IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 6 June 1981APPLYING POWER SYSTEM STABILIZERS

PART II: PERFORMANCE OBJECTIVES AND TUNING CONCEPTS

E.V. Larsen (Member) D.A. Swann (Member)General Electric Company, Schenectady, New York

ABSTRACT

This part of a three-part paper deals first withthe performance objectives of power system stabilizersin terms of the type of oscillations for which they areintended to provide damping, the operating conditionsfor which the requirement for stabilization is greatest,the need to accommodate multiple modes of oscillation,and the significance of interplant modes of oscillation.It next treats stabilizer tuning. General tuning guide-lines are developed as well as variations required fordifferent input signals. The operating conditions underwhich each type of stabilizer should be tuned are iden-tified. The relationship between phase compensationtuning and root locus analysis is presented. Finally,the relative performance characteristics of the threetypes of stabilizers are examined for both small per-turbations and large disturbances.

INTRODUCTION

Tuning of supplementary excitation controls forstabilizing system modes of oscillation has been thesubject of much research during the past 10 to 15 years.Two basic tuning techniques have been successfullyutilized with power system stabilizer applications:phase compensation and root locus. Phase compensationconsists of adjusting the stabilizer to compensate forthe phase lags through the generator, excitation system,and power system such that the stabilizer path providestorque changes which are in phase with speed changes[1,2,3,4,5,6]. This is the most straightforward ap-proach, easily understood and implemented in the field,and the most widely used. Synthesis by root locusinvolves shifting the eigenvalues associated with thepower system modes of oscillation by adjusting thestabilizer pole and zero locations in the s-plane [7,8].This approach gives additional insight to performance byworking directly with the closed-loop characteristics ofthe system, as opposed to the open-loop nature of thephase compensation technique, but is more complicated toapply, particularly in the field.

Independent of the technique utilized in tuningstabilizer equipment, it is necessary to recognize thenonlinear nature of power systems and that the objectiveof adding power system stabilizers is to extend powertransfer limits by stabilizing system oscillations;adding damping is not an end in itself, but a means toextending power transfer limits. This part of a three-part paper addresses the performance characteristics ofpower system stabilizers with respect to extending powertransfer stability limits for both remote generation andintertie situations. Both small and large disturbanceaspects of performance are included, resulting in adefinition of desired stabilizer performance to ensure a

80 SM 559-5 A paper recommended and approved by theIEEE Power Generation Committee of the IEEE PowerEngineering Society for presentation at the IEEE PESSummer MIeeting, Minneapolis, Minnesota, July 13-18,1980.Manuscript submitted March 14, 1980; madeavailable for printing May 7, 1980.

robust design meeting the system requirements. Inaddition, a relationship is established between desiredperformance and the phase compensation characteristics,laying the groundwork for a fairly straightforward fieldtuning procedure outlined in Part III.

PERFORMANCE OBJECTIVES

"Dynamic" or "Steady-State" Stability Limits

Applying power system stabilizers can extend powertransfer stability limits which are characterized bylightly damped or spontaneously growing oscillations inthe 0.2 to 2.5 Hz frequency range. This is accomplishedvia excitation control to contribute damping to thesystem modes of oscillation. Consequently, it is thestabilizer's ability to enhance damping under the leaststable conditions, i.e., the "performance conditions",which is important. Additional damping is primarilyrequired under conditions of weak transmission and heavyload as occurs, for example, when attempting to transmitpower over long transmission lines from remote generat-ing plants or over relatively weak ties between systems.Contingencies, such as line outages or fuel shortages,often precipitate such conditions. Hence, systems whichnormally have adequate damping can often benefit fromstabilizers during such abnormal conditions.

It is important to realize that the stabilizer isintended to provide damping for small excursions about asteady-state operating point, and not to enhance tran-sient stability, i.e., the ability to recover from asevere disturbance. In fact, the stabilizer will oftenhave a deleterious effect on transient stability byattempting to pull the generator field out of ceilingtoo early in response to a fault. The stabilizer outputis generally limited to prevent serious impact on tran-sient stability, but stabilizer tuning also has a sig-nificant impact upon system performance following alarge disturbance, as will be discussed.

System Modes of Oscillation

The power system oscillations of concern to sta-bility occur in the 0.2 to 2.5 Hz frequency range.These result when the rotors of machines, behaving asrigid bodies, oscillate with respect to one anotherusing the electrical transmission path between them toexchange energy. There are many different modes inwhich such oscillations may occur, often simultaneously.

The first widespread use of power system stabi-lizers occurred when the U.S. West Coast utilitiesdiscovered that they were unable to fully load their 500kV transmission lines connecting the Pacific Northwestand Southwest because of an oscillatory instability [1].Troublesome oscillations resulted as a consequence ofthe aggregate of units at one end of the intertie oscil-lating against the aggregate of units at the other end.This has become known as an intertie or interarea modeof oscillation, and has been experienced in severalsystems [1,9,10,11]. The natural frequency of oscilla-tion of intertie modes is typically in the range of 0.20to 0.5 Hz.

The use of power system stabilizers was extended toprovide damping for oscillations which occur when remotegenerating units are connected to a relatively largepower system through weak, essentially radial transmis-sion lines [12,13]. This has become known as a local

3025

3026mode of oscillation and its natural frequency is typi-cally in the range of 0.8 to 1.8 Hz.

Between the frequency extremes of the intertie andlocal modes exist other modes commonly encountered inweakly connected systems [14]. These intrasystem modesresult from oscillations between individual units withina system and tend to behave similar to local modes inthat a large portion of the power oscillation is typi-cally experienced by a few units. These modes will betreated as local modes in the discussion which follows.

Finally, it should be mentioned that if oscilla-tions occur between units in the same plant it is aconsequence of their controls interacting rather thanpower transfer stability limits. It is generally unde-sirable for a stabilizer to respond to these intraplantoscillations, typically ranging in frequency from 1.5 to2.5 Hz, as this detracts from its ability to enhancetransfer limits from the power plant. Some utilitieshave used average speed derived from multiple units in asingle plant as an input to all stabilizers in theplant, thereby preventing the stabilizers from respond-ing to intraplant oscillations [15], and summation ofpower has also been suggested. As described in Part I,ac bus frequency is inherently less sensitive to theseintraplant modes than speed or power input.

Experience suggests that it is not unusual for agenerating unit to participate in both local and inter-tie modes of oscillation. Power system stabilizers musttherefore be able to accommodate both modes. Since asingle unit or power plant is dominant in local modes,its stabilizer can have a very large impact on dampingthe oscillation. By contrast, a single unit experiencesonly a portion of the total magnitude of power oscilla-tion in the intertie mode. Therefore, a power systemstabilizer applied to a single unit can only contributeto the damping of an intertie mode in proportion to thepower generation capacity of the unit relative to thetotal capacity of the area of which it is a part. As aconsequence, a stabilizer should be designed to provideadequate local mode damping under all operating condi-tions, with particular attention to conditions of heavyload and weak transmission, and simultaneously to pro-vide a high contribution to damping of intertie modes.These criteria ensure good performance for a wide rangeof power system contingencies.

TUNING CONCEPTS

Stabilizers must be tuned to provide the desiredsystem performance under the condition which requiresstabilization, typically weak systems with heavy powertransfer, while at the same time being robust in thatundesirable interactions are avoided for all systemconditions. As described in Part I, the plant throughwhich the stabilizer must operate consists of the gener-ator, exciter, and power system:

GEP(s) = ATep/AEps (1)

where GEP(s) = the plant through which the stabi-lizer must operate.

T = component of electrical torque dueeP solely to stabilizer path.

Epss

= stabilizer output signal.

This plant has the highest gain and greatest phase lagunder conditions of full load on the unit and thestrongest transmission system. These conditions there-fore represent the limiting case for achievable gainwith a speed or power input stabilizer. With ac busfrequency as an input, the highest loop gain occurs with

a moderate to weak ac system, which fortunately also hasthe least phase lag. Hence, the "tuning condition" forspeed and power input stabilizers is with full load andthe strongest transmission system, but with a moderateto weak system for frequency input. The performancecondition occurs with a weak transmission system whichis different from the tuning condition for speed andpower input stabilizers. Since the gain of the plantdecreases as the system becomes weaker, when using speedor power the damping contribution for the strong systemshould be maximized so as to ensure best performancewith a weakened system.

An example will be used to illustrate the combineduse of phase compensation and root locus techniques tomeet the above objective for a speed input stabilizer.The example is of a large fossil turbine-generator unitoperated into a very strong system having a total of 20%external reactance', including step-up transformer. Thisrepresents a fairly extreme situation, because of thestrong system and relatively light inertia associatedwith large fossil units. A high initial response exci-tation system is assumed, with a transient gain of 20p.u. Efd/p.u. 8t As described in Part I, the speedinput stabilizer consists of a washout stage, a doublelead/lag stage, and a filter to attenuate high frequencycomponents:

T Ts (l+sT1)(l+sT3)PSS (s) = K 1+T s (l+sT2)(1+sT4)FILT(s)w s l+Tws (1+sTQ2 (l+sT4) (2)

The filter FILT(s) is represented with a second orderlag characteristic with complex roots at -17.5+j16 rad/sec. This representation provides phase lag equivalentto that of the torsional band reject filter [16] up toabout 3.5 Hz. To simplify illustration of the basicconcepts, the washout time constant is set at 10 sec-onds, thereby having virtually no impact upon the localmode, and the lead/lag stages are set identically, eachhaving a 10:1 spread between the lead and lag timeconstants. A parameter defined as the compensationcenter frequency, i.e.,

c = 1/2nJTVT2 = 410/2rT (3)

is varied to show the impact of different stabilizeradjustments.Phase Compensation.

Figure 1 shows the variation with lead/lag centerfrequency on the compensated phase, i.e., the phase ofthe complete stabilizer path from speed to torque:

(4)P(jw) = GEP(jw)PSS (jw) = P(w)/ (w)Key points to observe from this figure are the phase atthe local mode frequency of 1.6 Hz, 4 , and the fre-quency at which the phase passes through oo, fo90.

As shown in Appendix A of Part I, the initialdirection of eigenvalue migration as stabilizer gain isincreased from zero is determined by the phase at thelocal mode frequency. For perfect compensation, i.e.,

L= 0, pure positive damping will be applied and theLeigenvalue will move directly into the left half planewith no change in frequency. If phase lag exists, thefrequency will increase in proportion to the amount ofdamping increase, specifically

AWL = - tan L 'As (5)

where WL = local mode frequency (rad/sfc)aL = local mode decay rate (sec )A implies change due to stabilizer

For 0 = -450, frequency will increase at the same rateas damping, and for 0L = -90, no change in damping willtake place, but frequency will increase. This basicconcept is very useful in understanding the root locus.

0.5 0.7FREQUENCY (Hz)

FIREI COMPENSATED PHASE FOR VARIOUS LEAD/LAG CENTERFREQUENCIES (fc)

Root Locus

Root locus plots are shown in Figure 2 for threesets of stabilizer lead/lag adjustments. These plotsrepresent the migration of the eigenvalues as stabilizergain is increased from zero to infinity. Althoughseveral eigenvalues exist for the total system, only thedominant ones associated with stabilizer open-looptransfer function GH (s) (defined in Part I, Appendix B)are shown. The lightly damped eigenvalue near 10rad/sec represents the local mode of oscillation (1.6Hz). The eigenvalue which starts at -17.5+j16 rad/secresults from the filter equivalent in the stabilizer.In Figure 2A, the double pole at -20 sec and thedouble zero at -2 sec represent the lag and leadbreaks, respectively. Only the upper half of thes-plane is shown; the lower half is a mirror image ofthe upper half.

In root locus theory, the open loop system poleswill migrate to the open loop system zeros as gain isincreased from zero to infinity. Since there are sixdominant poles and only two zeros, four of the polesmust tend to infinity as gain is increased which implies

jw (r/s)

3027that an instability will develop at some value of gain.An optimum gain therefore exists at which the damping ismaximum. The eigenvalues corresponding to this optimumcondition for the three cases presented are shown on theroot locus curves by squares. For Figure 2A, the opti-mum is chosen where the decay rate, i.e., -o = -realpart of eigenvalue, of the least damped mode is maxi-mized. For Figure 2B, the optimum is chosen where thedamping ratio, i.e., the ratio of decay rate to fre-quency, associated with the so-called "exciter mode"[8], which is becoming less damped as gain increases,and the mode initially associated with local mode, whichis becoming more damped as gain increases, are equal.More or less gain than this optimum would result in oneroot having a lower damping ratio. In Figure 2C, damp-ing never increases, and a gain is chosen as the maximumbefore significant degrading of the existing dampingoccurs.

Phase Compensation, Root Locus Relationship

Of particular interest is the migration of theeigenvalue which started as the lightly damped localmode for Figures 2A and 2C. The phase compensation atthe local mode frequency for the adjustments of 2A is-330, but -90 for case 2C. As gain increases, bothexperience an increase in frequency. The direction ofmotion at any point along the locus is governed approxi-mately by the phase at the frequency which exists. Thischaracteristic is strictly true only for zero damping,but is approximately correct when the root is signifi-cantly underdamped, i.e., u/w

3028Summary of Tuning Example

The significant parameters associated with eachlead/lag setting are consolidated in Table I. Theseinclude phase compensation at the local mode frequency,$ 6 the frequency. at which the phase lag passes through9h , f 9 o, the optimum gain, KOPT' the decay rateassociated with the most lightly damped system mode withthe optimum stabilizer gain, GOPT' the gain and fre-quency at which an instability occurs, KINS , f NST'respectively, and the gain of the stabilizer a a ypi-cal intertie frequency of 0.4 Hz with the optimum stabi-lizer gain, KI.

Table I

SUMMARY OF TUNING EXAMPLE

fc OPTP-((Hz) (sec

1.02.03.45.010

-3.5-4.0-4.8-3.6-0.8

KOPT KI KL f-900(deg) (Hz)

2.5 3 -3308 11 -290

20 23 -42040 42 -59035 36 -90

2.753.303.553.501.60

KINST fINST(Hz)

7.5 2.925 3.365 3.7120 3.7130 2.6

It is seen from this table that very good local modedamping can be obtained with a wide range of lead/lagsettings, but decreases rapidly as the compensationcenter frequency becomes greater than 5 Hz. For com-pensation center frequencies up through 5 Hz, the bestlocal mode damping occurs with a center frequency near3.4 Hz. The highest gain at intertie frequencies,however, occurs with the higher compensation centerfrequency of 5 Hz. In general, the highest compensationcenter frequency which provides adequate local modedamping will yield the greatest contribution to intertiemodes of oscillation. The last four parameters of TableI suggest the following guidelines for setting thelead/lag stages to achieve adequate local mode dampingwith maximum contribution to intertie modes of oscilla-tion. Two basic criteria in terms of phase compensationare:

1. It is most important to maximize the bandwidthwithin which the phase lag remains less than 900.This is true even though less than perfect phasecompensation results at the local mode frequency.

TUNING WITH ALTERNATIVE INPUT SIGNALS

Speed Input Stabilizers

The system used in this and the following sectionsto establish the concepts of tuning the three basictypes of stabilizers differs from the previous examplecase in that a four-pole turbine-generator is used. Aswith the previous example, the tuning is examined forthe case with a strong transmission system of 20% reac-tance and full load on the generator since this repre-sents the most restrictive case for speed inpuit stabi-lizers. The lead/lag spread of the stabilizer timeconstants was initially set at 10:1, the same as used inthe previous analysis with the two-pole machine, andthe lead time constants at 0.2 seconds (f = 2.5 Hz).The locus of dominant roots as a function of stabilizergain are shown in Figure 3a. The local mode eigenvaluemoves to the left and increases in damping while theroot associated with the filtering in the stabilizerbecomes less stable and eventually goes unstable. Forthis case, the optimum gain is about 30 and the insta-bility gain is about 90.

The wide spread between the loci of the excitermode and local mode is indicative of excess stabilizerlead. Since the inertia and reactance of a four-polemachine are greater than for a two-pole machine, thelocal mode frequency is lower, other conditions beingequal. Consequently, the required phase lead at localmode frequency is less than with a two-pole machine, andthe lead/lag ratio can therefore be reduced. Figures 3band 3c show the resulting root loci for different leadtime constants, maintaining 6:1 spreads on both stages.The reduced phase lead of case 3b is close to optimumfor local mode. Placing the lead time constants athigher frequencies results in even less phase lead andthe local mode goes unstable rather than the excitermode as shown in Figure 3c.

It is instructive to compare the selected gains forthe three cases shown in Figure 3. Tabulated in Table

PT' K NST KH OKPTTlT3/ T2T4 representing thegain at 'high treqdencies, and K the gain at 0.4 HzIrepresenting the gain at an intertie frequency. Thetable also shows the local mode eigenvalues, \-OCAL'corresponding to KOPT.'

Table II

COMPARISON OF SPEED INPUT STABILIZER TUNING

2. The phase lag at the local mode frequency should beless than about 45 . This can be improved somewhatby decreasing the washout time constant, but toolow of a washout time constant will add phase leadand an associated desynchronizing effect to theintertie oscillations. In general, it is best tokeep the washout time constant greater than onesecond.

The gain and frequency at which an instability occursalso provide an indication of appropriate lead/lagsettings. The relationship of these parameters toperformance are useful in root locus analysis and infield testing.

3. The frequency at which an instability occurs ishighest for the best lead/lag settings. This isrelated to maximizing the bandwidth within whichthe phase lag remains less than 900.

4. The optimum gain for a particular lead/lag settingis consistently about one-third of the instabilitygain.

Fig T1/T2,T3/T4 "LOCAL OPT KINST KH KI3a .2/.02,.2/.02 -3.0+j 8.03b .2/.033,.3/.05 -3.5+j 8.53c .12/.02,.3/.033 -3.5+jll.5

302050

90 3000 3760 720 28

150 1800 58

All designs give good damping for local mode, but the6:1 lead/lag spread yields larger gain at intertiefrequency per gain at high frequency, i.e., K /KH islarger. Optimum tuning might lie between cases Mb, and3c with a trade-off required between high frequency gainand intertie damping contributions. Case 3b will beused for subsequent comparison with the performance ofother types of stabilizers. Note that for all cases theoptimum gain is about one-third of the instability gain,comparable to the previous example with a two-pole unit.

Power Input Stabilizer

As indicated in Part I, the interest in usingaccelerating power as a stabilizer input signal resultsfrom the inherently low level of torsional interactiondue to its non-minimum phase characteristic. As a

3029jw (r/s)

(a) T1/T2T3/T4

l7

LLuLJ U)

T-C)

-kgr-5

j20

(-17.5+16)

j'5

IlO

j5

[-/

LJ i,C-) :C/' c

-2.5 0 2.5a(sec )

FIGURE 3 ROOT LOCI WITH SPEED INPUT, VARIOUS SETTINGS

consequence, a single time constant lag at 0.06 secondis assumed to provide sufficient torsional attenuationfor this example. The general frequency characteristicsof a practical power input stabilizer are developed inPart I. Appropriate settings for this example weredetermined to be:

PSSp = K (1+.25s)(l+.15s) (1+.06s) (6)

The lag/lead stage of .5/.25 seconds contributes thephase lag required at low local mode frequencies (weaktransmission systems) and the lead/ lag stage of .15/.05seconds provides the phase lead required at high localmode frequencies (strong transmission systems).

jw((b) T1 /T2 :.2/.033

T3/T4 :.3/05

K INST

\ KOPT-20

7-

U ( Z* \~~~~~~~~~~~~~~~~~N

(r/s)

j20

5jl

j5

-5 -2.5 0 2.5c(sec -I ) a(sec l )

UNIT LOAD P :.95, Q: OXe : 0.2 p.u.

Figure 4a shows the root locus plot when varyingstabilizer gain while operating at the tuning conditionof full load into a strong transmission sys-tem. Theseroot locus curves are similar to the ones for a speedinput stabilizer, with two exceptions. With the speedinput stabilizer, complex roots at -17.5+j16 rad/secrepresented the phase lag characteristics of torsionalfiltering, whereas with the power input stabilizer asingle time constant lag of .06 sec. is used to repre-sent torsional filtering. In addition, the use of powerinput yields an extra zero at the origin in the open-loop transfer function, as described in Appendix B ofPart 1. Because of these differences, the exciter modeof the power input stabilizer becomes unstable at a muchhigher frequency and there is much larger gain marginbetween optimal and instability gain than occurs withthe speed input stabilizer.

jw ( r/s)1i2O

,w ( r/s)1i2O

j5

-20 -15 -10 -5 0a- (sec-1)

FIGURE4 ROOT LOCI WITH POWER INPUT, STRONG AND WEAK SYSTEM

-10a- (sec-I )

-/l

Ic

3030To check the effectiveness of the stabilizer for

the performance condition, a root locus was calculatedwith a weak transmission system as shown in Figure 4b.As expected, the gain established under strong transmis-sion system conditions gives less than optimum, althoughadequate local mode damping under weak tranmissionsystem conditions.

Frequency Input Stabilizer

The ac bus frequency input stabilizer has two majordifferences with respect to tuning. First, the fre-quency signal is less sensitive to intraplant oscilla-tions than either speed or power. These modes havehigher frequencies than the local mode of the powerplant to the power system, and the phase lag of thestabilizer loop is therefore greater. Hence, with speedor power input these modes will become unstable andimpose a limitation upon stabilizer performance. Sec-ondly, as described in Part I, the sensitivity of thefrequency signal to speed variations increases as theconnected transmission system becomes weaker. Thisoffsets the reduction in gain from voltage reference toelectrical torque, GEP(s), due to a weaker transmissionsystem. As a consequence, the frequency input stabi-lizer can be tuned for the best performance under weaktransmission conditions where the stabilizer contribu-tion is most required.

Although these differences in tuning criteria willgenerally result in less high frequency gain for fre-quency input stabilizers than for speed input stabi-lizers, significant attenuation is still required at thetorsional frequencies to prevent excessive torsionalinteraction. For purposes of the following analysis,the torsional filter equivalent is assumed to be thatused for the speed input stabilizer.

Root locus plots varying gain with a frequencyinput stabilizer are shown in Figures 5a and 5b for twodifferent sets of lead/lag combinations. A weak trans-mission system of 80% reactance is used. Comparativelysmall lead/lag spreads are needed to obtain phase com-pensation for the lower frequency of rotor oscillationassociated with weak transmission systems. The total

spread, i.e., T1T /T2T4, is 12:1 for the case in Figure5a and 16:1 for tge case in Figure 5b. These compare to36:1 to 100:1 with the speed input stabilizer. It willalso be noted that the high frequency gain, KH, for thecases of Figures 5a and 5b is 360 and 432, respectively,which compares to a range of 720 to 3000 with the speedinput stabilizer. The settings associated with thestabilizer of Figure 5a provide slightly better localmode improvement than those associated with Figure 5b,with lower high frequency gain, and therefore will beused for subsequent comparative analysis.

It should be noted that for the frequency inputstabilizer, the gain margin between optimum and insta-bility is about 1.5:1 for the weak transmission linecase, as opposed to 3:1 for the speed input stabilizerwith a strong transmission system and about 8:1 for thepower input stabilizer.

PERFORMANCE CHARACTERISTICS

Local Mode

The effect of various types of stabilizers on thedominant eigenvalues as the transmission system reac-tance is varied is shown in Figures 6a, b and c. Theexciter mode and the local mode are shown with theaddition of the lower frequency voltage regulation mode(around 1 rad/sec). All of these curves include asreference the local mode and voltage regulation modevariations without a power system stabilizer. It isapparent that the speed and power input stabilizersexhibit similar characteristics, with the power inputstabilizer yielding more local mode damping (due to thelower phase lag associated with torsional filtering).For both speed and power input stabilizers,.the excitermode becomes more stable as the system becomes weakerwhile the local mode becomes less stable. With thefrequency input stabilizer the exciter mode becomes lessstable as the transmission system weakens, as expecteddue to the increase in the input signal sensitivityfactor, while the local mode damping is relativelyinsensitive to transmission system strength.

(b) T, /T2 = .4/.IT3 T4- .2/.05

UNIT LOAD P :.95 0: 0Xe: .8p.u

FIGURE 5 ROOT LOCI WITH TERMINAL FREQUENCY INPUT, DIFFERENT SETTINGS

jw ( r/s )Ji2O

jI5

jilO

0 2.5

-(sec ) o(secK' )

Xe (Pu.).62.1.2 s .

jw(r/s)1 15

.2.2 ?-

(A) SPEED INPUT .6T1/T2 =.2/.033 .61T3/T4 =.3/05 1.2Ks = 20

-10-5 0

a- (sec-1)

.2 Xe(p.u.)e.6

1.2jIO

wj5\.2

(B) POWER INPUTT, /T2 = .15/.05T3/T4 =.25/.5Ks = 3

.2)

iwr/s)

-10 -5 0C (sec-I)

iw (r/s)I jl5i'5

X e(p.u.)jIO

VT4=.3/05 1.2 \= 30 -

-5a(sec-I )

x-WITH STABILIZER o- NO STABILIZER UNIT LOAD: P =.95p.u., Q=O

FIGURE 6 ROOT LOCI VARYING SYSTEM REACTANCE Xe, DIFFERENT INPUT SIGNALS

Figure 6 indicates that the power input stabilizerprovides the best overall local mode damping. The speedinput stabilizer provides better local mode damping thanthe frequency input stabilizer for strong transmissionsystems, whereas the local mode damping for the fre-quency input stabilizer is superior to that of the speedinput stabilizer for weak transmission systems. Notethat all designs allow stable operation for a very largesystem impedance of 1.2 p.u. with full load from theunit. Our experience in analyzing and applying thesetuning concepts with modern excitation systems indicatesthat stabilizers utilizing any of the input signals willprevent steady-state oscillatory instabilities fromlimiting power transfer for nearly any case which isotherwise possible, i.e., a case for which a load flowsolution exists.

It is significant to note that the large improve-ment in local mode damping associated with the powerinput stabilizer is obtained at the expense of stabilityof the voltage regulation mode. This is indicative ofthe trade-off required between adding damping and main-taining adequate synchronizing capability via voltageregulation. As subsequently illustrated, this effect ismost significant to system performance following a majordisturbance.

Interarea Mode

To explicitly evaluate the effect of the varioustypes of stabilizers on damping of interarea modes ofoscillation, a three machine system was simulated havingboth local and interarea modes of oscillation. Thesystem, shown in Figure 7, was chosen to represent theaddition of 1000 MVA nuclear unit (unit 1) to an areahaving a capacity of 10 GVA, connected with a weakintertie to another system of equal capacity. Each areais fully loaded serving its own load, with minimal flowover the intertie. A 3.5 per unit voltage responseratio high initial response excitation system is used onunit 1, with stabilizer output limits set to +10%.Units 2 and 3 represent area equivalents, simulated withspeed input stabilizers having gains set to approximatethe condition of 40% of the generating capacity in eacharea being equipped with these stabilizers. The per-formance is studied following a disturbance consistingof a 3-0 fault at the near end of the intertie which iscleared with the transmission line. Unit 1 sees aneffective change in system reactance from about .4 to .6pu between pre- and post-fault conditions.

Root locus analysis of this system with the varioustype stabilizers on Unit 1 were nearly identical withrespect to local mode as those obtained using the singlemachine when adjusted for apparent system reactance.Thus, the stabilizer settings previously establishedwere applied to this system. Eigenvalues calculated forthe post fault system with the various stabilizer inputsare shown in Table III.

Table III

EIGENVALUES WITH POST-FAULT SYSTEM

Stabilizer

None

Speed

Frequency

Power

,Local-0. 3+j5.9-1.4+j6.3-2. 2+j 8.7-2.7+j 6.2

xIntertie

-.030+j2.32-.140+j2.33-.213+j2.33-.247+j2.33

These eigenvalues represent the oscillation decayassociated with the various types of stabilizers afterthe system has recovered from the first few swings andentered the linear range of the excitation controlsystem. For a single machine situation, where localmode is the only consideration, only recovery from thefirst swing need be considered since the stabilizer willalways be acting correctly within its limits to aiddamping of the resulting oscillations. In a multi-

P2 = 9.0 PLI-86ALL LOADS,REACTANCES ON UNIT BASEFIGURE 7 3 MACHINE SYSTEM

3031

0

3032machine environment, however, more than the first swingmay be critical, and. the nonlinear performance of thestabilizer becomes important. This will be apparentfrom the large signal performance analysis which fol-lows.

The response of the system shown in Figure 7 to thefault is shown in Figure 8 for the case of no stabilizeron unit 1. The traces shown in Figure 8 are the speeddifferences between: (top) units 1 and 3 to indicateprimarily the interarea oscillatiQns, and (bottom) thespeed difference between .units 1 and 2 to indicateprimarily the local mode of oscillation. Figures 9a, b,and c show the effect of adding the speed, frequency,and power input stabilizers, respectively, to unit 1with the additional trace showing stabilizer output. Itis apparent that a significant difference exists withregard to the magnitude of the second swing of theinterarea mode. The speed input stabilizer does thebest job of limiting the swing, followed by frequency,with the power inpiut stabilizer providing the poorestperformance. Comparison with Table III indicates thatthis is exactly opposite to the ranking of performancebased on damping of small signals. This is a signif-icant observation, indicating that overly aggressiveaction with regard to higher frequency modes of oscilla-tion, such as local modes and intermachine modes withina plant, will cause the stabilizer to saturate in re-sponse to these oscillations following a major disturb-ance and thereby allow the interarea swings to increaseon the second swing. In this case, the second interareaswing is actually worse with the stabilizer having thegreatest small-signal damping than without a stabilizer.

STABILIZER OUTPUT:' +01Q

OCY)

FIGURE 9A FAULT RESPONSE WITH SPEED INPUT

SPEED 1- SPEED 2

2 3 4 5 6 7 8 9 10 11 12 13 14 15TIME IN SECONDS

FIGURE 9B FAULT RESPONSE WITH FREQUENCY INPUT

2 3 4 5 6 7 8 9 10 11 12TIME IN SECONDS

FIGURE 8 FAULT RESPONSE, NO STABILIZER ON UNIT

To further illustrate this phenomena., the tuning ofthe frequency input stabilizer was modified to produceless local mode damping. Eigenvalue comparisons of thisstabilizer versus the one used for time response ofFigure 9b are shown in Table IV.

Table IV

EIGENVALUES WITH POST-FAULT SYSTEMAND DIFFERENT FREQUENCY INPUT DESIGNS

FIGURE 9C FAULT RESPONSE-POWER INPUT

:zi STABILIZER OUTPUTwo3:

Figure KSTI/T2 T3/T49b 30,.4/.2,.3/.0510 27,.4/.l,.2/.05

"Local xIntertie-2.2+j 8..7 -.213+j2.33-l.7+j6.4 -.190+j2.32

Although the small-signal performance in terms of damp-ing is not as good with the modified stabilizer design,the response to the fault shown in Figure 10 indicatesmuch improved performance by reducing the second swingof the intertie mode (which occurs at about 8 seconns.).This substantiates the above observation regarding thetrade-off between small-signal damping and performancefollowing a major system disturbance.

SPEED - SPED E2

0 2 3 4 5 6 7 8. 9 10 11 12 13 14 15TIME IN SECONDS

FIGURE 10 FAULT RESPONSE WITH FREQUENCY INPUT, SETTINGMODIFIED FOR LESS SMALL SIGNAL DAMPING

SUMMARY AND CONCLUSIONS

The objective of power system stabilizers is toextend stability limits on power, transfer by enhancingdamping of system oscillations via generator excitationcontrol. Lightly damped oscillations can limit powertransfer under weak system conditions, associated witheither remote generation transmitting power over longdistances or relatively weak interties connecting largeareas. Stabilizer performance must therefore be meas-ured in terms of enhancing damping under these weaksystem conditions. This measure must include not onlythe small-signal damping contributions to all modes ofsystem oscillation, but the impact upon system perform-ance following large disturbances, when all jnodes of thesystem are excited simultaneously. Based upon thismeasure, it is shown that the most appropriate stabi-lizer tuning criteria is to provide an adequate amountof damping to local modes of oscillation and a highcontribution to interarea modes of oscillation. Excesslocal mode damping is unnecessary and is often obtainedat the expense of system performance following a largedisturbance.

Stabilizers utilizing inputs of speed, power, andfrequency have been analyzed with respect to both tuningconcepts and performance capabilities. Frequency hassome inherent qualities which contribute to the desiredperformance criteria. However, any of these signals canbe used to prevent oscillatory instabilities from limit-ing power transfer capability, at least to the pointwhere other system considerations become limiting.Thus, the choice of input signal depends upon factorsother than system performance alone.

The tuning concepts and performance criteria devel-oped in this paper, including the relationship to phasecompensation characteristics, provide the groundwork fora fairly straightforward field tuning procedure which isdescribed in Part III.

REFERENCES

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3. C. Concordia, F.P. de Mello, "Concepts of Synchro-nous Machine Stability as Affected by ExcitationControl," IEEE Trans, Vol. PAS-88, April 1969, pp.316-329.

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System Stabilizers for Thermal Units: AnalyticalTechniques and On-Site Validation," Paper F80-227-9presented at IEEE PES Winter Meeting, New York,February 1980.

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11. K.E. Bollinger, R. Winsor, A. Campbell, "FrequencyResponse Methods for Tuning Stabilizers to Damp OutTie-line Power Oscillations: Theory and Field-TestResults,t" IEEE Trans, Vol. PAS-98, September/October 1979, pp. 1509-1515.

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For Combined discussion see page 3024