IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 5, May 1983

Control Design and PerformanceAnalysis of a 6 MW Wind

Turbine-Generator

A. Murdoch,Member,IEEEJ.R. Winkelman ,Member,IEEES.H. Javid,Member,IEEE

R.S. Barton

General Electric Co.Schenectady, N.Y.

ABSTRACT

This paper discusses an approach to the modelingand performance for the preliminary design phase of alarge (6.2 MW) horizontal axis wind turbine generator(WTG). Two control philosophies are presented, bothof which are based on linearized models of the WTmechanical and electrical systems. The controldesigns are compared by showing the performancethrough detailed non-linear time simulation. Thedisturbances considered are wind gusts, and electricalfaults near the WT terminals.

INTRODUCTION

The MOD-5A Wind Turbine Generator program is abasic element in the overall Federal WindProgram[l12i. The goal of the MOD-5A program is todevelop a reliable, commercially viable wind energysystem, able to produce electricity at a competitivecost of energy at a site with a 14 MPH annualaverage wind speed at 32.8' reference height (6.2 m/sat 10 meters). The program is sponsored by the DOE,,with technical management by the NASA Lewis ResearchCenter.

The program began in July of 1980, and is

organized into three design phases: ConceptualDesign, which was completed in March, 1981;Preliminary Design, which is scheduled to be completedin 1982; and Final Design, scheduled to begin in early1982. Fabrication of hardware is to begin late in1982, with installation and checkout of the first unitcompleted in 1984, followed by a two year Operationand Maintenance phase. At this point in time, a sitefor the first MOD-5A has not yet been identified.

The MOD-5A system has been developed for a windregime having a mean wind speed of 14 rMPH (referenceheight, 32.8', miles per hour). System size andfeatures were established as a result of tradeoff andoptimization studies driven by minimizing the systemcost of energy (COE). This led to a 400' (122 m)rotor diameter size, and a synchronous generatorrating of 6200 kW. The cut-in wind speed was selectedto assure maximum output and to pre-empt "falsestarts" in low winds wherein mechanical and electricallosses are likely to exceed the energy to be derivedfrom the wind. A cut-in wind speed of 14 hMPH (hubheight, 250', miles per hour) has been established. A25% blade tip length was found necessary for

82 SM 414-1 A paper recommended and approved by the IEEE

Power Systems Engineering Committee of the IEEE Power

Engineering Society for presentation at the IEEE PES 1982

Summer Meeting, San Francisco, California, July 18-23,1982. Manuscript submitted February 4, 1982; made avail-

able for printing May 17, 1982.

General Electric Co.Valley Forge, PA

satisfactory startup. Low cut-out is established at11.5 hbPH, based on rotor underspeed. Gear shiftingfor two speed operation occurs near 21 hMPH and ratingis reached at 29 hMPH.

The purpose of this paper is to report on the

design of the primary control systems for operation ofthe WTG in a power system environment. The twocontrol paths involve regulation of terminal voltageand electrical power output. The field excitation ofthe synchronous generator to regulate terminal voltageis a well understood problem that is not new to anyaspect of bulk power generation.

The unique feature of the WTG that presentschallenges in the control design is the variability ofthe turbine power. Unlike conventional generationwhere input energy can be scheduled and regulated,wind energy is not a controllable resource. A controlloop on blade pitch serves to regulate the percentageof energy that the WTG is extracting from the wind atany given instant. To withstand severe wind gusts theturbine control is designed to respond rapidly tochanges in output power. The bandwidth of the powercontrol path is comparable to the voltage regulator.

Two designs for unit controls that satisfy thedesign criteria are described. To verify therobustness of the designs, the performance of the WTGsystem was evaluated for both wind gust disturbancesand electrical faults near the unit terminals. Thestudy work indicates that the design goals can be metwith good transient performance.

WIND TURBINE MODELING

The basic components involved in therepresentation of a single WTG are shown in the blockdiagram in Figure 1.

Inf initebus

Wind and Blade 2-nmass SynchronousTorque Calcs 10torsional GeneratolsYr

XI

U Ie,Vfdl e lA',V p

Actuator Sensor

Dynamics Dynamics

o OutputFeedbackControl

Figure 1 Block Diagram of WT Model

The three basic elements of the plant model arethe synchronous generator and network electricaldynamics, a mechanical torsional system, and thetorque producing characteristics of the turbine blades.Also a part of the plant are models for the actuators,

0018-9510/83/0500-1340$01.00 1983 IEEE

1340

in this case the pitch angle hydraulics and therotating exciter, and the sensor dynamics involved inmeasuring the system output variables.

The regimes of operation for the wind turbine overwhich the models must be designed are shown inFigure 2, where normalized power on the unit base isplotted versus wind speed at the hub. Start-up ofthe turbine occurs when time averaged wind speed isgreater than 14 hMPH (6.2 mJs). The curve in thisregion is cubic in nature, reflecting the basicequation relating power to wind speed.

P = npV3R2C /2 (1)p

where p is the mass density of air, V is windvelocity, R is the rotor diameter, and Cp is a powercoefficient representing the aerodynamic efficiency ofthe blades at the operating point. In the sub-ratedpower regime the gearbox has a switch point at21 hMPH, designed for maximizing energy capture.

Rated Power

a.

zO

20 -30Wind Speed at the Hub (MPH)

Figure 2 WT Operating Regimes

When the wind velocity reaches 29 hMPH, rated poweroperation is reached and the pitch angle controlsswitch to a mode where unit power is regulated torated. It is in this regime that the study resultspresented in this paper were generated. The variouselements of the models used in the studies are nowdescribed; first the drive train dynamics, then theturbine aerodynamic characteristics, and finally thegenerator and control system models.

DRIVE TRAIN DYNAMICS

The rotor, to which the blades are attached,operates through a gearbox to supply power to thesynchronous generator which is a 6 pole machine (1200RPM). The two speed gearbox has a shift point at21 hMPH in the subrated power regime. At low windspeeds the rotor velocity is 13.25 RPM and at higherpower levels switches to 17.9 RPM.

One of the salient features in the present designis the mechanical damping present in the gearbox. Thefirst stage of the gearbox, the complete structure ofwhich is described in reference (21, has epicyclicgearing with the outer ring gear constrained by atorsion bar suspension. Adding mechanical dashpots tothe suspension significantly increases the equivalentmechanical damping in the gearbox, without changingthe gearing efficiency.

1341

Enough mechanical damping is present in thetorsional system to have the open loop damping of thefirst torsional mode (local mode) increased to nearly30% of critical damping. The implications of thisincreased natural system damping are twofold. First,the mechanical and electrical control paths becomeeffectively decoupled, and second the need for dampingimprovement with a power system stabilizer in theexcitation system is eliminated.

A two mass model represents the torsional system.One mass represents the lumped equivalent of theblades and rotor structure, and the second mass is thesynchronous generator rotor. The gearbox effects aretranslated into an equivalent spring and dampingconstant in the shaft that connects the rotor and thegenerator. The first torsional mode (local mode) isat approximately 0.16 Hz and the upper torsionalfrequency is near 2.5 Hz.

The blades are not represented in the torsionaldynamics since the present design includes a teeterdegree of freedom in blade mounting. This simulationassumption decouples the blade response from anysignificant participation in the torsional dynamics.The data for the reduced order torsional model isgiven in the appendix.

AERODYNAMIC MODELS

Without individual representation of the twoblades, there is no need to include wind shear andtower shadow effects at a detailed level. The windmodels which are available include an additive termrepresenting the net effect of rotationalnon-linearities in the driving torque. The additiveterm has a frequency of twice the rotor speed (denoted2P) due to the two blade configuration. The level ofthe 2P signal is approximately 6% half range on windspeed and 18% half range on rotor full load torque atrated conditions.

The model of the turbine power is then given byequation (1) and the following closed form approximaterelationship for C

C = (.44 - .0167 S) sin[2(X-3) (X-3) (.00184 B)p [7.5 - .156j- 2

where a is the blade tip pitch angle, and X isblade tip speed ratio, a function of wind speed, V.

W RA = V

In this equation WH is hub speed and the productwHR is tip velocity. Only the outer 25% of theblade surface is articulated so the pitch angle refersto the control position of this surface.

Three types of wind models were available in thecontrol design development and performance analysis;1) A single 1-cosine (versine) gust with variablemagnitude and period, 2) sinusoidal forcing at singleor multiple frequencies, and 3) a severe wind gustrepresenting a low probability of occurence (seereference 3).

GENERATOR AND CONTROL SYSTEM MODELS

The generator model is a conventional two axisrepresentation of the synchronous machinet4]. Thestudy objectives and spectrum of system eigenvaluesindicate that stator electrical transients (pVterms) can be neglected. The resulting electrical

(3)

1342

model is of fourth order if two circuits per-axis arerepresented. The machine parameters are given in theAppendix.

The control system representation depends on thedynamics involved in sensing the outputs (transducerdynamics), and the actuator dynamics in the twocontrol paths; pitch angle and field voltage.Transducer dynamics involve first order equivalenttime constants and non regulated variables usewashouts (high-pass filters) on the outputmeasurements. The field voltage path includes a firstorder representation of the rotating shaft-drivenexciter, including saturation in the magneticcircuits. The pitch angle actuator is a first orderequivalent with a rate limit of +10 degrees/sec. and atransport delay of 50 milliseconds to represent thefluid flow between the supply at the hub and the servovalve at the controllable blade tip section.

All of the models described above are programmedinto a modularly structured simulation program,POSSIM, which represents all the electromechanicaldynamics in the system [5]. This program has thecapability of time simulation with the full non-linearmodel, and can create linearized system state matricesat any specified operating point. The linearizedstate matrices are used in the control design and theresulting designs can be checked with time simulationsover a wide range of operation. This gives anindication of the robustness of the control design andthe performance capability.

The details of two control systems considered forthe wind turbine are given in the next section.

CONTROL SYSTEM DESIGN

Two paths are available for control of the windturbine. Field voltage control in the synchronousgenerator allows for regulation of the terminalvoltage to a setpoint. The second path is control ofthe blade pitch angle which, together with availablewind, effects the mechanical input power to thegenerator. The blade pitch control input is analogousto the throttle valve in conventional steam turbines,except that the bandwidth of the control, unlike theslow time scale dynamics used in a steam turbinegovernor control, is the same as that of the voltagecontrol path. Both paths can be used to providedamping for local mode (the mode representing theelectromechanical interaction of the WT with the restof the power system). This regulation and dampingmust take place in the presence of random variationsin wind, and electrical disturbances such as faultsand line switchings.

The performance goals which influenced the designprocess include limiting transient excursions interminal voltage to less than 5% for all disturbancesexcept during faults and providing tight regulationfor steady-state operation. To limit mechanicalstress in the WT torsional system, a limit ontransient power swings to 140% of rated power isimposed. This limiting level should be reached onlyinfrequently to minimize cyclic stress levels. Also,there is both a rate limit (+10 degrees/second) and asteady state motion limit (+0.2 degrees) on the bladepitch actuator which controls the mechanical power.In addition, the closed loop damping on the local modeoscillation is desired to be 25% or better of criticaldamping. The remainder of this section will focus ondescribing the resulting control design and theoptions in implementing the voltage regulator.

The design methodologies used to synthesize thecontrol systems in this paper are based on linear

models. The non-linear model of the wind turbinedescribed above was linearized around a nominaloperating point. The linearized wind turbine model isboth controllable and observable, and takes thefollowing form:

x = Ax + Bu(4)

y = Cx

where x is the n-dimensional state vector, u is them-dimensional control vector, and y is ther-dimensional output vector. The problem is to designa control system of the form u = K(s)y to satisfy theperformance goals, where s is the laplace operator.

The two control designs discussed in this sectionwere designed using different design approaches. Thefirst, a single loop design, uses a decentralizedinformation pattern, that is, different measurementsare used to determine each control, and classicaldesign techniques. The second design approachcoordinates the controls by using modern controldesign techniques with a centralized informationpattern. In the following paragraphs we discuss thedesign of each controller, the performance analysisand a comparison between the two designs will be givenin a subsequent section.

Single Loop Design

From Table I we see that the open loop damping ofthe Local Mode is about 30% of critical. With such ahigh value it was felt that a power system stabilizerwould not be needed. The voltage regulator packageused in an earlier multi-megawatt WTG design waschosen as baseline for this initial design effort.Power regulation is achieved through a PI controllerwith an input from hub speed as a stabilizing signal.The block diagram of the control is shown in Figure 3.

Avt.Vreg regulator

voltage

Figure 3 Decentralized Control Design

The closed loop eigenvalues for the decentralizedcontroller were evaluated using linearized statematrices generated at an operating point correspondingto a 30 hMPH windspeed. The local mode damping hasdecreased from a value of near 30% of critical in theopen loop system to 11%. This is somewhat less thanthe value of desired damping given in the designspecifications.

Increased gain in the hub speed path of the powerregulator can be used to increase local mode damping,

however, this gain is limited by the steady statelimit on the blade pitch actuator motion. Anon-linear gain in the hub speed path based on themagnitude of hub speed error meets steady staterequirements and provides increased stabilizationduring large disturbances. Values for the controllerparameters may be found in the Appendix.

Multivariable Output Regulator

In the design of a multivariable output regulatorfor a wind turbine we would like to regulate certainoutput measurements while minimizing the use of thecontrol. This can be mathematically posed asminimizing a performance index of the form

00

J= 1 (xT Q x + UT R u) dt . (5)2 0

An important part of the design process is choosing Qand R. A variety of methods are available forchoosing these matrices[6 81. The method used hereis iterative, using engineering judgment and acombination of output and control weightings. For anyQ and R matrix the optimal solution to the LQR problemis obtained by minimizing J with respect to u, subjectto (4). The optimal solution is obtained by findingthe symmetric positive definite M satisfying

ATM,+ MA - MBR-lBTM + Q = O (6)

and setting

u =-R B Mx =Gx (7)

The corresponding closed loop system is

-T

x=(A - BR B M)x = (A + BG)x (8)

Once M has been obtained in ths manner, theresults presented inL9-11) are used to compute thestatic output feedback regulator. As described inthese papers, r optimal eigenvalue and eigenvectorplacements can be retained with the r (assumedindependent) measurements in y. In particular if welet Xr be an n x r matrix contain r generalizedright eigenvectors of (A + BG) corresponding to the reigenvalues chosen to be retained in the outputfeedback design, then output feedback controlis10-11]

1343

In this paper we focus on the practical aspects ofusing this design method in developing output feedbackcontrols for wind turbine generators. Preliminarywork in developing the design methodology for the WTGproblem has been reported in Reference (12].

To satisfy the steady state motion limits of theblade pitch actuator a -10 dB 2P filter was insertedinto the actuator path of each control. Consistentwith the +10 degree/second rate limit in the bladepitch hydraulics, the output of the control was alsorate limited at +10 degrees/second.

It was clear early in the design process that ahigh weighting on terminal voltage error, AVt, andelectrical power error, APe, was needed to provideadequate regulation. In addition, some weights on theintegrals, JAVt, and electrical power error,JAPe, were needed to allow the introduction ofintegral controls which insure zero steady-stateerror. The output weights resulting from theiterative design process are as follows:

OutputAvtIAVtAPe

JAPe

Weight8 x lo0100040001000

This resulted in the eigenvalue placement for fullstate feedback shown in Table I of the Appendix. Thenext stage in the design was to choose whichmeasurements to use, and which eigenvalues to retain.The high AVt weight has primary effect on fiveeigenvalues -- local mode and three real electricalmachine eigenvalues. Two of these machine eigenvaluescombine to create a complex pair. Tight voltageregulation can be obtained by retaining the remainingreal eigenvalue which is placed at -14.8 from -15.1.Thus, the measurement, AVt, is used to retainthis. Modal observability shows that AWH (changein hub speed) and APe are good measurements toretain the new local mode placement. In addition the

IAvt and JAPe are used to retain theintegrator eigenvalue placements. Thus fivemeasurements are used. The choice to retain a realeigenvalue which decreases in magnitude (from -15.1 to-14.7) may seem counter-intuitive; however, one mustrealize that the philosophy underlying the designprocess is to retain modes which will keep theessential aspects of the full state optimal design.Retaining this eigenvalue achieved the design goals.

The resulting output feedback gain takes the form

-lT -l Au = -R B M X (CXr) y = Ky.

The closed loop system is

x = (A + BKC)x = ACLx ,

(9)A 1 774 24.6 3.3

Avregj L39.8 98.8 14.7

L L

24.3 11.511.6 -.97j

(10)

and the matrix ACL has the r desired eigenvalues andeigenvectors. If the remaining n-r eigenvalues ofACL have negative real parts, this control is thesolution to a suboptimal output feedback controlprobleml 11]

For the derivation of these equations, the costcorresponding to the output feedback design and therelation of this design method to others in thecontrol literature, the reader should refer to[l11.

AwHAvtfAVtAP

e

fApe

(11)

and the resulting eigenvalues are for the staticoutput feedback shown in the last column of Table I inthe Appendix.

The next section presents some results obtainedfrom non-linear simulation tests.

1344

Performance Analysis

The two regulator designs for the baseline singleloop control and the multivariable control wereimplemented in the non-linear simulation program. Twodisturbance inputs were chosen to compare theperformance of the controls on the single WTG system.One is a severe wind gust and the second is a threephase stub fault at the high side of the unittransformer. These two inputs cover most of the ratedpower operating range, in which the control wasdesigned, so that a determination on the robustness ofthe control can be made.

The wind gust input chosen for the first of thetwo stud4es was determined in a previous DOE contracteffort . It consists of a fast rise time gustwhich has a low probability of occurrence. It wasdetermined by analyzing a large number of actual winddata records and determining their statistics, whichwere used to synthesize the corresponding inputtrajectory. The initial wind speed is 30 hMPH, nearthe low end of rated power operation, and the peak ofthe gust at 50 hMPH is near cut-out wind speed. Sinceonly 10 seconds of data was available, the windvelocity was held constant for the remainder of the 20seconds simulation time. Superimposed on the inputwind velocity is a component at twice per hubrevolution frequency (2P) to represent the aggregateeffects of wind shear and tower turbulence.

Compared in Figures 4 and 5 are the response ofthe WTG to the severe wind gust for the baselinecontrol and the multivariable control, respectively.

10

8

0

M

0

I

a:

6

4

2

0

. 1.04-

X4¶ 1.02-

0P 1.00

X .98

1- .96

15

10

00 50)

0

-5

0

S0

0

Plotted are electrical and mechanical power inper-unit, terminal voltage and voltage regulatorsignal in per-unit, blade pitch demand and pitch anglein degrees, and wind speed at the hub in miles perhour.

The response with the baseline single loopcontrols, Figure 4, shows that the electrical powerswing meets the 40% criteria. Mechanical power, whichis not measurable, does have transient excursionslarger than 50%. Both local mode oscillations and 2Poscillations are seen in the response. The terminalvoltage shows a 3.5% dip following the peak of thewind gust, and the regulator signal shows the controlaction used in this effort. The wind speed indicatesthat the gust initiates near 30 hMPH, peaks at 50 hMPH(near cut-out), and has a final steady state level of40 hMPH. The pitch angle demand signal shows theeffect of the dual mode gain switch in the control.The high gain mode is initiated when hub speeddeviations exceed a predetermined level. Its effecton pitch angle is apparent, and during these periodsof time the pitch actuator is in rate limitedoperation.

The multivariable control design simulationresults, Figure 5, show a regulation on electricalpower of slightly over 25%, and mechanical powerswings show the effects of the tight regulationpeaking at about 40%. The terminal voltage excursionsare significantly smaller, with regulation to about 1%for this gust input. Both the voltage regulatorsignal and blade pitch demand show smaller excursionsand less motion in the control. This is a function of

10

0

a.6

> 4

3v207a

2

Time (Sec.)

Figure 4 Response of the WTG to a severe wind g,with conventional control

1.6

1.4

c 1.2

a, 1.0-0.

0.8

0.6

c 1.04 -

1.02

0~100[_

XC .98 -

EF .96 L

15 -

10 -

5-

0

0 -

-5 -

0

0.SD

Time (Sec.)Figure 5 Response of the WTG to a severe wind gust

with multivariable control

1345

the weighting on control energy which was included inthe performance index and tends to minimize energyconsistent with the other performance goals. Notethat the pitch angle demand signal plotted is takenbefore the 2P notch filter which explains the 2Pcomponent, which is reduced by 10 dB at the actuatorinput.

The second disturbance input used to evaluate theperformance of the control was a three phase stubfault at the high side of the unit transformer. Thetime to clear the fault was fixed at 5 cycles and itwas assumed that at the time of fault clearing thesystem configuration was identical to pre-fault. Forthese studies the transmission line reactance wasreduced to 10%, together with the unit transformer of10%, for a total tie reactance of 20%.

The performance of the WTG with the baselinesingle loop controls is given in Figure 6. Theplotted variables are the same as those from the windgust study with the exception of wind speed, thebottom curve, which was replaced by generator rotorangle in degrees. The average wind speed was fixed at30 hMPH for the fault studies, however, the equivalent2P forcing input was present. It is apparent thatelectrical disturbances do not involve the highinertia rotor. A small amount of the 2.5 Hz secondtorsional can be seen in mechanical power at theinitiation of the fault, but the dominant signal isthe 2P induced power variation. The electrical powershows the second torsional signal which is well damped

0

a.

0

0C

20 1.2

12 . M1.0

4 -I 0.810

-4

-12~

-20L

15

100

0

0

5

0

-5

160

120InQ

a 80

40

0 l

Blade PitchDemand

Blade Pitch

Time (Sec.)

Figure 6 WTG performance with a five cycle stubfault - conventional control

and little, if any, local mode or 2P response. Thevoltage regulator output is limited to +20 per unitdue to hardware design. The regulator goes topositive ceiling when the fault is applied and thesubsequent rotor angle swing reaches 140 degrees, nearcritical clearing time. The pitch angle demandsignals goes slightly negative, however, the pitchangle remains positive.

The response with the multivariable control isshown in Figure 7. With this design tighterregulation of both voltage and power is achieved atthe expense of slightly greater control effort whencompared with that of the single loop design. As wasthe case with the single loop design, the mechanicalpower has only a small amount of 2.5 Hz torsional modepresent. Electrical power, as one would expect,exhibits a significant amount of the 2.5 Hz torsionalmode. However, it is well damped. Examination of theterminal voltage shows excellent post faultperformance. Again, pitch angle demand is shownbefore the 2P filter and thus has a steady statecomponent of 2P present. During the initial periodwhere the large 2.5 Hz torsional mode is seen inelectrical power error, the control output is in ratelimit preventing an otherwise overactive controleffort.

16e

1.4 Mechanical

- 1.2 I

20r

if

0

10

0i

12

4

-4

-12

-20

1.2

*:D 1.00-

0.8a0

~ .40

I-

0.2

15

10

maD

5

0

-51

160

12014

c 80a I

40

Blade Pitch Demand

B P

- ~~~~~Blade Pitch

Rotor Angle

1 2 3 4 5

Time (Sec.)

Figure 7 WTG performance with a fiive cycle stubfault - multivariable control

0

,iic

E4)

Rotor Angle

1 2 3 4

1346

CONCLUSIONS

The key issues that have been demonstrated by thispaper can be summarized in the following points.

O The modeling aspects of the current MOD-5AWTG design have been analyzed in sufficientdetail to be representative of actualperformance, and presented so thatcomparisons between existing or proposed WTcontrol designs can be made.

O Excellent performance has been achieved forboth control designs during wind gusts andelectrical system disturbances. Regulationon terminal voltage and electrical power iswell within design goals.

O The baseline control yields good performancewithout a power system stabilizer due to theincreased mechanical damping in the gearbox,which does not vary appreciably with powerlevel.

o The baseline control will be used for theprototype machine since it integrates withexisting hardware; an analog voltageregulation package and pitch angle controlimplemented by software in the digitalcontroller.

FUTURE RESEARCH ISSUES

The further research areas that were not coveredin this paper and form the basis for current andpotential future work are as follows

3) "System Dynamics of Multi-UnitConversion Systems Applications,"78SDS4206, prepared for DOE/ERDA,1978.

Wind EnergyFinal ReportFebruary 15,

4) T.J. Hammons and D.J. Winning, "Comparisons ofSynchronous-Machine Models in the Study of theTransient Behavior of Electrical Power Systems,"Proc IEE, Vol. 118, No. 10, October, 1971.

5) E.V. Larsen and W.W. Price, "MANSTAB/POSSIM PowerSystem Dynamic Analysis Programs - A New ApproachCombining Non-linear Simulation and LinearizedState-Space/Frequency Domain Capabilities," IEEEPICA Conf., Toronto, May, 1977.

6) B.D.O. Anderson and J.B. Moore, Linear OptimalControl, Prentice Hall, Inc., Englewood Cliffs,NJ, 1971.

7) O.A. Solheim, "Design of Optimal Control Systemswith Prescribed Eigenvalues," Int. J. Control,Vol. 15, No. 1, pp. 143-160, 1972.

8) C.A. Harvey an G. Stein, "Quadratic Weights forAsymptotic Regulator Properties," IEEE Trans. onAutomatic Control, Vol. AC-23, pp. 378-387, 1978.

9) J. Medanic, "On Stabilization and Optimization byOutput Feedback," 12th Annual Asilomar Conferenceon Circuits and Systems, Pacific Grove, CA,November, 1978.

10) J. Medanic, "Design of Low Order Optimal DynamicRegulators for Linear Time-Invariant Systems,"1979 Conference on Information Science and Systems.

o Investigate the sensitivity of the baselinecontrol design to changes in the regulationfunctions, and system operating conditions.The baseline settings and structure of thevoltage and pitch angle regulators will bemodified to improve the transient response.

O Investigate implementation of the pitch anglecontrol in a digital environment. Thisincludes selecting a sample time, determiningstability margins, and structuring thealgorithm to interface with the otherfunctions within the controller hardware.

O Evaluate the effect of disturbance inputs andcontrol design on other structural dynamicsin the WT, such as the tower mode, whichrepresefts the nacelle motion due to bladeaxial thrust forces.

11) W.E. Hopkins, Jr., J. Medanic and W.R. Perkins,"Output Feedback Pole Placement in the Design ofSuboptimal Linear Quadratic Regulators," to bepublished in Int. J. Control.

12) S.H. Javid, A. Murdoch, and J.R. Winkelman,"Control Design for a Wind Turbine Generator UsingOutput Feedback," Presented at the 20th IEEEControl and Decision Conference, December 16-18,1981, San Diego, California.

APPENDIX

Synchronous Machine Parameters

6200 kW 6 Pole 5500 volt

xk = 0.1 pu

ACKNOWLEDGEMENT ra .0104 pu

Funding for this work was received underDepartment of Energy Contract DEN3-153, managed byNASA Lewis Research Center.

REFERENCES

1) W.H. Robbins and R.L. Thomas, "Large HorizontalAxis Wind Turbine Development," NASA TM-79174 orDOE/NASA 1059-79/2, Wind Energy Innovative Sys.Conf., Colorado Springs, May, 1979.

2) R.S. Barton and W.C. Lucas, "Conceptual Design ofthe 6 MW Mod-SA Wind Turbine Generator," FifthBiennial Wind Energy Conference and Workshop,Washington, D.C., October 5-7, 1981.

Xd= 2.16 pu

Xd=

it

X =d_Tdo=

Td=do

x = 1.28 pu

.29 pu xq

.18 pu

4.3 sec

itxq

Tqo

.03 secit

T =qo

.27 pu

.18 pu

.1422 sec

.003 sec

1347

Turbine Specifications

Saturation Curve

pu E Pu Xad fd

.72 .72

.8 .83

.9 .991.0 1.151.1 1.37

Torsional Data - 2 mass equivalent

Hub heightRotor diameterLow speed rotorHigh speed rotorGenerator Speed

= 250 FT= 400 FT- 13.25 RPM= 17.9 RPM= 1200 RPM

Wind Speed (at hub)Start = 14 MPHShift = 21 MPHRated > 29 MPHCut-out = 60 MPH

Excitation System - Conventional regulator

KATAVreg (limits)

= 320= .02= + 20

Kf =

T1 =

T2 =

T3 =

.015.02.49

.085Inertias

H1 (hub) = 16.72 puH2 (gen) = .9393 pu

Stiffness - DampingK12 = 10.26 puD12 = 8.778 pu

Rotating shaftsaturation.

driven exciter modeled including

Transmission LineXi = .4 purt = .04 pu

TABLE I - Selected

Power (Pitch Angle) regulator - Baseline Design

Proportional gain, K = 6.2 degrees/puIntegral gain, KI = 9.22 degrees/puSpeed damping, Ks = 46.9 degrees/puGain increases on speed damping when AwH > .008radians/second by a factor of 30.

Eigenvaiable Control Design

Full State Feedback Output Feedback

-1.29 + j16.3

-14.8 *

-9.16 + j7.25

-1.17 + jl.60 *

-.47 *

-.16 *

-1.08 + j15.3 Torsional mode

-14.8 * \ Generator

-2.90 + j6.71J Dynamics

-1.17 + jl.60 * Local Mode

-47 *Integrals of V,P

-.16 * Measurements

Note: asterik denotes those modes retained in the output feedback design

System Data

TransformerXT = .1 purT = -Ol pu

Open Loop

1 , 2

3

4 , 5

6 , 7

8

9

-.97 + j15.9

-15.1

-6.3 , -.204

-.32 + j.99

0

0