6 Optimal Control of a Variable Speed Wind Turbine Under Dynamic Wind

8/13/2019 6 Optimal Control of a Variable Speed Wind Turbine Under Dynamic Wind

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Optimal C ontrol of a Variable Speed Wind Turbine under Dynam ic WindConditions

A . McIver, D.G. Holmes, P. FreereDepartment of E lectrical and Computer Systems EngineeringMonash Un iversityWellington Road, Clayton, 3168Australia

Abstract--Variable speed wind tu rbi ne systems have thepotential for significantly increasing the energy that is extractedfrom the wind com pared to constant speed turbines, since theyallow the ro tor to continue to op erate with max imum efficiencyas the wind speed varies. However, such systems r equi re back-to-back inverters, o r specially wound motors, to achieve thevariable frequency to constant frequency conversion that isrequired. Since this adds to the cost and complexity of thesystem, it is desirable to make sure that the nett energy gainoutweighs the increased cost.This paper explores this issue, by presenting controlst rategies for opera t ing a var iable wind speed turb ine und ervarying wind conditions, and determing the increase in energythat can he achieved using these strategies. The results areverified both by simulation and l abo rator y experiment using amodel turb ine systems, and show tha t a 9 t o 15 improvementin net energy extraction from the wind is achievable. F urt herimprovements can also be obtained optimizing the generatorexcitation voltage for the varying speed conditions to reducelosses.

I. INTRODUCTIONRecent research has suggested that variable speed windturbines offer the potential for a significant increase in theenergy extracted from the wind compared to constant or nearconstant speed turbines [1,2], since in a variable speedturbine, the turbine rotor speed can follow changes in windspeed to keep the rotor extracting energy from the wind withmaximum efficiency. Despite this advantage, constant speedwind turbines dominate current installations, primarilybecause of the comp lexity of converting the generated powerto a constant magnitude, constant frequency supply to feedinto a grid. However, recent advances in power electronicsnow offer a practical method of achieving variable speedgeneration.The essential challenges with a variable speed windgeneration system are:(i) to control the turbine rotor speed to achieve maximumpower transfer from the w ind as the wind speed varies;(ii) to convert the resultant variable frequency, variablemagnitude AC output from the turbine generator into aconstant frequency, constant magnitude supply whichcan feed into an ele ctrial grid network .A number of approaches have been proposed to solve thevariable frequency generation problem, of which the most

common is either a back-to-back AC-DC-AC inverter system(Figure. l), or a slip recovery system/doubly wound statormachine system for higher pow er applications [2,3,4]. Bothsolutions are more expensive than a simple fixed speedinduction generator, and it is important for a practical windgeneration system to be confident that the gain in recoveredenergy under variable speed operation exceeds the additionalcost of the power electronics and/or machine m odifications.Much of the work reported to date has concentrated ontechniques for converting the variable rotor speed from theturbine into a constant frequency supply, primarily relying onsimulations to c o n f m the results. In this paper, theperformance of a complete variable speed wind generationsystem, consisting of a squirrel cage induction generatorconnected to the grid through back-to-back voltage sourceinverters, is investigated under dynamically varying windconditions. Further improvements in system efficiency arethen obtained by opthising the generator excitation voltagefor varying speed conditions. Both simulation and laboratoryresults are presente d.

11. MODELLINGHEWIND GENERATIONYSTEMA wind generation system com prises a num ber of sectionsas shown in Figure 2, each of which must be modelled if theoverall performance of the system is to be evaluated. Thefollowing approach has been used to develop the variouscomponent models.For evaluation of the energy output between differing windregime types, the wind regime can be modelled as a longterm (eg over a year) probability function (W eibull function),multiplied by a short term (eg up to one hour) powerInverters

d

GeneratorFigure 1: Variable speed wind turbine system

0-7803-3544-9196 5.00 1996 IEEE1692


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PowerGenerator >ICL3ontrol System

Figure 2 : Block diagram of a wind turbinespectrum derived function. This enables a representation of awind regime as a time domain function, with the requisitepower spectrum and probability function. This wind regimeis then applied to a rotor m odel, which is essentially a powercoefficient versus tip speed ratio curve. The mechanicallinkages are modelled as a simple inertia function with aconstant friction torque and the generator is modelled as astandard induction motor with resistive losses and a constantpower current harmonics loss.A. WindModelThe variable wind speed has been m odelled as long termvariations in average wind speed using a Weibulldistribution, together w ith short term fluctuations around thisaverage using a spectral power density model. This approachallows a realistic variable wind speed regime to be simulatedfor a variety of average wind speeds and turbulenceconditions, without requiring a full set of measured site data.

I Short Term indModelThe short term wind regime is based on the w ind energyspectrum defined by (1) [ 5 ] , ie:

where: S n) = spectral power densityn = frequencyz = height above groundfm = fluctuation constant = 0.06rs =w ind speed standard deviation? = hourly mean wind speedEquation (1) is modified by a turbulence intensityparameter (Tu ) which allows the spectrum to be varied toinclude good and bad turbulence sites by changing thestandard deviation of the wind speed. eg for flat terrain Tu=

0.1, while at the ou tskirts of a town with building s and treesTu=0.3 where:

The spatial and time dep endent turbulent structures in thewind d o not alway s have a scale much g reater than the rotoritself. This results in the rotor experien cing the effec ts ofdifferent wind speed s along the length of its blades. This canbe accounted for by assum ing that the sum of the forces on

the blade from the varying air speed is approximated byusing an averaging filter on the incom ing wind and applyinga single wind speed across the face o f the rotor [ 5 ,6 ] . Thisfilter has a spectrum described by (3), where T is the rotortime constant defined by 4), viz:(3)

T = Dv where D = rotor diameter 4)Equation 5 then gives the resultant wind speed as afunction of time [SI,viz:V r ( t )= c @ ( n i ) . F (n, ) . An)llZ cos(2n nit p i ) ( 5 )

where: Vdt) = filtered win d speed at time tni = ith frequencyAn = frequency spacingpi = random angleOnce the wind speed is known, the average power outputof the wind turbine can be found using the turbinesimulation taking variable speed or constant speed operationinto account as appropriate.

2) Long Term WindModellingThe limitation of this short term w ind mod el on its own isthat it only produces short term instantaneous data. Theshort term wind spectrum is a function of the hourly meanwind speed and produces wind speed variations around thismean. However, a long term w ind simulation can be derivedby com bining a series of short term simulations where themean wind speeds follow a long term wind speeddistribution. The Weibull distribution 6) describes theprobability of wind speeds at a site being greater than areference value.

Hence the p robability of a wind speed being between twogiven values is:

where: V i , V2 = given wind speed limitsk = Weibull shape parameterc = Weibull scale param eterThe parameters, c and k, re known for various sites, andcan be extracted from existing wind records.Equation 8 shows how these results can be used tocalculate an annual energy yield using the Weibulldistribution and simulations of separate average windspeeds, ie.

i = N

i=l

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where: Pgrid(V) = supplied grid power for a w ind speed VH = number of hours in a year(from the turbine simulation)Esentially, (7) determines the probability of a particularaverage wind speed occurring using the long term windmodel (the Weibull distribution), and (8) sums the wind

turbine generator output over a full year based on thisprobability to determine the annual energy yield for aparticular turbine model.

C p 0.250.200.150.100.05

B. Rotor Modelturbine is given by:The power extracted from the wind by the rotor of a wind

1 \~.~~~~~~..

(9)where: p = air density

A = blade areaV = wind velocityand the power co-efficient, Cp, is the proportion of the pow erextracted from the wind to the total power available in thewind. Cp varies as the turbine rotational speed and windvelocity vary, and is uniquely specified for each turbine. Cpis generally assumed to be a function of the tip-speed-ratio(TSR) as shown in Fig. 3, where TSR is:

wRTSR = Vwhere: w = turbine rotational speedR = blade radius = 2.5mV = filtered wind speed from 5 )The wind turbine model used in this paper is based on asimple Cp curve model, so that for a given rotor and windspeed, the optimum tip speed ratio can be calculated from

(lo ), C p measured from the relevant Cp curve (Fig. 3), andthe rotor power Pro,,, can be calculated using (9)C. Mechanical LinkageThe mechanical linkage is modelled as a single inertiaelement, a single friction element and an ideal gearbox

connected by ideal shafts (i.e. no friction, no inertia and notorsional flexibility). The available power for electro-mechanical conversion from the high speed shaft into thegenerator is then given by 1 1).hss = 'rotor rotor= friction (11)

where: phss = mechanical power of the high speed shaftCOrotor = rotor speedProtor = power from rotorTfriction= friction torque = 10NmD. eneratorThe generator is modelled as an ideal mechanical toelectrical energy conversion with a constant torque loss torepresent bearing friction and windage, an d an electrical lossproportional to the square of the cu rrent to include the effectof resistive losses. This model gives an approximatelycorrect steady state efficiency without considering anydynamic effects, and is easily extended for the variablespeed turbine to account for the generator losses due to theinverter switching harmonics (12).

'elec = phss 31 hmm (12)where: I = generator current

= generator equivalent resistance = 6.6Qharmgenerator losses due to inverter switchingharmonics = 53W (approximated as a constant)

E. Frequency Con verterThere is a switching loss incurred by each switch in theinverter every time it turns on and off, and conduction lossesin each switch caused by the current flow. Equation 13approximates these power losses for a given switchingfrequency and load cu rrent as:

h s s = 2pswitch f 4 1ph onpgrid = pelec oss

(13)

(14)so that the power fed into the grid becomes:

where: Pswitch = switching loss for one switch = 1.2mJf = switching frequencyIph = phase currentVon = switch on state voltage = 1.6VPelec = electrical power produc ed by generator

111. CONTROLF A VARIABLEPEEDWIND TURBINEThe response time of the turbine rotor speed is determined

by the large rotor inertia, which is much slower than thegenerator electrical response time. Thus the optimisingcontroller can be split into two sub sections; speed control ofthe turbine and generation control of the generator, as shownin Fig. 4.The speed controller calculates the generator torquerequired to vary the turbine speed to maintain constant TSR,and the generator controller adjusts the inverter to extract theappropriate power from the generator to ac hieve this torque.1694


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I Ia v Speed

GeneratorFigure 4:Variable Speed Turbine Speed and Generator Power ControllerThe two controllers are decou pled by their speed of responsesimilar to speed and current control loops in a co nventionalvariable speed drive system.

controllerV..-

,pref Generator'gen controller

A . Turbine Speed ControllerFigure 3 shows that the power extracted from the w ind willbe maximised when TSR is maintained constant at theoptimum value. Thus the control strategy for a variable speedwind turbine is to control the rotor speed to maintain theoptimum TSR as the wind speed changes.The mechanical behaviour of a wind turbine is describedby:

/ \

a

1 - 1

WindFigure 5 : Turbine speed controller

produced by the wind is known accurately and the generatortorque is contro lled precisely .Integral control is added to the system to remove any errorsintroduced by imperfections in the system. Rotor torque canbe estimated by applying the measured wind speed to amodel of the turbine. Thus the measurement of wind speedand the turbine model are both sources of error. Theknowledge of the generator torque is limited to the accuracyof the generator control system. A small level of integralcontrol is required to remove the effects of these errors.The rotor torque due to the wind is estimated using theknown C, curve for the rotor, and wind and rotor speedmeasurements. This is a simple method for torque estimation,but it does require measurement of wind speed. It has beenassumed that the wind speed is already measured todetermine the tip speed ratio reference in this case.The output of the turbine controller can therefore beexpresse d as:

c= 1

where: T~~~ = generator torqueJ = turbine and generator inertia = 20 kgm'which means that the generator torque becomes the controlvariable to maintain the optimum TSR as the wind speedvaries. Generator torque is directly related to generatedelectrical power and can be determined from the DC linkpower with a correction for losses in the inverter and thegenerator if the rotor speed is known. This avoids the needfor a shaft torque transducer to determine zgen.TurbineSpeed ControllerThis controller determin es the power that is to be ex tractedfrom the rotor. Some of this power is dissipated as generatorlosses and the rest is converted into electrical power. Theoverall structure of the co ntroller is shown in Figure 5.

The m ain controller objectives are to maintain the optimumTSR with no steady state error, and without large processingrequirements so that this controller can be implemented in a

where: a = speed ratio error (derived from TSR error)Kp = proportional gain = 0.2K, = integral gain = 0.0001

B. Generator Power ControllerThe aim of this controller is to determine the magnitudeand frequency signals for input to the inverter so that thegenerator power follows the power reference signal. Thepower reference signal is calculated to be the p ower such thatthe turbine operates at its maximum output power. Figure 6shows a block diagram of the final controller. The 'plant' tobe controlled by the generator controller comprises theinverter and the induction machine.The controller requirements can be summarized as follows:a power reference input - from the turbine control loopa feedback signal - the generated powera conversion of a power error into a frequency andmagnitude signal

micro con troller along with the gene rator power controller.The derivative term in (15) determines the type ofcontroller used. While a PI type system is desirable, thepresence of the derivative term in the 'plant' equation means Filterthat the proportional control alone is sufficient to drive the - 4 3 Jsteady state error to zero assuming that the rotor torque , ,Figure 6 : Generator power controller1695


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This last requirement involved some plant modelling, andit was eventually decided to convert the power error into afrequency error to feed directly into the PI control section sothat the inverter frequency could be determ ined directly. (Theinverter output voltage magnitude was kept proportional tothe frequency for constant Vlf operation).The relationship between power error and frequency errorcan be found from the torque speed equation of an inductionmachine. Taking the derivative with respect to frequency andassuming that the slip is small (and hence o m , ) ives: Lower Refe:ence ITurbine Tip speed ratioJ;if e n = . v2

tdata logging

where: f = electrical frequencyr2 = rotor resistanceV = terminal voltageNote that (17) is an approximate relationship between thepower error and the frequency error, and does showdependency on other factors such as terminal voltage androtor resistance. However, any errors introduced by theassumptions made deriving this expression are not significantin the final control system since the integral component ofthe PI section drives the steady state error to zero anyway .A low pass filter with a time constant of 47ms was alsoadded to the power feedback signal to remove noise. Themain source of noise is the measured DC current, since atpresent the grid side inverter is a four quadrant DC driveoperating in constant dc voltage mode. Since this drive uses athyristor inverter, the current is far from smooth, particularlyduring discontinuous conduction.

IV. SJMULATIONThe wind turbine system was simulated using a Cprogramme which assumed that, due to the small electricaltime constant of the generarator compared to the mechanicaltime constant of the turbine, the generator reached its steadystate operating point instantaneously relative to the turbine.The generator control strategy was assessed for stabilitybefore experimental validation, by simulating it in the powerelectronics simulation package KRE AN.

v. LABORATORYXPERIMENTALONFIRMAnONA complete experimental test bed has been constructed to

confirm the operation of the variable speed wind generatorand control system in the laboratory, as shown in Figure 7.The test bed comprises of a 34kW, 2900rpm DC motorcontrolled by a four quadrant variable speed DC drive, whichis driven to follow the output shaft torque that would beachieved by a real wind turbine and its mechanical linkagesoperating under a given variable wind regime. The drive hasbeen programmed to incorporate the random nature of wind,the non-linear power output of the rotor blades as wind andturbine speed,change, and the dynamics of the rotor blades,

3 phase su plyP

Gridl l

Mach ne In_ I :. S.(grid-sidePowerController I

PowerkW

2

1 61 22 01 61 2

Measured

Reference

0 5Time (seconds)Figure 8: Experimental Response to Step Change in Demanded Power

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command was stepped from 1OkW to 2.0kW. This confirmsthe capability of the controller to maintain a commandedgeneration level.VI. RESULTS

Figures 9 and 10 show the operation of the completesystem in varying wind regim es, and there is excellent matchbetween simu lation and laboratory experiment.From these figures, it can be seen how the controllersattempt to maintain the optimum TSR of just below 10, butthere are some transient deviation s from optimum as the windspeed changes since the rotor inertia limits the maximumacceleration of the rotor.In Figures 11 and 12, the effect of the use of a variablespeed turbine is shown on the power output at an averagewind speed for a given turbulence.For the constant wind speeds (ie. turbulence is zero), thevariable speed turbine is able to have a higher output inregions where the constant speed turbine is unable to operateat maximum efficiency. However, as the wind speedincreases, the con stant speed turbine operates at its maximumefficiency, and the extra losses in the con verter system for thevariable speed turbine ensure that the variable speed turbinehas a lower output.As the wind turbulence increases, the constant speed

2 2I / / / / / l I II l l I / I l / l

11 1 1 1 I 1 I 1 1 00 5 111 I5 211 25 311 35 40 45 50

lime 3Figure 9 : Simulated and Experimental Control of Tip Speed R atio underDynamic Wind Conditions - Low Turbulence Conditions

Figure 10 : Simulated and Experimental Control of Tip Sp eed Ratio underDynamic Wind Conditions - High Turbulence Conditions

turbine is unable to follow the wind velocity excursions, andhence operates below optimum at all times. Under theseconditions, the variable speed turbine has a significantadvantage in power output even when the average windspeed is within the maximum efficiency region of theconstant speed turbine. In fact, because of the normalvariation of average wind speed over a full year under theassumption of a WeibulI distribution, under low turbulenceconditions (Tu = 0.1) a variable rotor speed system gains9.2 more energy than a constant speed system. In highturbulence winds (Tu = 0.3), the gain is much greater15.1 /).

VI1 INCREASED EFFICIENCYY REDUCING EXCITATION OSSESThe induction generator requires external excitation tooperate, and this reactive power is normally supplied by thegenerator inverter in the back-to-back configuration. Thisarrangement gives the flexibility to control the generator

excitation independently of the real power transfer.Conventional variable speed drives maintain a constant V/fexcitation ratio which keeps a fixed magnetic flux in themotor and essentially constant magnetizing losses. Thisconstant excitation of the induction generator results in lowefficiency as the generated power drops at low wind speeds.There is potential for considerable gain in efficiency for

4 5 5 5 6 5 7 5 8 5 9 5 I U S 1 1 5 125 1 3 5 145WindSpeed (mls)

Figure 11: Electrical power v s Wind SpeedConstant Wind Speed Conditions (Tu = 0)

5lIW45M1 Constant speed401m5w:2 1x1

I5WIOW500

4 5 5 5 6 5 7 5 X 5 9 5 1 0 5 1 1 5 1 2 5 1 3 5 145Wind S d 4 s )

Figure 12:Electrical pow er v's Wind SpeedHigh Turbulence Conditions (Tu = 0.3)

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80 9 100 110 120 130 140 150Line voltageFigure 13 : Comparison of reduced excitation for simulation andexperiment at constant speed

variable speed wind generation systems at low wind speeds ifthe induction generator excitation is reduced for lower poweroperation. The approach taken is to heu ristically determinethe optimum excitation voltage for various speeds and powerlevels.Figure 13shows an exa mple of the benefits of reducing themachine excitation levels. Both the m odel and experimentalresults show that significantly lower machine losses can beachieved simply through regulation of the terminal voltageand hence the excitation losses.Table 1compares the voltageand losses for reduced e xcitation operation with constant Vlf.

VIII. CONCLUSIONThis paper presents the results of a theoretical andlaboratory experimental investigation into the benefits ofvariable speed generation for a wind turbine. It show s how asquirrel cage induction generator can be controlled using a

PWh4 voltage source inverter and a simple speed controllerto maintain optimum power transfer conditions for the windturbine in varying wind speed conditions. The main limit tothe ability of the system to follow wind speed changes is thelarge rotor inertia preventing the rapid acceleration of therotor. Further efficiencies have also been shown to beobtainable by optimising the generator excitation forparticular operating conditions.The results of this work show that a variable speed turbinecan extract significantly more power from wind compared to

TABLECOMPARISON OF CONSTANT v/F WITH REDUCED EXCITATIONPERATION

Reduced Constantexca I V Pgen 1kW .. Ziu.e..F.) ....o = 100 ra ds Ploss w)Efficiency 75 65%. ..

a constant speed rotor, but the net gain in energy yield maybe low in non turbulent wind regimes because of theadditional losses incurred in frequency con version. Carefulevaluation is required in each individual situation to confirmthe econo mic benefit of moving to variable speed operation.REFFXENCES

Carlson, and Hylander, J., Electrical System withFrequency Conversion for Variable Speed Operationof Wind T urbines, Wind Engineering, Vol. 13,No. 5 ,1989.Spee, R. et al, A daptive control strategies for variable-speed doubly-fed wind power generation systems,Nakra, H.L. et al, Slip power recovery inductiongenerators for large vertical axis wind turbines, IEEETrans on Energy Conv., pp733-7, Dec 1988Brune, C. et al, Expe rimental evaluation of a variable-speed, doubly-fed wind-power generation system,Beyer, H. et al, Wind Energy Converters in a RealWindfield: Calculation of Hourly M ean Pow er Output,Wind Engineering, Vol. 10,No. 2, 1986.Beyer, H. et al, Optimization of Hourly M ean Pow erOutput of Wind Energy Converters with VariableRotatinal Speed using a Dynamic Model, EuropeanCommunity Wind Energy Conference Proceedings,June 1988.Bechly, M.E. et al, Development of a resin injectiontechnique for manufacturing composite blades forsmall wind turbines, pp47-54, Solar95, Australian andNew Zealand Solar Energy Society, 1995.

~ ~ 5 4 5 - 5 5 2 ,ES, IEEE, 1994.

~ ~ 4 8 0 - 4 8 7 ,ES, IEEE, 1993.

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6 Optimal Control of a Variable Speed Wind Turbine Under Dynamic Wind

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