7 Torque and Power Limitations of Variable Speed Wind Turbines Using Pitch Control and Generator...

8/13/2019 7 Torque and Power Limitations of Variable Speed Wind Turbines Using Pitch Control and Generator Power Control

1/6

Torque and Power Limitations ofVariableSpeed Wind Turbines Using

Pitch Control and Generator Power ControlN, Horiuchi T. KawahitoTakamatsuNational College of Technology355 Chokushi-cho,TakamatsuCity, 761-8058 Japan

Abstract: Variable speed operation of wind turbines has thepotential to increase energy capture and reduce fatigue damage,comparing with fixed speed operation. Cage inductiongenerators with their brush-less and rigid structure are atpresent widely used for tixed speed wind systems. To make thecage induction generators widely used also at variable speedsystems, proper control strategies should be developed as well asthe development of low cost and reliable power electronicdevices.

At high wind speeds, as is conventional fixed speed system, itis very important to limit the variable speed system to its ratingswithout mechanical and electrical stresses induced by wind gustsand/or control process. This paper introduces a configuration ofvariable speed system which includes a pitch controllablehorizontal axis wind turbine, a cage induction generator, aPWM pulse width modulation converter and a PWM inverter,the last one being connected to utility grid. Also, the paperproposes and investigates a class of control strategies forlimiting the system to its ratings, from the view point of avoidingaxial torque andlor generator power fluctuations induced bywind gusts and control errors. The class adopts paralleloperation of pitch angle control and electrical power control.The pitch control aims at limiting turbine rotational speed,while generator power control aims at eliminating torque and/orpower fluctuations. Simulation results in time domain arepresented to verify the effectiveness of the class of controls.Index Terms: Cage induction generator, pitch control, powercontrol, PWM converter, PWM inverter, variable speed, V/fcontrol, wind turbine.

I. INTRODUCTIONWorldwide wind turbine generators(WTGs) are operating

mostly on constant speed operation scheme. The main reasonis the simplicity of their scheme that it does not needfrequency conversion of power from generators to utility grid.Recently, variable speed operation of wind turbines isbecoming to be noticed of its advantage as:1) More energy capture by optimum speed operation ofwind turbine.

2) Less mechanical fatigue at drive train and less powerfluctuation to utility grid, due to the fact that:aerodynamic energy surge to wind turbine induced bywind turbulence is possibly stored as kinetic energy inthe turbines moment of inertia, not being directlyconducted to drive train.

Recent works on control strategies for variable speedWTGS have been addressed to maximizing power [1]-[5],

and limiting power [2], [6], [7]. For both of maximizingpower at medium wind speeds and limiting power at highwind speeds, it is very important to consider that the controlstrategy should avoid torque surges at drive train in thepresence of wind turbulence and control error. To avoid axialtorque surges in limiting power, it is a necessaryconsideration to absorb aerodynamic torque surge of turbineby its intrinsic large moment of inertia. However, littlepreceding works seem to have adopted the consideration inexploring control strategies. This paper offers a class ofcontrol strategies in accordance with the consideration,especially in aerodynamic power limiting region.

The system configuration studied in this paper includescage induction generator, Cage induction generators, owingto their rigid and brush-less structure, accordingly to theirmaintenance freeness, are widely used in fixed speed systems.Using this type of generators in variable speed systemsrequires additional high capacity power electronic devices forpower transmission from its variable frequency output toconstant frequency utility grid. Nevertheless, recentdevelopments in power electronics and semiconductordevices will make cage induction generators widely usedwith admissible total cost.

II. DISCUSSION OF CONTROL STRATEGIESIn this chapter, we present a class of control strategies and

discuss their features. In Fig. 1, pwl - pW4 represents windturbines aerodynamic power produced by each given windspeed, and thick line PG denotes reference for generatoroutput .

*

rotor speed Om m RFig.1. Aerodynamic power and output reference versus rotor speed

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE0-7803-7173-9/01/ 10.00 2001 IEEE 638


2/6

The reference pG* is produced by observing rotor speedm QmR and PGRdenote rated rotor speed and generatoroutput respectively.

~ the region where Um < f2mR, the control Strategy ksuch that: Set PG* to tKtCe maximum power points of windturbine such as PI,, pz, P3 with the blade pitch angle fixedat its optimum value. The curve which traces the maximumpower points can be expressed as a function of o)~ and it isproportional to the cube of Om [5], [8].Accordingly, we set pG* as

PG*=cpg m: (1)where Cpg is a power control coefficient.If the generator power is instantly controlled to be equal toPG* with given Corn, the difference between pG* andaerodynamic power PW causes acceleration or deceleration ofthe wind turbine, and the rotor speed moves to equilibriumpoints such as PI -- P3 .

When wind speed imxeases to exceed its rating, theaerodynamic power curve is as pW4 in Fig.1. Theequilibrium point is P4 and hence reducing aerodynamicpower is necessary. The region where co~ > ~~R is thepower limiting region. Aerodynamic power PW should bereduced by controlling the pitch angle, Here, we set thegradient angle ofp~ to a constant value 0 , as shown inFig. L

If the cage induction generator is excited at the point byconstant frequency of voltage, the angle 0 is nearly equal to90 (deg). In this case, the turbine operates at almost fixedspeed ;f near rated speed ~mR, because of small slip of thegenerator. This situation should be avoided since:

1) Aerodynamic wind power is directly applied to driveaxis, causing severe torque and output surge with windturbulence, because acceleration or deceleration of thewind turbine cannot be expected as much.

2) Very high speed of blade pitch angle control isnecessary andlor mechanical compliance and dampingat drive train is necessary to avoid the surges.

Therefore we recommend the angle 6 at some valuebelow 90 (deg), where electrical power control of thegenerator is possible by varying the exciting frequency. Thenaerodynamic power can be controlled by controlling theblade pitch angle with the control objective: regulate rotorspeed at some value somewhat above the rated value ~~R.Electrical power ccmtrol of the cage induction generator usingpower converter is substantially fast and exact to get desiredgenerator power, hence it becomes possible to store thetransient aerodynamic energy into the turbines kineticenergy.

Here we especially propose the angle d: OS 8 S 4.5

(deg), with co~ and PG by per unit (p.u.) expression.Between rated and shut down wind speeds (note that the shutdown wind speed is practically about the double of the ratedone), constant electrical output will be gained with d = O(deg), or constant torque will be gained with 19=45 (deg),even when rotor speed control error extends to some range.

III. CONTROL SCHEME AND SYSTEM EQUATIONSFig.2 shows a configuration of the variable speed WTGwhich we will investigate. A V/f PWM converter connected

to PWM inverter via a dc link provides variable frequencyand variable voltage excitation of a cage induction generatorwhich is driven by a wind turbine, extracting electrical powerfrom the generator and supplying the power to the dc link.The PWM inverter can transfer the power from the dc link topower grid with power factor of 1.0 [9].

Cage Vlf PWMWmd PWM PoweInduction Converter

Wind -

=,Gridlrwerwr

iI e[ ~ PGd/ PCPower Reference * -+EE zEE1

Fig.2 System configuration of variable speed WTGA. Control Scheme for Electrical Power control

Here we will introduce a control scheme for electricalpower control. Electrical power will be tracked to thereference pG* by controlling exciting frequency coe for thecage induction generator. The command CO.* to the V/fPWM converter for me is given as* m~i- me (2)where m~ is the command for slip frequency cv~, andcv~ is given by PI control scheme as*.v~ = c(@(pG*- p~)()(D)=KP 1+* 1 (3)(4)where D denotes differential operator, and KP and TLdenote control parameters.B. Control Scheme for Mechanical Speed Control

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE0-7803-7173-9/01/ 10.00 2001 IEEE 639


3/6

Speed regulation in power limiting region wherecon >~@wi]] be implemented by controlling blade pitchangle ~. The command P* tothepitch regulator for P isgiven by PID control scheme as

P = -CP(D)(%LI - @m) 5)

where Clmu is the reference for the regulation which we setat a value somewhat greater than the rated rotor speed, andK PP T@ Tdp and y denote control parameters.C. System Equations

The aerodynamic torque TWproduced by wind turbine isgenerally expressed as [10]

TW=0.5p7rRW3C~A,j?)VW2 7)where p is air density, RW is radius of rotor, VW is windspeed, CT denotes torque coefficient of wind turbine, 2 istip speed ratio, and ~ denotes pitch angle. Note that the tipspeed ratio 2 is defined as

2 = RW QWVW 8)where f2W denotes rotor speed of the turbine.Torque equation is expressed as

9)where JW and JG denote the moment of inertia of turbineand generator respectively, lG is generator input torque,ClG is generator speed , and GW is gear ratio given by

GW=QG/QW (lo)Here, we transform equation (9) to torque equation per oneelectrical phase of 3-phase induction generator and that is

= ,JW, dtwe mm +tGdtwhere twe and tc denote the turbineand generator input torque respectively,and JWe is moment of inertia. Noteconstants are expressed as

(11)aerodynamic torqueOn is rotor speed,

these variables andcom= Npfd(; , twe=Tw/ 3Gw) , t =TG 13,Jwe =~- [1w JG3NP GW (12)

where NP is number of pole pairs of the generator.Since the dynamics of the system is not very fast, we use

steady state approach to obtain gtXK3MtOr input tOrqUC. tarrd electrical output p ~ . Steady state equivalent circuit perphase of the generator is shown in F1g.3. Electrical outputp~ is given by

PG -v?Re[ (13)where Re[ ] denotes real part of complex number , andYG denotes admittance looking into the equivalent circuitthrough the terminals a, b . Complex admittance YG isgiven as

y coe), Re [Yc ] is negative, andhence PG in (13) is positive.Generator input torque t is given by

(16)where PM denotes mechanical input power to the generator,and the rotor current Ir is given by

I,=- V,z, +2, +z,z[,Ym (17)The transfer functions of the V/f PWM converter and the

pitch regulator with rate limiter are assumed to be of firstorder as given in the appendix.

~o bRm, R,, R, :magnetizing, stator and rotor resistance,Lm, L8, Lr :magnetizing, stator, and rotor inductance,V~:stator voltage, 1, , 1, :stator and rotor current, S :slip

Fig.3 Equivalent circuit of induction generator referred to stator

IV. SIMULATION AND ITS RESULTSWe performed simulation to test the control strategies.

Descriptions and results will be shown in p.u, (per unit)expression. The scale of the tested system, the base quantities,system and control parameters are shown in the appendix.

We tested three strategies of (3=0, 45 and 90 (deg). Thecontrol method in power maximizing region (con < ~mR ) iscommon for all of the three strategies. In the region, onlyelectrical power control is performed as described in 111.A.The difference exists in power limiting region. The strategiesin the region are summarized as follows.1) System with 8 =90 (deg)

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE0-7803-7173-9/01/ 10.00 2001 IEEE 640


4/6

In this system, upper limit of exciting frequency Oe isfixed tO ~mR . When Ue = Cl~R, electrical powercontrol is suspended and instead, pitch control begins andkeeps its operation for purpose of generator powerregulation. Equation (5) for speed control is replaced by~ = Cp (~)(pGu - ) (18)

for objective of power control, where CP (D) waspreviously given in (6), and PGU denotes the referencefor regulation. The control parameters in CP (D) wasempirically determined by simulation and, as a result, wefound that there were no significant differences in thecontrol parameters of (5) and (18).

2) System with O=:0or 45 (deg)The control methods were previously described in 111.Aand B. Note that the exciting frequency cog is enabled tovary crossing over ~@.

Simulated time responses are shown in Fig.4 and Fig.5.The input wind speed is shown in Fig.4 (a), which wasgenerated by computer simulation [11] with 10-minute meanvelocity of 1 (p.u.) (13m/s) and the root mean square offluctuating component of 0.3 (p.u.). The wind profile mayseem to be very severe compared with those at practicalturbine sites, consequently the simulation results may showdistinctive natures among the strategies.

Time responses of the systems with O and 90 (deg) areshown in Fig.4 (b)-(d). Generator output PC and inputtorque t in the case of 9 =90 deg are observed withlarge fluctuations. With 6=0 (deg): PG has long periods ofconstant value of 0.87 (p.u.) which is substantially equal toits rating (0.86 p.u.); maximum input torque t was 0.907(p.u.) and substantially limited to its rating of 0.905 (p.u.);both PG and t change very slowly.Fig.4 (d) shows the rotor speed. With 19=90 (deg), themaximum of rotor speed was 1.02 @u.) which issubstantially equal to its rated value of 1.0 (p.u.). With O=0(deg), the rotor speed reached up to 1.20 (p.u.), exceeding itsrating of 1.0 (p.u.).

Flg,5 shows the results of the simulation with 0 =45(deg ) and again with 6=0 (deg) for the sake of comparison.The time response of rotor speed arm with d =45 (deg) wasvery similar to that with 19=0 (deg). So one can refer for it tothe result with 6=0 (deg) which is shown in Fig.4 (d).

As shown in Fig.5 (a), with O=45 (deg), the power PGfluctuates up to 1.03 (p.u.); whereas, the torque t inFig.5(b) has long periods of constant value which is 0.923(P.u.), exceeding its rating by 2 (%).Fig.6 shows locus of PG with mm during the 30seconds of the simulation for 0 =90 and 45 (deg). In theregion where am < 1.() (p.u.), we can see that the electricalpower control has no substantial errors in the two graphs. Inthe region where ton >1.0 (p.u.), difference between the two

is evident. When 8 =90 (deg), Om is limited to about 1.0(p.u.), but the peak of PG reaches up to about 1.73 (p.u.).When @=45 (deg), Pfj extends to about 1.03 (p.u.) andUm extends to about 1.18 (p.u.)

0.5 F -i

0 5 10 15 20 25 30time (s)(a) simulated wind speed

1 1 I ,1.5 I~ . ....... ~=goo 1 :1p e= (J. , ;~lzl . ,,$.< 0.5 -kLwAJo 5 10 15 20 25 30

time (s)(b) generator output

I I 1 I , I , , , ,1.5 - I I::qs \, ::, .,,61 - ,,,Q

- 0.5 -

00 5 10 15 20 25 30time (s)

(c) generator input torque I 1 I 1

n3 - .,E30L 2 _J10 20 30time (s)

(d) Rotor speedFig.4 Time response by simulation with $=0 and 90 (deg)

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE0-7803-7173-9/01/ 10.00 2001 IEEE 641


5/6

o;~,~-~yo 5 20 25 30time (s)

(a) generator output

Lr-----.-~a~ 0.5 . (3.45oo

o0 5 10 15 20 25 30

time (s)(b) generator input torque

Fig.5 Time response by simulation with @= Oand 45 (deg).2

1.5~&uq 0.5

0 Do 0.5 1Com(p


6/6

5) V/f PWM converterFirst order system with gain of 1 and time constant of 0.10(s) .The ratio V/f was set as V, /0, =1.0 (p.u.) in normaloperation and the ratio was reduced in starting operation.

B. Control ParametersPI or PID control parameters were empirically tested by

simulation and acljusted to values which seemed to beoptimal.

Constants for reference signals (p.u.):f.lm~ = 1.0, 2m~ =1.05, P~~ = 0.86,P~~ = 0.86x ] 05 Cpg = 0 86

Power control PI parameters (p.u.):Kp =1.0, ~ =0.1 (s)

Pitch control PID parameters (p.u.):KPP =50 (deg/p.u.), ~P =().5 (s), TdP =0.8 (s), y =5

VII. REFERENCES[1] M.G. Simoes, B.K. Bose, and R.J. Spiegel, Design and PerformanceEvaluation of a Fuzzy Logic Based Variable Speed Wind GenerationSystem, Conference Record of the IEEE Industrial Applications Conference,VO1.1996, No.VOL1, 1996, pp.349-356[2] A. Miller, E. Muljadi, and D.S. Zinger, A Variable Speed Wind TurbinePower Controf, IEEE Trans. on Energy Conversion, VO1.12, No.2, June1997, pp.181-186[3] A.S. Neris, N.A. Vovos, and G.B.Giannakrpoulos, A Variable SpeedWind Energy Conversion Scheme for Connection to Weak AC Systems,IEEE Trans. on Energy Conversion, VO1.14,No.l ,March 1999, pp.122-127[4] R. Chedid, F. Mind, and M. Basma, Intelligent Control of a Class ofWind Energy Conversion Systems, IEEE Trans. on Energy Conversion,

VOM4, No.4, Dec. 1999, pp.1597-1604[5] Y.D. Song and B. Dhinakamn, Nonlinear Variable Speed Control ofWind Turbines, Proc. IEEE Int. Conf. Control. Appl., VO1.1999, No. VO1.11999, pp.814-819[6] R. Cardenas, G.M. Asher, W.F. Ray, and R. Penar, Power Limitation inVariable Speed Wind Turbines with Fixed Pitch Angle, IEE Conf. PubI.,No.419, 1996 pp.44-48[7] E. Muljadi and C.P. Butterfield, Pitch Controlled Variable-Speed WindTurbine Generation, Conference Record of the IEEE Industrial ApplicationsConference, VOI.1999, No.VOI.11999, pp.323-330[8] H.R. Bolton and V.C. Nicodemou, Operation of Self-Exited Generatorsfor Windmill application, Proc. IEE, VOL126, No.9, 1979, pp.815-820[9] R. Jones and G. Smith, High flrality Mains Power from Variable SpeedWind Turbines, Wind Engineering, VO1.18,No.1, 1994, pp.45-50[10] S. Heier, Grid Integration of Wind Energy Conversion Systems, JohnWiley & Sons, 1998[11] T. Knudsen, A Stochastic Wind Model Covering Periods Ranging froma Fortnight to a Second, Wind Engineering, VO1.14,No.6, 1990, pp.387-404

VIII. BIOGRAPHIESNorimichi Horisrchi was born in Okayama, Japan, on May 22, 1946. Hereceived the M.E. degree in 1972 from Fukuoka University. He joinedTOSHIBA Cooperation, Tokyo, Japan in 1972, where he worked for designof industrial applications of motors. Since 1993, he has been with TakamatsuNational College of Technology, where he is a Research Associate. He hasbeen engaged in research on variable speed wind power systems. Mr.Horiuchi is a member of the Institute of Electrical Engineers of Japan (IEEJ)and the Society of Instrument and Control Engineers (SICE).Takashi Kawahito was born in Tokushima, Japan, on May 17, 1939. Hereceived the B,E. degree in 1962 and the D.E. degree in 1994 from TheUniversity of Tokushima, Tokushima, Japan. He joined Fujitsu, Ltd., Tokyo,Japan in 1962, where he worked for designing telephone exchange systems.Since 1974, he has been with Takamatsu National College of Technology,where he is presently a Professor. He has been entydged in research on windpower systems. Dr. Kawahito is a member of IEEJ and Japan Wind EnergyAssociation (JWEA)

0-7803-7031-7/01/ 10.00 (C) 2001 IEEE0-7803-7173-9/01/ 10.00 2001 IEEE 643

7 Torque and Power Limitations of Variable Speed Wind Turbines Using Pitch Control and Generator...

Documents

Transcript of 7 Torque and Power Limitations of Variable Speed Wind Turbines Using Pitch Control and Generator...