1095IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 5, May 1985

SIMULATOR STUDY OF A VERTICAL AXIS WIND TURBINE GENERATORCONNECTED TO A SMALL HYDRO NETWORK

S. Lefebvre, L. Dessaint, B. Dubg, H. Nakra, A. Pgrocheau

Institut de Recherche d'Hydro-Qugbec (IREQ)Varennes, Qugbec, Canada

ABSTRACT

The paper describes a simulator study of a verti-cal axis wind turbine generator connected to a smallisolated hydro network. The connection to the networkis done through a back-to-back dc link, which is usedas a static frequency changer. The penetration levelof the wind turbine is in the range 13% - 33% of therating of the AC network. The study includes the tran-sient performance of the dc link and the wind turbinedrive during electrical braking and for system distur-bances such as AC system faults.

The study shows that the use of a stabilizationsignal in the dc link helps to reduce large torsionalvibrations in the wind turbine low speed shaft. Thesevibrations are observed after AC system faults. Thestudy also shows that it is possible to obtain satis-factory operation of the overall system by adoptingsuitable control strategies.

INTRODUCTION

Escalating costs of fossil fuel and environmentalconcerns in the last decade have led to renewed inter-est into the use of alternate energy sources. Windenergy is one such source and recently various windturbine generating systems have been proposed and stud-ied.

There are basically two families of wind turbines(WT). The horizontal axis wind turbine (HAWT) consistsof a propeller with/without variable pitch control.Vertical axis wind turbines (VAWT) are usually of theDarrieus type. There is no control mechanism on aDarrieus turbine. It is possible to further divideeach family of WT into two large classes, based on theoperating condition of the wind turbine generator(WTG): constant-speed systems and variable-speed sys-tems.

The interest in this paper is for WTG in remotelocations, e.g. Canadian northern country, where theisolated AC network has a power rating of the sameorder of magnitude as the WTG. For such systems the ACnetwork cannot be assumed stiff and its own dynamicsmust be included in most studies. Furthermore, thestudy concerns more specifically Darrieus VAWT as thisis the emphasis of the current Canadian Wind Energy R&DProgram. The study was performed as part of a ResearchProject (223G342) for the Canadian Electrical Associa-tion (CEA).

84 SM 573-2 A paper recommended and approvedby the IEEE Power System Engineering Committee ofthe IEEE Power Engineering Society for presentationat the IEEE/PES 1984 Summer Meeting, Seattle,Washington, July 15 - 20, 1984. Manuscript submit-ted February 2, 1984; made available for printingMay 10, 1984.

When a WT has to be integrated into a relativelysmall power system, variable-speed operation of the WTis more likely. Variable-speed operation permits toextract more energy from the wind since it is possibleto operate always close to optimum rotor speed. Eithera synchronous alternator or an induction generator canbe used. Typically the machine is connected to thenetwork through a back-to-back dc link. The machine iscoupled to the WT with or without a gearbox. Thissystem makes the alternator operation independent ofthe AC network. This alleviates the WTG synchronisa-tion problems. Aside from this, the principal advanta-ges of such a scheme are the following: (1) direct-drive capability using a low-speed alternator, (2) in-creased turbine efficiency, (3) electrical braking cap-ability through the dc link, (4) capabilities forsmooth starting. For Darrieus VWTG, the dc link is infact the only control interface available.

The main problem of variable-speed operation ofthe WT with a dc link is the relatively high cost ofthe link compared to a conventional HAWT pitch-controlsystem. Despite this fact, the scheme is receivingincreased attention for both HAWT and VAWT. Otherproblems of concern are also due to the dc link: (1)harmonics generated by the converters, (2) power factorproblems due to converter consumption of reactivepower.

A WTG-system was studied on the IREQ dc simula-tor. The system consists of a Darrieus VAWTG connectedto an isolated small hydro network. The power ratingof the VAWTG, 224 kW, is typical of medium-size WT sus-ceptible to being installed in a small isolated powergrid. Diesel generators which could be replaced by theWTG would normally serve as back-up to the WTG. Pro-duction of power with WTG differs from conventionalpower sources by the facts that (1) the prime movertorque is oscillatory (aerodynamic torque) and (2) theaverage prime mover torque is variable as it is subjec-ted to the wind. These phenomena could influence thesmall AC networks to which the WTG are connected. Theother concern is for the transient performance of thedc link and the WT drive during electrical braking andfor various types of system disturbances such as ACsystem faults.

Several studies have been made on the transientdynamics of VAWTG in constant-speed type of operation[1-3]. These studies have shown that, during trans-ients such as start-up, the first torsional vibrationmode of the low speed shaft is crossed. As a result,resonnance phenomena appear in the low speed shafttorque, hereafter Ti, during such transients. It isshown in the paper that this torsional mode is also ex-

cited by AC system disturbances even though the WTG isat variable speed.

In the study, the dc link was controlled to regu-late the WTG power and speed. Therefore this provideda mechanism to adjust the turbine efficiency, to absorbthe wind gust energy, and to increase damping for shaftoscillations. In particular, large torsional torques

0018-9510/85/0005-1095$01.00©1985 IEEE

1096

observed after AC system faults were quickly eliminatedby a dc link modulation.

SYSTEM DESCRIPTION AND SIMULATION

System

The single-line diagram of the system simulated isshown in Figure 1. The synchronous generator is me-chanically coupled to the WT by gearboxes and it iselectrically connected to the power grid through a dclink which effectively operates as a static frequencyconverter. The external system is simply a transmis-sion line, a load and a hydro-generator. As required,AC filters are added at the commutating bus on the ACnetwork.

SnchronousgenetorDC link

Mechanicaltransmissionsystem

F: filtersC: capacitors for power factor correction

Fig. 1 System Simulated

The dc link consists essentially in two convertersconnected back-to-back through a smoothing inductance.Each converter is a 6-pulse Graetz bridge. Althoughthe harmonic content is much larger than with 12-pulseconverters, the 6-pulse bridge has the advantage of re-

quiring no transformer on the machine-side converter.

On the machine-side, a diode rectifier is used asconverter. The result is a less expensive dc link.The diode rectifier in the context of WTG is expectedto perform satisfactorily because the WTG inertia islarge and because recovery from commutation failures or

from AC or dc faults does not have to be extremelyfast.

The thyristor inverter on the network-side is usedto control the windmill. As the diode rectifier doesnot allow the power flow to be from the network to theWTG and since the Darrieus WT is not self-starting,special measures are required at start-up (small auxil-iary motor and higher wind speed conditions).

The other problem with a diode rectifier concerns

system protection. As no controls are available at therectifier, such as forced retard, it is necessary touse bre,aker CB1 to protect the synchronous machine.The breaker is opened at fault detection and it isreclosed after an adjustable time delay. Simpleactions on the voltage regulator of the WTG could alsobe sufficient to recover from commutation failures atthe inverter [4].

The harmonic generation at the rectifier is atminimum with a diode rectifier. It is well below thetolerable level of harmonics for a well designed gener-ator. This is without harmonic filters as the frequen-cy on the,machine-side varies. The generator is a 10-

pole, 224 kw, synchronous generator with a 3-phase,60Hz, 1.08 kV output. The rated speed of the generatoris 720 rpm.

The penetration level of the WTG, Pw, is used to

characterize the relative size of the WTG. By defini-tion,

Pw = Rated power of WTGRated power of WTG + Rated power of network

The penetration level is related to the short-circuit ratio of the dc link which is a well knowndesign criteria for HVdc systems.

The hydro-generator rating is varied during thestudy so that the effects of different penetrationlevels Pw can be investigated (Pw'is in the range 13%to 33%). Typically for small reservoirs, the hydroturbine is the propeller type and the plant is in therun of the river mode.

The dc system is rated at 1.45 kV, 154.5 A. WithPw = 13%, the smoothing inductance is 2.2 mH. For thelarger penetration level, Pw = 33%, a smoothing induct-ance of 9.4 mH is used. An overload of 20% is possibleon the dc link.

System parameters are given in the Appendix.

IREQ dc Simulator

The system was simulated on the IREQ real-time dcsimulator.

The dc simulator is a scaled electrical model'ofan AC/dc transmission system with all essential compo-nents represented by devices with equivalent electricalcharacteristics. The main components of the simulatorare the converter valve groups with associated con-trols, converter transformers, rotating machines andthe AC and dc transmission line sections. The ratingof the simulator is adjustable up to 100 W.

The converter valve groups are built either insix-pulse or twelve-pule units. A valve is modelled bya single thyristor or diode. Associated with eachvalve group is a negative resistance unit designed tocompensate for the excess voltage drop across thevalves.

The converter control systems are of the equidis-tant firing pulse type. The control systems have beensupplied by three different HVdc equipment manufactur-ers for existing HVdc schemes.

The rotating machines are'modelled by Park's equa-tions which are solved for a given set of parameters byanalog computational techniques [5]. Each machine canbe used either as generator or motor and can representa synchronous machine, a squirrel cage induction ma-chine or a wound-rotor induction machine.

Wind Turbine Modelling

The WT associated with the system in Figure 1 issimilar to the Magdalen 'Islands VWT operated by Hydro-Quebec [6]. The WT is shown in Figure 2. The turbinehas a nominal height of 36.6 m and its diameter is24.4 m. The turbine is installed on a tower of 9.3 mso that the total effective height is 45.9 m. On sucha small turbine the wind shear phenomenon is negligi-ble. The turbine is rated at 224 kW, its nominal speedis 36.6 rpm, the nominal wind is 14.4 m/s.

The blades angle of attack with respect to windchanges continuously during the rotation of the WT.This produces an oscillatory aerodynamic torque Tawhich is not steady and contains several harmonics.These oscillations vary in frequency and in amplitudewith the wind speed, the turbulence of the wind and thegeometric properties of the blades.

36

torque Ta on the WT blades can

Ta = 2Ta= 2 PCP A Vw/X

Fig. 2 VWT Simulated

where p is the density of air, Vw is the wind speed, Ais the area swept by the WT blades, Cp is the power co-

efficient which is a complex function of the bladevelocity, Vb , the wind velocity and the angle of theblades with respect to the wind, 0b. In equation (1)the tip-speed ratio is defined as

X =Vb (2)Vw

The Magdalen Islands WT achieves its best extrac-tion efficiency for 4 < X (8. In that range Cp variesapproximately from 0.35 to 0.43. Several models of theinteraction of the wind on the WT blades are avail-able. Due to limitations of the different aerodynamictheories, only constant wind and slow wind gusts can beconsidered in this study.

A real-time simulation of the Magdalen Islands WTwas developed at IREQ [7] and it has been testedagainst 'field data. In this simulator, a table ofvalues of Ta is stored in a microprocessor memory. Theactual torque Ta is obtained by interpolation in func-tion of Vw, Vb and 0b-

Mechanical System

The blade power is transmitted to the generatorvia the drive train shown in Figure 3. The rotor isdivided into two discs of equal inertia (Jr/2) linkedby a shaft with rigidity Kr and damping factor Cr. Therigidity coefficient is selected so that the first tor-sional mode of the WT at 2.495 Hz, is represented ade-quately. The damping factor is determined empiricallyfrom field data. It is assumed that the discs areloaded equally by Ta. The low speed, intermediatespeed and high speed shaft rigidities (Ki, Ki, Kh) areincluded in the simulation. The gearboxes are rigid

1097be with ratio NI for the gearbox between the low speed and

the intermediate speed shafts, and N2 for the gearboxbetween the intermediate speed and the high speed

(1) shafts. The viscous damping of the gearboxes are takeninto account in the various shafts by the parametersCg, Ci and Ch. In practice', the gearboxes have nonlinear rigidity and damping characteristics due toteeth for example. The analog representation of thedrive train however, assumes for simplicity perfectgearboxes.

Broke Generotor

Turbine Low Transmission Highspeed speedshaft shaft

Fig. 3 WTG Mechanical System Model

As mentioned in the introduction, the first tor-sional mode at 2.495 Hz is of interest. Simulationshave shown that this mode is excited by AC systemfaults. It will be shown how the dc link can be usedto increase the damping on this mode. The'mode in-volves an oscillation where the low speed shaft and theblades swing as a coherent mass against the generator.

OPERATING STRATEGY

Justification

In the operation of the WT, there are two regionsof power production and two regions where the WT is

stalled. When the wind is below' the cut-in speed,(0.26 pu) no attempt is made to extract power from thewind. Likewise, no attempt is made to obtain any out-put power'above the cut-out speed, (1.74 pu). The tworegions or modes of power production are the areas be-tween cut-in and rated output (low mode), and betweenrated power output and cut-out (high mode). Transitionbetween the two modes occur at 0.78 pu.

Figure 4 shows the maximum WTG power as functionof Vw. In the low mode the maximum power is a functionof VW. To maximize the power capture, the ideal con-

trol system 'would maintain the maximum C in the lowmode, whereas in the high mode C would be adjusted tomaintain the rated power. But this is not a practi-cable approach since the generator torque requirementsfor accielerating the WT are severe in view of the largeWT inertia. Furthermore the resulting variation inelectrical power is unacceptable as the WTG is connec-

ted to' a small AC network. Such a design would not berobust as it would be based on a direct measurement ofVw. This measure is highly unreliable.

A different strategy is used which is a tradeoffbetween Cp-tracking as a function of wind velocity, thevariation of the electrical power delivered by the WTGand the overall system relative stability. The controlsystem distinguishes the low mode operation from thehigh mode. The reason for this is following. Considerthe simplified swing equation of the WTG

2Ha dWt/dt = ATa ATe (3)

where Te is the electrical torque and Ha is the inertiatime constant. For a constant wind velocity

The aerodynamicexpressed by

I

/I

,' Low High/" mode 'mode,,.-

-11.

0.26 0.78a) Maximum Power of WT

b) WT speed to obtoin Maximum Pi

Control of the Network-Side Converter

Two different control structures are used to regu-late the WT variables through the network-side con-verter. The structure used depends on the value of thewind speed Vw (low mode of operation and high mode ofoperation). In practice, a measurement of Vw throughthe blades would require anemometers located at severalpoints around the WT. Although it is envisageable toobtain a representative value of Vw for the smaller WT,this would be difficult for larger ones (in the MWrange). Hence the control system was designed withminor reliance on the actual value of wind speed.

The regulators used in controlling the WT in thei.74 Vw, pu two modes of operation are briefly explained below.

The dc controls are also presented.

Wind Turbine Controls in Low Mode. The principleof the low mode WT control is shown in Figure 5.Firstly, the reference power is compared with theelectrical power and the error signal goes to a low-pass filter to obtain the reference speed Wref. Thesignal Wref is compared with the actual speed of windturbine, Wt. A constant value Wrefo corresponding toto a bias of the power controller is added to thisdifference. The stabilization signal Wstab is sub-stracted to obtain the speed regulator input Ew. Thespeed regulator is simply a proportional plus integralcontrol. The output of the speed regulator, Isup, isadded to the bias value of the reference dc current,

4 Vw,pu Irefo, to obtain the reference current fed to thelower converter dc controls.

Fig. 4 Operating Limits of WT

AT = D AWa tw t

where Dtw iscient. Then

(4)

called the aerodynamic damping coeffi-

2Ha dW /dt D Wwt ATa t tw e

(5)

It follows from this equation that the system isstable in the zone of operation where Dtw is negative.From [8] one obtains

D = K (X dC /dX - C )tw tw o p po

(6)

where Ktw is a positive constant and where the index o

refers to variables at the operating point. Hence themore stable points of operation on the Cp curve are

characterized by

F(X) = X dC - CPo < ° (7)

In the low mode of operation, the Magdalen IslandsWT is in a zone where F(X) is negative. In the highmode of operation, F(X) is nearly zero or positive andmore power that can be extracted is available from thewind. Hence in this mode, it is very important to havea good control over the WT speed as the operation ap-pears less stable. This is not so important in the lowmode of operation. Rather the power must be controlledrigorously so that the power order does not exceed themaximum power available from the wind.

Control of the Wind Turbine Generator

The control of the synchronous machine is limitedto excitation control via a static exciter. The refer-ence voltage at the input of the WTG voltage regulatoris selected such that the machine flux does not exceedits rated value.

f(VW)Fig. 5 Controls of WT

The reference power signal is limited between 0and a maximum value which depends on an average meas-

urement of the wind speed. Limits are also applied tothe power regulator and the speed regulator outputs.

Wind Turbine Controls in High Mode. The regula-tors of the high mode WT control are similar to thosein Figure 5, however the tunings are different. Inthis mode of operation, a fast power regulator is notneeded because the maximum theoretical power availablefrom the wind is well above the machine ratings. Theconverter controls suffice to limit the WT power. Infact it was observed during the tests that a fast power

regulator had a destabilizing effect. This is under-standable because at high wind speeds the harmonic con-

tent in the aerodynamic torque Ta becomes very impor-tant.

Damping of Torque Oscillations. The damping con-troller used has for input the low-speed torque TX or

the firing angle a, the output serves to modulate theWT speed reference. The schematic diagram of the damp-ing controller is given in Figure 5. The damping con-

1098

1.01

a4,

.05a-o- 0.5I

I -

troller has a band-pass function, dc and low harmoniccomponents are filtered out by this controller so thatthe steady-state operating point is not disturbed. Atfrequencies higher than 2.5 Hz, the gain is sufficient-ly small so that in steady-state there is no possibili-ty of adverse interactions with the WT drive train.This gain is sufficiently high however to provide damp-ing following a network fault.

dc Controls. Figure 6 shows the dc link steady-state operating characteristics. Normally the invertercontrols the dc current. The operating point corre-sponds to the intersection between the Current Control(CC) characteristic of the inverter and the diode rec-tifier characteristic (alpha = 0). This is point A inthe figure.

2Wt averageP.LL1.00.8 -

0.6V I I I I I I I .-11 I I VAI* 1

1.5 To

HE5..._._

t (s)(absolute) Id ,pu

Fig. 6 Steady-State Characteristics of the dc Link

Voltage Dependent Current Order Limits, VDCOL, areincorporated in the inverter dc controls. The VDCOLreduce the maximum allowable dc current when the dcvoltage falls below a predetermined level. In the pre-sent application the VDCOL operates mainly if the WTGAC voltage is low. For a voltage collapse on thenetwork-side, the inverter VDCOL would not be usefulbecause there would be no intersection between the twoconverter characteristics. Such faults could result incommutation failures at the inverter. A commutationfailure is indicated by a logic signal being high.This signal is used to trip breaker CB1 in Figure 1.The breaker is reclosed after a small time delay.

SYSTEM PERFORMANCE

A few of the results obtained are presented be-low. The tests selected for this paper representsevere conditions for the system.

Electrical Braking of the Wind Turbine

Figure 7 shows an electrical braking of the WTG.This is for a penetration level of 13%. The wind speedis 0.845 pu (high mode).

At the beginning, the WTG is in steady-state. TheWT speed is 1.1 pu and the dc current is nominal. Whenelectrical braking is ordered, the reference dc currentis forced to the maximum value. This is about 1.2 pu.In response the inverter alpha is reduced which forcesan increase in the dc current. This increases theelectrical load torque and in this way slows down theWTG. The WT speed decays first slowly and then morerapidly as the average aerodynamic torque drops rapidlyas Wt is reduced.

During this test the exciter reference voltage ismaintained at 1 pu even though the WTG speed is drop-

Fig. 7 Electrical Braking with P. = 13%

ping. This is done to maintain the product Vd Id suf-ficiently high for obtaining rapid shut-down. Therecording of the torsional low-speed shaft torque TX,shows that TX increases during braking. The speed ofthe hydro-generator is initially increased because ofthe sudden increase of WT power. The maximum deviationin speed is about 1.9 per cent, curve AWth. This iswith a constant impedance load.

With a larger penetration level, 33% in Figure 8,the hydro-generator speed is more disturbed by the'WTbraking. The speed of this generator, Wth, varies byabout 3.1 per cent when braking is initiated. Afterthe initial transients, the speed error is reduced toless than 1 per cent. A large disturbance on thehydro-generator is expected near the end of the test

Wt average

1.0

0.8

0.6 .I I I lI

AWt hydro.024 E7II1p.u. f

.Oi2-f

0 5 40 15- ~ ~~~~t(s)

Fig. 8 Electrical Braking with Pw = 33%

1099

-I .- , I I I I I I . I I I I I.

I I I a , I , I I a I , I I.1

rmwiiI"

I i I I I I I I I I I I I I I 1,

tdw

1. 1. 1. I I I I I LI j I I --I I I I

I

I I 1- I I 1. I I 1. I I I I I -.L-L-I-

20 25

1100

when the WT becomes stalled. This was not recordedbecause of model deficiencies.

Three-Phase Faults at the Inverter

Bolted three-phase faults on the network commuta-tion bus are shown in Figures 9 and 10. The fault isapplied at 50 ms and released at 100 ms into the test.Wind speed is 0.845 pu. The penetration level is 13%.

In Figure 9 the test is without the damping con-troller of Figure 5. When the fault is applied Id goesinitially to 3.8 pu, a commutation failure results andbreaker CBI is automatically opened. After a shortdelay, CBI is reclosed and power transmission resumes.The recovery is sufficiently smooth so that commutationfailures are limited to the fault duration. The curveof TR is most interesting. Clearly after a three-phasefault oscillations are introduced in TJ. The oscilla-tions have only a small damping factor. The time con-stant on these oscillations is about 6.6 seconds. Therecording of the electrical power delivered by the WTG,Pe shows that it is of acceptable quality.

I ref average

1.07p.u.1.01

uU -91 *1 '' aI''1. *' .. ..

Pe electrical powerp.m

1.5

0.5

-0.5 II

2 5

111 1 I 1 11 tI t tI t|IIfI I1 11 Il| llI [II Ill III0 6 12 18 24 3

t (s)Fig. 9 Three-Phase Bolted Fault on Inverter

No damping controller

The test was repeated with a damping controllerbased on a measure of the torque Ti. The result isshown in Figure lOa. The action of the damping con-

troller on the dc current order is very clear in thecurve of Iref average. The action is mainly limited tothe first three-seconds. The efficacy of this control-ler can be appreciated by comparing the new curve ofTt, with Ti in Figure 9.

The problem with the damping controller is that itis based on a measure of TX. Such a measure may bedifficult and expensive. An alternate way of obtainingdamping is proposed in Figure lOb. The controller now

uses a measurement of the firing angle a. This isbased on the fact that the oscillations in Ti are ob-servable on a. That measure of a is standard in HVdctechnology. The curve of Ti in Figure lOb shows thatthe new damping controller is also very effective in

1.04p.u

0.9.

0.8C

0.5

1.04p.u.0.92

0.80L3 i

pAU2

0

-1 L0

25.p.ULi.5

I ref average

Ii l i L|I |@1 11 1| I I I I I

0 6 12 18 24 t(s)3a) damping with TX

Iref averaqe__lii i II11f IIIIjIjIIIIII

7,11111111 ii 111 I tIII

[Ij

TtIlIlli.111111111111111 I

6 12 18b) damping with a

3

24 t(s)30

Fig. 10 Three-Phase Bolted Fault on Inverter

eliminating the vibrations. The damping in this testis not as good as in Figure 10a, however. This is dueto the parameters of the controller not being fullyoptimized.

It has previously been reported that random windfluctuation may result in torsional oscillations inHAWT [9]. Based on the results of our paper, it ap-

pears that in a WTG-system using a dc link, the dc linkcould also be used to eliminate such a problem.

CONCLUSIONS

(1) A WT control system which can achieve good powercapture has been designed. The control system isa tradeoff between energy capture and smoothnessof delivered power.

(2) The method of controlling the power coefficient ofa Darrieus WT with a dc link is also applicable toHAWT. In this case the blade-pitch controller isnot required.

(3) Methods of damping torsional oscillations with dccurrent modulation have been proposed.

(4) It has been shown that the penetration level or

such WTG can be relatively high, i.e. the AC net-work does not suffer from the presence of an un-

T1

jiII~~~~~~~~~:W4 A ^af .AA 1 -

X~~~~V~ v Av

IIIIt,, I1.,I, tiII III,,I,. I,,, I, ,I,..,t,..,..III

I

III

steady power source. For this reason the WTG iswell suited for remote locations.

(5) Further work is indicated in the following areas:

different type of rotating machine, e.g.wound-rotor induction machine with slipenergy recovery

analysis of the quality of the electricpower delivered by the WTG with respect toharmonic contents

different start-up strategies

ACKNOWLEDGEMENT

The research work reported in this paper was sup-ported by the Canadian Electrical Association (CEA)under the contract 223G342 "Comparative Technical Eval-uation of Large Power Trains on the Basis of theirDynamic Performance".

REFERENCES

[1] Clauss D.B., Carne T.G., "Vertical axis wind tur-bine drive train transient dynamics," Second DOE/NASA Wind Turbine Dynamics Workshop Cleveland,Ohio, Feb. 1981

[21 Beaulieu G., Masse B., "Dynamique du train detransmission de puissance des goliennes a axe ver-tical," Technical Report IREQ-2380, July 1981

[31 Beaulieu G., Masse B., Dubg B., "Darrieus windturbine power train dynamics," Wind and SolarEnergy Technology Conference, Kansas City, April1982

[4] Bowles J.P., Turner A.B., Vaughan R.L., "Studies for HVDC Circuit Breakers," Electric PowerResearch Institute, Report EL-1260, Dec. 1979

[5] Jasmin G., Bowles J., Mukhedkar D., Leroux A.,"Electronic simulation of a hydro-generator withstatic excitation," IEEE Trans. Power Apparatusand Systems, Vol. PAS-100, No. 9, pp. 4207-4215,Sept. 1981

[6] P6rocheau A., "Description des modales mEcaniqueet agrodynamique utilisgs dans les simulations detrain de puissance d'adrogEngrateurs," TechnicalReport IREQ-2902, Nov. 1983

1101

The WTG drive train of Figure 3 is represented bya set of four differential equations. The variables WIto W4 represent the angular speed of the various drivetrain components. The input torque on the rotor isdivided between the two discs (Tal and Ta2). The elec-trical torque Te is produced by the synchronous genera-tor and is calculated by the synchronous machine modelitself. The parameters of the WT and drive train arelisted in Table A-2. The equations describing themechanical system are given in [8].

Table A-2: Parameters of Mechanical System

Parameter Description Value

2 Hr inertia of VWT rotor 30.1 s2 Ht inertia of transmission 57.9 ms2 Hg inertia of generator 0.58 sKr rigidity of VWT rotor 1980.8/sKI rigidity of LS shaft 330/sKi rigidity of IS shaft infiniteKh rigidity of HS shaft 5000/sCr damping factor, VWT rotor 0.84 puCl damping factor, LS shaft 0.091 puNi gear box ratio, LS-IS 15.73N2 gear box ratio, IS-HS 1.2506N Ni*N2 19.67Wt base nominal speed of WT 36.6 rpmWg base nominal speed of generator 720 rpmPb nominal power 224 kW

For a penetration level of 33%, the AC transmis-sion line has an impedance of 100.5 Q and the load is670 kVA with a power factor of 0.85 at nominal volt-age. For a penetration level of 13%, the AC transmis-sion line has an impedance of 202.4 Q and the load is1.64 MVA at unitary power factor.

A commutation reactance of 0.7 Q is located be-tween the WTG and the diode rectifier (1.8 mH). Thisreactance is beneficial in obtaining proper commutationin the WT generator. It also protects the generator incase of system faults. The transformer associated withthe converter on the network side is a Yg-Y transformerwith a leakage of 15 per cent on its own base value,namely 264 kVA. The transformation ratio is 20 kV/1.1kV. The leakage impedance is assumed entirely on thesecondary side of the transformer. The transformer islinear. The converter associated with the hydraulicgenerator has a leakage of 9 per cent, the knee is at1.3 pu.

Table A-1: Parameters of Synchronous Machines

[7] Dessaint L., Nakra H.L., Mukhedkar D., "Simulationof a vertical-axis wind-turbine generator con-nected to a utility network by a static frequencychanger," Conference Record, IPEC-Tokyo, Vol. 2,March 1983

[81 Lefebvre S., Deslauriers M., Jeanson G., "Simula-tor Study of a Synchronous Machine Variable SpeedGenerator for Small Wind Energy Systems," Techni-cal Report IREQ-2926, Dec. 1983

[9] Wasynczuk O., Man D.T., Sullivan J.P., "Dynamicbehavior of a class of wind turbine generatorsduring random wind fluctuations," IEEE Transac-tions on Power Apparatus and Systems, Vol. PAS-100, No. 6, pp. 2837-2845, June 1981

APPENDIX

Table A-1 gives the parameters of machine MA andMB for the system in Figure 1. Machine saturation wasrepresented in the study [8].

(1) see Table A-2(2) this includes the inertia of the hydraulic turbine

MA MB

Rs pu 0.0008 0.0008Rkq pu 0.022 0.032Rkd pu 0.010 0.010Rfd pu 0.001 0.0005Xls pu 0.0833 0.0833Xaq pu 0.750 0.416Xad pu 0.750 0.750Xlkq pu 0.044 0.046Xlkd pu 0.055 0.083Xlfd pu 0.214 0.2142 Hg s (1) 8.00(2)Power 224 448

(kW)Voltage 1.08 13.8

(kV)Frequency 60 60

(Hz)