain, Gg

206

2020

Inertiaconstant

H53-53-53-5

overall transient stability, as may be seen from Fig. 3. Theconjoint effect of governor and regulator action is here seento greatly exceed their separate effects.

It was found that too high a gain of the velocity-governorcontrol loop could lead to self induced oscillations, especiallywith low inertia constants and small viscous damping. Exceptat very low inertia constants, these oscillations never occurredwith gains of 30 or less, and increasing the governor gain ledto reduction of the positive damping contribution. At highergains the positive damping inherent in the governor actionPROC. IEE, Vol. Ill, No. 1, JANUARY 1964

It was essential to keep the study free from the extraneouseffects of self oscillation, and accordingly attention wasmainly confined to the lower velocity-governor gains shown inthe Figures.

3 Acceleration governor3.1 General

On competition of the study of the widely usedvelocity governor, it was concluded that a more substantial

101

improvement in the transient performance of the synchro-nous generator might be produced by replacing the velocity-actuating signal by one proportional to the rotor accelera-tion, since acceleration is directly related to the powerdifference Pl — Pe on which stability ultimately depends. Theeffect of 3-phase-to-earth, 2-phase-to-earth, phase-to-phaseand single-phase-to-earth faults on machines fitted withvelocity and acceleration governors have been studied, butonly the least severe and most severe have been reproducedin curves b and c in Figs. 7 and 8, which show, respectively,

1-5

1 0

0 0-25 0-5 0-75critical clearing time, sec

Fig. 7Effect of governor type on stability boundary3-phase-to-earth fault. H = 5kWs/kVAa Compound governor, G9 = 20, Gag = 10b Acceleration governor, Gag = 10c Velocity governor, Gg = 20d Position governor, Gv = 20

1-0

0 0-25 0-5 0-75 10critical clearing time, sec

Fig. 8Effect of governor type on stability boundarySingle-phase-to-earth fault. H •= 5kWs/kVAa Compound governor, Gg •= 20, Gag •= 10b Acceleration governor, Gag = 10c Velocity governor, Gg = 20

the stability trends for velocity and acceleration governorrestraint. Curves a each represent the effect of a combinedgovernor response as described in Section 4, whilst curve din Fig. 7 indicates the stability trend for the position governordescribed in Section 5. An inertia constant of 5kWs/kVAhas been chosen for all these curves. A gain of 20 for avelocity governor at this value of inertia gives a measurableimprovement in stability without any likelihood of selfinduced oscillations.

Acceleration governor gain is defined in a similar way tovelocity governor gain. An acceleration of 0-04p.u. (persistingfor the appropriate period) will completely close the input,valve with an acceleration governor gain of 25. 1 p.u. accelera-tion is defined as unit change of speed in unit time.

At high prefault power levels and severe fault conditions,102

the acceleration governor seems to be more effective in themaintenance of stability than the velocity governor, becauseof the greater initial acceleration and the more limited timeduring which governor action may be effective. It is evidentthat velocity-governor action is superior when long clearingtimes are possible, although these clearing times may not bepermissible in practice.

3.2 Study detailsFig. 9 relates the critical clearing time to the accelera-

tion governor gain for a generator with an initial load of

0-5

0-25

0 10 20 30acceleration governor gain

Fig. 9Effect of acceleration-governor gain on clearance time2-phase-to-earth-fault. Peo = 1 -5 p.u. H = 5kWs/kVA

l-5p.u., subjected to a 2-phase-to-earth fault, alternativeinertia constants not being considered. The rate at whichimprovement in system transient performance increases withacceleration governor gain does not justify gains in excess ofabout 25. In conditions of high initial loads or severe faults,the acceleration governor gives appreciably improved per-formance as compared with the velocity governor, for it isimmediately sensitive to the acceleration produced by the lossof load. In the limit, increasing gain produces little improve-ment, chiefly because of the time delays inherent in thegovernor prime-mover control loop.

Fig. 10 relates the critical clearing time and the inertia

. 0-5

2-5 50 7-5inertia constant, kWs/kVA

10

Fig. 10Effect of inertia on critical clearing time for various types of governor2-phase-to-earth fault. Peo = l-36p.u.a Compound governor, Gg = 20, Gag = 10b Acceleration governor, Gag = 10c Velocity governor, Gg = 20

constant for an initial power level of l-36p.u. for differenttypes of governor characteristic; curves b and c describe theeffects of acceleration and velocity governors, respectively.Curve a is for the combined governor described in Section 4.The acceleration governor shows less improvement in critical

PROC. IEE, Vol. Ill, No. 1, JANUARY 1964

clearing time than does the velocity governor at inertiaconstants greater than about 5kWs/kVA.

For any given disturbance, the initial rotor accelerationwill be inversely proportional to the inertia constant, so thatfor high inertias the acceleration governor will be less effectivewhilst the machine is inherently slower in response to dis-turbance, so that these effects tend to cancel.

Fig. 11 relates rotor acceleration, prime-mover input and

100

significant contribution to transient stability than does theconventional velocity governor.

4 A combined governor4.1 General

Curves b and c in Figs. 7 and 8 demonstrate thatneither a velocity governor nor an acceleration governor as

time, sec

.5= 0-5-

time, sec

0-1 ^

d.-0-05

o

"-0-05

-0-1

1-0 time, sec2 0 3 0

Fig. 11Rotor swing, input power and rotor acceleration with acceleration governor2-phase-to-earth fault

Clearancetime, sec

0-350-250-35

Governorgain, Gag

103

10

Inertiaconstant

H55

3-5

rotor angle for a machine fitted with an acceleration governor,subjected to a 2-phase-to-earth fault, with an initial load ofI • 23 p.u. These are the same load iand fault conditions asfor the velocity-governed machine whose swing curves areshown in Fig. 6, but the faults can be allowed to persist forlonger periods, with less disturbance to the rotor.

The acceleration governor is seen to give more heavilydamped rotor oscillations and much reduced frequency ofoscillation compared with the velocity governor, i.e. theacceleration governor has the effect of greatly increasing theapparent machine inertia. It is concluded that, except at longclearance times, the acceleration governor makes a morePROC. IEE, Vol. Ill, No, 1, JANUARY 1964

described above has the best characteristics for all faulttypes, clearing times and initial loads, but suggest that acombination of their characteristics might be beneficial. Thereare many conceivable ways of effecting a combination, e.g.by making the greater signal of the two the operating signalor by arranging that initial load or duration of fault decidesthe signal selected, but in the event it was decided simply toadd the two signals and investigate the effects of varying thegain of each.

It was found that a combined governor offers the possi-bility of greater assistance, not only to transient stability butalso to the elimination of self induced oscillations arising from

103

. 1-5

0-5. 0-25critical . 0-5 t. 075

clearing time, sec 10

Fig. 12Effect of various compound governors on stability boundary3-phase-to-earth fault. H = 5kWs/kVAa Ge<~ 20, Ggg = 20b Gg = 40, Gag = 10c Gg= 20, Gag = 10d Ga — 60, Caff = 5

large gains in velocity governors, as discussed in Section 2.2,so that an acceleration signal has a substantial stabilisingeffect on a velocity governor that tends to self oscillation.

4.2 Study detailsCurves a in Figs. 7 and 8 show the improvement in

generator transient performance produced by compoundgoverning over that obtained by either a velocity or anacceleration governor.

Fig. 12 shows the stability boundaries for a generator withan inertia constant of 5kWs/kVA when subjected to a3-phase-to-earth fault. These curves show the stability effectsof different relative amounts of the two control signalsproduced by varying their gains.

Fig. 10 curve a shows the effects of inertia on stability fora machine with a compound governor of acceleration gain10 and velocity gain 20, and permits comparison with theperformance of purely velocity and purely accelerationgovernors.

Fig. 13 relates rotor acceleration, prime-mover input and

time, sec

2-0 3 0time, sec

104

Fig. 13

Rotor swing, input power and rotor acceleration with compound governor

2-phase-to-earth fault. PeQ = l-23p.u.

Clearancetime, sec

0-350-35

Governor gainGg Gag

2060

Inertiaconstant

H55

PROC. IEE, Vol. Ill, No. 1, JANUARY 1964

rotor angle for a machine with the same initial load andsubjected to the same fault conditions as Figs. 6 and 11.Damping is increased still further with the compoundgovernor than with the simple acceleration governor. Fig 136is especially interesting since, with this velocity-governorgain, self induced oscillations were apparent in the absenceof acceleration feedback.

5 Rotor-angle governorThe rotor angle has been proposed as a possible input-

power controlling signal10 and has been investigated as partof this study. It was found to be much less satisfactory thanvelocity, as might be expected, since rotor displacement, theintegral of velocity, introduces a further phase shift into theinput-power control loop, giving instability problems even atlower levels of gain.

Fig. Id gives some indication of the stability limit with arotor-angle governor, compared with velocity and accelera-tion governors. This curve explains why the rotor-anglegovernor was not regarded as making any practicable contri-bution to transient stability.

6 Effects of alternative transfer function forgovernor loopAppendix 11.2 describes the transfer function for the

governor used in the main study, and also postulates analternative transfer function for representing the governorloop that takes account of the time delay inherent in themovement of the input valve and a longer delay in the oilservomechanism. These longer time constants seemed likelyto reduce the governor contribution to transient stability, andtheir effect was therefore investigated. Fig. 14 includes a

.1-5

0-50-25 0-5 0-75

critical clearing time, sec1-0

Fig. 14Effect of alternative transfer-function representation of turbine and•acceleration governor on stability boundaryH « 5kWs/kVA•a Acceleration governor, Gag ••b Acceleration governor, Gag

10, first transfer function10, second transfer function

stability boundary for a 2-phase-to-earth fault occurringwhen the generator prime mover is controlled by this slowerresponse governor and compares it with the governor transferfunction assumed earlier in the paper. The governor isacuated by an acceleration signal, and it is seen that the trendis not altered by increased governor time constants, but thestability boundary is reduced. It should be noted that apessimistic time constant has been used for the oil-servo-mechanism representation.

7 Single-line faultsAn acute transient-stability problem can arise when a

generator is connected to a large power system by a singlePROC. 1EE, Vol. Ill, No. 1, JANUARY 1964

7 P4

transmission line. Fast automatic reclosure after fault trippingcan often restore the synchronous tie and maintain generatorstability. The stability boundary of a single-line system can bedefined in the same way as in Section 2, if 'reclose' is sub-stituted for 'clearing'.

A typical single-line system was assumed, whose transmis-sion-line length was half that shown in Fig. 2, so that theinitial conditions defined in Appendix 11.4 can be retained.

A 3-phase-fault clearing time of 0 1 sec and successful3-phase reclosure is assumed to occur. Fig. 15 shows the

1-5

: 1 0

0 5 0-25 0-5 0/75critical reclose time, sec

1-0

Fig. 15Effect of various compound governors on stability boundary forsingle-line system

3-phase-to-earth fault. H = 3-5kWs/kVA, tc = 0-1 seca (Jff = 60, Gag = 56 C , = 40, Ga<l •= 10C Gg = 20, Gag = 20d Velocity governor, Gg = 10

stability boundaries for a machine subjected to a 3-phase-to-earth fault at the local end of a single tie line, with threealternative compound governors and, for comparison, avelocity-actuated governor of gain 10. The inertia constant is3 • 5kWs/kVA for all the curves.

8 ConclusionsWith the aid of an appropriate combined computer,

the effect of conventional velocity governors on synchronous-generator transient stability shows that the potential improve-ment of power-system stability by these governors is limited,but that substantial improvements will be effected by theinclusion of acceleration signals in governor-actuating mech-anisms. These, signals may be used alone or combined withvelocity signals, but the manifest advantages of the compoundgovernor have been demonstrated.

At practicable fault-clearing times, system stability will beimproved and system design problems correspondinglyrelieved by employing the appropriate forms of compoundgoverning outlined in the paper, with optimisation of theproportion of the component signals.

In addition, improvement of the steady-state stability ofhigh-gain velocity governors seems to be possible by the useof acceleration feedback techniques. It is believed that apurely acceleration-operated governor will prove less usefulthan a compound governor as some velocity signal must beused to control power input in conditions of slowly changingload.

Load-rejection problems cannot be solved on the computer,which employs a reference frame of synchronous speed, butthe improved performance obtained with acceleration andcompound governors on severe faults suggests that load-rejection performance will be similarly improved.

105

9 AcknowledgmentsThis work is part of a comprehensive programme of

studies on power-system transient stability at the Universityof Newcastle upon Tyne. The authors would like to acknow-ledge the interest and encouragement of Prof. R. L. Russelland Mr. W. D. Horsley, and the very important work ofDr. W. D. Humpage on the combined computer. The Depart-ment of Scientific and Industrial Research, C. A. Parsons andCo. Ltd., and the International Research and DevelopmentCo. Ltd. are thanked for their financial support and advice.

Eqn. 3 is applicable for the study of Section 2, eqn. 4 forSection 3 and eqn. 5 for Section 4.

(6)

Eqn. 6 describes the alternative transfer function discussedin Section 6.

Table 1 gives the details of the various governor timeconstants used throughout the study.

10 References1 HORSLEY, w. D.: 'The stability characteristics of alternators and of

large interconnected systems', / . IEE, 1935, 77, p. 5772 DINELEY, j . L., and HUMPAGE, w. D. : 'Aids in the calculation of

transient stability', ibid., 1962, 8, p. 863 BS 132: 1951: 'Steam turbines', p. 64 ALDRED, A. s., and DOYLE, p. A. : 'Electronic-analogue-computer

study of synchronous-machine transient stability', Proc. IEE, 1956,104 A, p. 152

5 ALDRED, A. s., and SHACKSHAFT, G. : 'The effect of a voltage regu-lator on the study-state and transient stability of a synchronousgenerator', ibid., 1958, 105 A, p. 420

6 CONCORDIA, c , CRARY, s. B., and PARKER, E. E. : 'Effect of primemover speed control characteristics on power-system frequencyvariations and time-line power swings', Trans Amer. Inst. Elect.Engrs, 1941,60, p. 559

7 ALDRED, A. s.: 'Electronic analogue computer simulation ofmulti-machine power-system networks', Proc. IEE, 1962, 109 A,p. 195

8 MILES, J. G.: 'Analysis of overall stability of multi-machine powersystems', ibid., 1962, 109 A, p. 203

9 DINELEY, j . L., and KENNEDY, M. w.: 'Concept of synchronousgenerator stability' (see p. 95)

10 WALKER, P. A. w., and ALDRED, A. s.: 'Frequency-response analysisof displacement governing in synchronous power systems', Proc.I.E.E. 1961, 108 C, p. 471

11 Appendixes11.1 Test generator and system principal details

The principal details of the system studied, whichremained unchanged throughout the study, are:

Generator: Xd = 08p.u. X'd = 0-3p.u. Xq = 0-5p.u.rd0 = 5 sec

Transformers: Xtl = Xl2 = O l p . u .

Double-circuit transmission lines:

X, = 0-4p.u. R, = O l p . u . Xc = lOOp.u.

Single-circuit transmission line:X, = 0-2p.u. R, = 0 05p.u. Xc = 20-0p.u.

11.2 Governor transfer functionThe governors used throughout the study are described

by

pBG' (3)

(4)

(5)

P28Gag

(1 +prl)(l+pr3) '

p8Gg+p28Gag

Table 1

GOVERNOR TIME CONSTANTS

Equation

3456

0 10 10 10-5

T2

0 1

0-50-50-50-5

11.3 Automatic-voltage-regulator transfer functionThe automatic voltage regulator, though not forming

the subject of the paper, was present during the study, unlessotherwise stated. The transfer function is summarised belowin terms of the gain and time constants of the componentpart:

max (')pr6)(l +pr7). cmi"

K,VV f m a x . . . . ( 8 )

_ pK58 (1 +pr9) +

pK5

y= vd

(1 +/>T|0)

V — VYm yg •

(1(9)

(10)

where Vd, Vm and Vg are the demanded terminal voltage,actual terminal voltage and stabilising regulator feedbackvoltage, respectively.

11.4 Initial conditionsAll steady-state initial system variables were computed

digitally. The rotor angle was chosen as the independentvariable, and the corresponding prefault powers are shownin Table 2.

Table 2INITIAL

8

102030405060

CONDITIONS

P,o

0-260-490-730-971-231-5

cos <f> (lag)

0-870-910-900-860-80-73

106 PROC. IEE, Vol. Ul, No. I, JANUARY 1964