Three-Phase Grid-Connected WECS with Mechanical

Three-Phase Grid-Connected WECS with Mechanical Power Control Jéssica Santos Guimarães1, Bruno Ricardo de Almeida1, Fernando Lessa Tofoli2, Demercil de Souza Oliveira Jr.1 1 Federal University of Ceará, Department of Electrical Engineering 2 Federal University of São João del-Rei, Department of Electrical Engineering e-mail: [email protected], [email protected], [email protected], [email protected] Abstract—This paper presents a grid-connected wind energy conversion system (WECS) based on a permanent magnet synchronous generator (PMSG) operating with variable speed. Considering that the wind has intrinsic intermittent nature, it is desirable to maximize the extracted energy, as a maximum power point tracking (MPPT) strategy is described for this purpose. Otherwise, the MPPT algorithm is disabled to maintain the rated power condition and avoid damage to the PMSG, as an external mechanical power control loop associated to active stall is introduced in this work, whose power extraction characteristic is similar to that obtained with pitch control. The WECS employs a bridgeless boost rectifier, which provides power factor correction using self-control strategy, with the advantages of reduced conduction losses, simplified drive circuitry for the active switches, and high input power factor without the need to use multipliers in the control system and impose a sinusoidal reference to the input current unlike average current mode control. Connection with the power grid occurs through a threephase full-bridge inverter, as experimental results on a 6-kW prototype are presented and discussed in detail in order to validate the proposed approach. Keywords—active stall, maximum power point tracking, mechanical power control, renewable energy sources, wind energy.

I. INTRODUCTION The increasing power demand and need to diversify the energy matrix have led to significant investments in renewable energy technologies [1]. Among the existing sources, solar photovoltaic and wind energy can be stated as the most successful and popular approaches for either standalone or grid-connected applications, even though several technical and economic issues must be taken into account for their proper implementation [2]. In both cases, power electronics plays a key role regarding the proper power control among distinct renewable energy sources and loads, especially in most recent applications [3]. Variable speed operation is typically used in modern WECSs aiming to increase energy efficiency. The constant search for the reduced cost per generated megawatt leads to the conception of higher power capacity components, which include the wind turbine, generator, and related power converters [4]. Even though doubly-fed induction generators (DFIG) or field-excited synchronous generators are common choices, PMSGs have become quite cost attractive if compared with the aforementioned approaches, especially for small-size WECSs, although they are also used in also in medium- and high-power wind turbines. Besides, PMSGs aggregate prominent advantages e.g. low maintenance needs associated to high power-size ratio and gearless transmission capability,

which causes mechanical efficiency and robustness to increase [5]. A typical grid-connected WECS based on PMSG is shown in Fig. 1. Considering that the power extracted from the wind turbine and the generator varies according to the wind speed, an ac-dc stage is necessary, which may consist of a diode rectifier or a high power factor topology [6]. Even though single-stage WECSs can be used, it is worth to mention that the existing dc link in the two-stage approach plays an important role. Although large-size capacitors may be required with inherent appreciable cost and reduced useful life, they are employed not only to transfer energy from the wind turbine to the ac grid, but also to uncouple the generator and the grid. Finally, the dc-ac stage is necessary so that nearly sinusoidal currents with low harmonic content and consequently high power factor are injected. There are numerous possible configurations described in literature to obtain two-stage, three-phase WECSs. For instance, back-to-back topologies are based on two-level voltage source converters (VSCs) and widely employed in low-voltage systems. The voltage source rectifier (VSR) controls the generator torque and speed, while the voltage source inverter (VSI) controls both the dc-link voltage and power injected into the power grid. This topology has been successfully used in DFIG-based systems [7] and PMSGbased ones [8]. CSC (Current Source Converter) topologies can also be used in back-to-back configuration, being this approach better recommended for medium-voltage PMSGs due to the high efficiency and wide commercial availability [9]. The structure based on parallel-connected VSCs is adequate to high-power applications or even dc links with distinct voltage ratings [10]. However, as the power levels increase, the appreciable number of modules and/or parallel converters compromises both cost and complexity regarding the system, as this solution is more viable for medium voltages i.e. between 1 kV and 35 kV. Diode-clamped multilevel converters are also employed in medium-voltage applications e.g. NPC (Neutral Point Clamped), ANPC (Active Neutral Point Clamped), FCbased (Flying Capacitor) topologies, among others [11]. Since unidirectional power flow exists in WECSs i.e. from the generator to the grid and the rotor flux on PMSGs is due to permanent magnets, diode rectifiers can be used in the acdc stage [12]. The main drawback in this case lies in the high harmonic content associated to current and voltage waveforms in the generator side, which affects the very efficiency of the machine. Harmonics also lead to increased heating due to

apppreciable ironn and copper llosses at highh frequencies, ripple torque, and audiible noise emiission. In order to minimize suchh harmonic coontent and inccrease the system efficciency, a semii-controlled reectifier can bee used instead [13]. Thhis topology aaggregates proominent advanntages e.gg. simple drrive circuitryy of the acttive switchess and im mpossibility oof short-circuiit through thhe legs, but power p factor correctioon (PFC) is onnly achieved during the poositive haalf-cycle of thee phase voltagge. Within this ccontext, this paper p proposess a WECS bassed on a controlled reectifier to achhieve high poower factor, w which coonsists in a tthree-phase acc-dc bridgeleess boost connverter opperating with self-control technique [144]. Unlike avverage cuurrent mode control, the afo forementioned approach doees not require the desiggn of a currennt control loopp and a proper shape to be imposedd to the inpuut current, thuus simplifyinng the coonverter designn. The ac-dc converter c alsoo presents com mmonsoource connectiion for all active switches, as there is noo need to use isolated drive circuitrry. An MPPT T algorithm iss also addopted to deteermine the PM MSG speed, which w is responsible foor ensuring itss operation whhen the availaable wind pow wer is lesss than the ggenerator pow wer rating. Ottherwise, MP PPT is disabled and a mechanicall system actuuates to limiit the m maximum extraacted power. O On the other haand, the dc-acc stage is composed byy a VSC topoology correspponding to a threephhase full-bridgge inverter, which w perform ms connectionn with the ac grid. Thee detailed anaalysis of the system is presented, whhile experimeental results onn a 6-kW proototype are prooperly discussed in ordder to validate its performannce.

Figg. 1. Grid-connnected three-phaase WECS.

II. PROPO OSED WECS Wind poweer generationn associated to variable speed opperation allow ws the possibiility of extraccting the maxximum poower for a w wide range off wind speedss [15]. Amonng the exxisting solutioons, the PMSG G has becomee the most obbvious chhoice for smalll-size WECSs due to the llack of brushees and reduced maintennance needs, w while the use of o gearboxes iis also avvoided [16]. The proposed system is presented inn Fig. 2, which is coomposed of a unidirectional u rectifier withh reduced num mber of acctive switchess, as well as minimized coost and compplexity regarding the ddrive circuitry since the acttive semiconduuctors arre connected to t the same rreference nodee. The WECS S also em mploys a prooper power ccontrol strateggy, which caan be deescribed accorrding to four regions r represeented in Fig. 33. The wiind speed in Region R I is loower than the threshold vallue, as the system doess not impose aany resistant toorque, thus enaabling the wind turbinne acceleration. Region II corresponds tto the M MPPT operatioon, while the mechanical ppower is limitted in region III if the wind sppeed exceedss a predeterm mined maximum valuee and a properr control schem me actuates foor this m

purrpose. Finally,, the wind speeed in region IV is higher than the maximum vvalue supportted by the blades b and poower genneration is dissabled. The aaforementioneed regions cann be desscribed by the following exppression: if 0 m s  vwind  4 m s 00,  , if 4 m s  vwind  10 m s P  mec  max  (1) Pmec    Pmec (rated) , if 100 m s  vwind  25 m s 00, if vwwind  25 m s  wheere Pmec is thee mechanical ppower; Pmec(maax) is the maxim mum mecchanical pow wer defined according tto the geneerator chaaracteristics; Pmec(rated) is thee rated mechaanical power; and vwinnd is the wind speed. s According to (2), Pmec reprresents only paart of the available winnd power Pwindd and dependss on the turbinne radius R; thhe air masss density ; the wind speed vwind; and the poower coeefficient Cp(λ, β). On the oother hand, pparameter Cp(λλ, β) varries according to the blade pitch angle β and the tip-speed ratiio (TSR) λ ass given by (3)), where ω reepresents the shaft anggular speed. 3 Pmec  Pwind  Cp  ,    0..5      R2  vwwind  Cp  ,   (2)

  R   vwind

(3) The mechaniical power is converted innto electric poower P3ΦΦ(generator) by tthe PMSG. The extracted power is then proocessed by a two-stage grrid-connected power electrronic system. The ac-ddc stage is com mposed by a thhree-phase verrsion of tthe bridgelesss boost rectifiier introducedd in [17] and [18], whiile a three-phhase full-bridgge PWM inverrter is responnsible for performing grid connectiion. A detailed explanatioon is proovided as folloows. A. Unidirectionaal Bridgeless Boost B PFC Reectifier Literature preesents some control c approaches that caan be wer factor recctifiers in ordeer to achieve PFC, P useed by high pow beinng classified as either direect (e.g. hysteresis control [19], aveerage current mode control [19], and peeak-current coontrol [199]) or indirect techniques (ee.g. one-cyclee control [20] and selff-control [14]). Among theem, the so-caalled indirect ones present remarkabble performancce as there is nno need to im mpose a sinusoidal refeerence to the input currentt. Consequenttly, a prooper loop to coontrol the induuctor current iss not necessarry, as welll as voltage seensors to sampple the rectifieed ac input voltage are not required. In this case, an external inductor i is noot necessary as a in typical rectifiers since the phhase currents flow throughh the synnchronous indductances of the PMSG in Fig. 2. The unidirectional reectifier emplooys the self-control strateggy to keeep nearly unityy power factorr, being this teechnique descrribed in detail in [14], as only onne phase reggarding the poower connverter is repreesented in Figg. 4 for simpliicity. Current iga is sam mpled directly in the circuit through a shuunt resistor Rshh and multiplied by a ggiven gain ki determined d byy either the M MPPT algoorithm (ki(mppt))) or the control loop that iss supposed to limit the maximum eextracted mecchanical power (ki(power conntrol)). Thuus its respecttive value reemains withinn the limits of a triaangular modulating signal, being then compared wiith a saw wtooth wave too generate the drive signals of active swittches S1,aa and S2,a.

Figg. 2. Proposed WECS.

Figg. 3. Behaviorr of the mechannical power as a function of thee wind speed.

Thus, param meter ki is rresponsible foor determininng the resistant torque imposed by tthe generator to t the wind tuurbine. It is worth to m mention that pparameters ki, ki(mppt), and ki(power rding to the giiven wind speeed. conntrol) vary accor B. MPPT Algorrithm There are several MPPT T techniques thhat can be ussed to exxtract the maxiimum availablle power from m the wind, whhich in this case is coonverted to electric energyy injected intto the uttility grid. TSR R control is a rrather simple strategy that aallows deetermining thee optimum vvalue for the TSR, althouugh it requires the usee of anemometters [21]. Other methhods based oon MPPT teechniques typpically appplied to solarr photovoltaic systems e.g. pperturb and obbserve (P P&O) and hilll climbing (H HC) have also been suggestted in litterature, but tthey are not aable to determ mine the maxximum poower when rappid wind speedd variation occurs [22]. Sinnce the usse of anemom meters impliess increased ccost of the W WECS, opptimal torque (OT) controll provides thee adjustment of o the PM MSG torque according too a maximum m reference value asssociated to a given wind speed withouut the need off such seensors [23]. Let us connsider that thhe rectifier shhown in Fig. 4 is reppresented acccording to thee block diagrram in Fig. 55. The avverage voltagee Vgi(t)T is ccontrolled so that it is in phase wiith current Igi(t), which must preseent low harm monic distortion.

Fig. 4. Self-control P PFC technique.

P PMSG

Lgi

R gi



~ E (t )

I gi ( t )

i

 

Vgi (t )

T

Rsh

ki ( t )

1 V pk

d '( t)

V dc d

Fig. 5. One-phase eqquivalent circuit of o the controlled reectifier.

U Under steady--state conditioon, the followiing expressionn can be eeasily demonsstrated:

I gi 

Ei ki  Rsh  1 V pk   Vdcc

(4)

wheere Igi is the ppeak value of tthe induced cuurrent in phasee i of the PMSG; Ei is the peak vaalue of the innduced voltagge in phaase i of the PM MSG; ki is a constant assoociated to the selfconntrol techniquee as explainedd in [14]; Vpk is the peak-to-peak voltage associateed to the sawtoooth signal i.ee. the carrier w wave; andd Vdc is the avverage voltagge across the ddc link. Sincee the phaase current deppends on ki, it is possible to write:

Pmec

 Pmec max  , if ki  ki mpppt    Prated , iff ki  ki poweer _ control 

(5)

In other worrds, considerinng that the cuurrent is determ mined byy the MPPT algorithm acccording to thhe wind speedd, the vaalue assumed by ki is ki(mpppt) to ensure that the maxximum poower Pmec(max) is extracted. Otherwise, O ki=k = i(power_control) sso that the extracted poower does not exceed the converter rated power p Prrated. The mechannical torque varies as a funnction of the wind turbine angular speed in Fig. 6 for distinct w where wind speeds, w Tmmec(opt) correspoonds to the cuurve that musst be tracked bby the M MPPT algorithhm. Consideriing that the wind turbinee and PM MSG represennt a coupled mechanical system, the speed vaariation is deteermined by thhe difference bbetween the toorques asssociated to thee aforementioned elements.. For instance,, if the wiind speed is cconstant at 8 m/s and the system operaates in steeady-state coondition correesponding too point “a”, both torques remain constant. When the w wind turbine ooperates in reggion II accordding to Fiig. 3, then thee optimum vaalues are achieeved i.e. Cp=C Cp(max) annd λ=λoptimum. C Consequently,, expression (33) can be emplloyed: R (6) vwind  optimum Besides, thee extracted m mechanical pow wer is equal tto the maximum poweer i.e. m 3 Pmmec  Pmec  max   00.5    A  vwind  C p  max  (7) whhere A is the sswept area of bblades. Substitutingg (6) in (7) gives: 3

Pmec  Pmec max m 

whhere:

 R   0.5    A    koptimum  3 (8)   Cp max m   optimum  





koptiimum  0.5    A  R3  C p max  1 optimum

(9)

It can be stated that the maximum m power deepends baasically on thee angular speeed , which is determinedd from the optimum meechanical torqque Tmec(opt) as:

Tturbbine  Tmec  opt  

Pmec  max 



 k optimumm   2

(10)

wheere Tturbine is thhe torque impoosed by the wind turbine. The maximuum mechanicaal power Pmecc(max) is conveerted intoo electric pow wer P3Φ(generaator) as in (111), which cann be wriitten in terms of the shaft sppeed and ki. From F (8) and (11), the expression thhat defines thee operation off the MPPT caan be deteermined as ((12). In otherr words, the MPPT algorrithm monitors the shaaft speed ω annd calculates tthe optimum vvalue ki(mp e resistant toorque Tgeneratoor is mppt), so that the adequate impposed to thee PMSG andd the system m operates att the maxximum powerr point (MPP).. P3 ( generatorr )  3  ki ( mppt ) 

k2 2 Ei I gi 3     2 2 2 Rsh  1 Vpkk   Vdc ki

3  k2 1 1   k1   2  Rsh  1 Vpk   Vdc  koptimum 

(11) (12)

wheere: k 

Ei

 3  k2 k1  2  Rsh  1 Vpk   Vdc  koptimumm

(13) (14)

C. Mechanical Power P Controll When the winnd speed assum mes values higgher than the rrated connditions, propper mechanism ms for the limitation off the mecchanical poweer are a must.. The active ppitch control eeither throough hydrauliic or electric mechanisms is responsiblee for rotaating the bladees and increasing the pitch aangle positively so thatt the power remains withhin the nominnal ratings. W When usinng passive staall control, iff the wind speed increases, the attaack angle alsoo does (even though the ppitch angle is kept connstant), resultiing in the loss of lift forcees and conseqquent deccrease of the extracted m mechanical poower. Active-sstallbassed systems tyypically emplloy a mechannical element (e.g. spriings) that cauuses the bladess to rotate tow wards the planne of rotaation with incrreasing wind sspeed. This phhenomenon caauses the pitch angle too increase neggatively as theere is a decreaase in the lift coefficiennt as well as inn the extractedd power [24]. Fig. 7 pressents the m major differennces among the aforementioned ttechniques. Piitch control is the most accuurate andd robust apprroach while presenting thhe highest ennergy effiiciency amongg its counterpaarts. Howeverr, due to high cost assoociated to thhe actuators that exist inn each blade and robbustness issuess, it is rarely uused in small-size WECS. IIf the extrracted power is less than thhe nominal value, the blades are built with fixed nonzero n pitch angle in systtems using passsive stalll. Consequenttly, energy loosses are ineviitable as show wn in region 1 in Fig. 7. On the othher hand, the aactive stall control alloows improvedd performance but it causes some overshooot in the extracted pow wer (region 22), which can overload bothh the gennerator and thee power electronic converterr.

Figg. 6. Mechaniical power as a function of tthe angular speeed for disstinct values off the wind speedd.

Within this context, this work propooses an electrronic conntrol system that allows oobtaining a m mechanical poower extrraction curve with nearly tthe same behaavior as the ccurve presented by systems with pitcch control. Thhe main advanntage liess in the increeased amount of extractedd energy for w wind speeeds ranging bbetween 4 m m/s and 10 m/s. m In additioon, it

eliiminates the ppower overshooot and does not require thhe use off hydraulics orr stepper motoors as in activee stall mechaniisms. According tto Fig. 7, thee active stall system is abble to im mprove the wiind energy genneration in reegion I if com mpared wiith the passivve stall system m, at the cosst of exceedinng the raated power in region II. How wever, this isssue can be prooperly haandled througgh the carefu ful design off the electricc and eleectronic compponents. The m major concern lies in the adeequate addjustment of thhe spring systtem. If the sprring is too tighht, the m maximum power will exceeed the rated power p significcantly, whhat could dam mage the WEC CS. Otherwise,, if the spring is too loose, it will acct as a passivee stall system. Besides, sitess with low wind speeed profiles require tightter adjustmennts to im mprove powerr generation aat such low w wind speeds. When high speed proofiles exist, thhe adjustmentt must be looose to avvoid system damage. Thhe proposed electronic system coombined with active stall aallows the usee of tight sprinngs in eitther case, sincce near optimuum generationn can be achievved at low speeds. On the other hand, the active power p is determ mined byy the rated valuue. This is perfoormed by an external e controol loop which limits the mechanical power to a fiixed referencee Pmec(rated) usinng the internal shaft sspeed controll loop seen iin Fig. 8. Beesides, CPmec (s) and C(s) represent the controllers employed in the P loops responsible for controllling the mechaanical power Pmec(s) annd speed (s)), respectivelyy; Igi(s) is thee PMSG curreent in phhase i; and HPPmec(s) and H((s) are the gainns correspondding to the mechanical power and speeed samples, rrespectively. Some transsfer functionss that describbe the mechhanical syystem compossed by the w wind turbine and generatoor are obbtained from (15), ( where Tgenerator is the torque impossed by the generator; aand J is the ineertia moment of o the wind tuurbine. Thhe transfer fuunction given in (16) is obbtained considdering Ttuurbine as an exxternal disturrbance. If thee same behavvior is coonsidered for P3Φ(generator), the system can be lineaarized arround a speciffic quiescent ooperating poinnt (ω=ωop), w while a sm mall-signal moodel is obtaineed and the trannsfer function of the anngular speed too mechanical power p is givenn in (17).

Fig.. 8. Controll strategy usedd in the limitation of extrracted mecchanical power..

Tturbine  Tgeneerator  J 

d dt

 (s)

3  K  I gi ( s ) 2  J  s

Pmec  P3 ( generator g )  J 

d P (s)    mec   J   op   s dt  (s)

(15) (16) (17)

D. Three-Phase Full-Bridge Innverter and C Control Strateggy The three-phaase inverter iss responsible ffor controllingg the dc-link voltage; performing grid g connectioon; controllingg the pow wer transferredd from the dcc-link to the ggrid, as well as the pow wer quality asssociated to the t injected ccurrents [25]. The connverter can be modeled usinng the Park traansform as in [26]. Thee output curreents (ia, ib, ic) aare sampled and a a dq transform block is used too obtain id ((d-axis currennt) and iq (q-axis currrent). At this point, a quaddrature Phase-Locked Loopp (qPLL L) strategy [27] is empployed to ennsure the prroper synnchronization between thhe phase cuurrents and their resppective voltagges. Fig. 9 show ws that two control c loops are necessarry to conntrol both currents, wheere Cv(s) annd Ci(s) are the com mpensators em mployed in thhe voltage annd current coontrol loopps; Fm(s) reprresents the puulse width modulator; Hv(s)) and Hi(ss) are the gaains associateed to the voltage and cuurrent sam mples; dˆd  s  and dˆq  s  arre the duty cyycles associateed to currrents iˆd  s  annd iˆq  s  , resppectively; andd vˆdc  s  is thee dclinkk voltage.

d A current looop with zero reference value for the d-axis currrent componnent ensures that only active poweer is trannsferred to thee grid, while the referencee associated thhe qaxiss current loopp is determinedd by an externnal voltage control According too the loopp that regulaates the dc-liink voltage. A metthodology desscribed in [28]], the followinng expressionss can be eeasily demonsstrated:

Figg. 7. Compaarison of technniques used too limit the exttracted meechanical poweer.

i (s) Vdc id ( s )   q d d ( s ) d q ( s ) s  Lgi  Rgi

(18)

vdc ( s) 1  iq (s) s  Cbus

(19)

wheere Cbus is the dc link capacitance.

Figg. 9. Control sttrategy used in tthe grid-conneccted inverter.

III. DISCUSSIION OF RESULTTS A. Experimentaal Performancce of The Propposed WECS An experim mental prototyype of the prooposed WECS has beeen implemennted consideriing the desiggn specificatioons in Taable I. The experimentall prototype and the prooposed m mechanical pow wer control syystem are reprresented in Fig. 10 annd Fig. 11, resppectively. A DSP (digital signal pprocessor) TM MS320F283777S by Teexas Instrumeents and a prrogrammable microcontrolller by M Microchip moddel dsPIC30F44011 have beeen employed in the im mplementationn of the whole control system m. The followinng semiconduuctors elementts have been cchosen in the rectifieer stage: IG GBTs (Insulaated Gate B Bipolar Trransistors) moodel IRG4PF550WD by Inteernational Recctifier; CR REE SiC Dioodes model C4D05120A. C O On the other hand, IG GBT modules model GA35X XCP12-247 (w with embeddeed SiC freeewheeling diodes) by GeneeSiC have beeen used in the threephhase inverter. Fig. 12 pressents the phasee voltage and the behavior of the q--PLL algorithhm associated to phase anngle θPLL wheen the syystem operatess under rated cconditions i.e. rms phase vooltage off 220 V and ggrid frequencyy of 60 Hz. A small delay ccan be seeen associatedd to the aforementioned waaveforms, whhich is duue to the use of a RC (resiistor-capacitorr) filter responsible foor D/A (digitaal-analog) connversion, filter elements ussed in vooltage sensingg, and processsing time of tthe microcontrroller. Beesides, a frequuency step is applied in Fiig. 13, as it can c be staated that the qq-PLL algorithhm is able to provide the pproper anngle for the cuurrents injectedd in the powerr grid.

Fig.. 10. Experimenntal prototype.

Fig. 11. Active sttall spring-based system used inn wind turbine m model VER RNE555.

TABLE I. SPECIFIC CATIONS OF THE WECS W Power Elecctronic System M Maximum Outputt Power

Po=6 kW

D Dc link voltage

Vdcc=700 V

G Grid rms line volttage

Vi=380 V

G Grid frequency

660 Hz

S Switching frequenncy

221 kHz bine and PMSG Wind Turb

Modeel G Generator type N Number of poles R Rotor diameter M Mechanical powerr control S Steering mechanissm N Number of bladess

VERNE5555 by Enersud Axial--flux PMSG 30 55.55 m Spring-based active stall contrrol associated to aan electronic systeem Ruddder-type Three twisty blaades, with five airrfoils alongg the profile

Fig. 12. Phase voltaage van (100 V/diiv., 5 ms/div.) annd phase angle θPLL (1 V/diiv., 5 ms/div.) undder steady-state operation o and rated condition.

Figg. 13. Phase volltage van (100 V//div., 5 ms/div.) and phase angle θPLL (1 V//div., 5 ms/div.) w when the frequenccy varies from 45 Hz to 85 Hz.

Fig. 15. Currents injected i in the ppower grid after filtering (5 A/ddiv., 5 ms/ddiv.).

Fig. 14 andd Fig. 15 coorrespond to the phase cuurrents beefore and aftter the low-ppass filter, respectively, r w where id__ref(rms)=0 andd iq_ref(rms)=9.009 A. It cann be seen thaat the cuurrents are nearly sinusoidaal in both casses, while thee total haarmonic distorrtion of the cuurrents injected in the poweer grid is THDI=1.639% %. In order to validate the proper operaation of the control loop responsible for regulatinng the dc-linkk voltage at 4400 V, load steps from 2.4 kW to 1.22 kW are applied to the systtem as seeen in Fig. 17. It can be seeen that the seettling time is about 1220 ms, while existing oveershoot is low wer than 10% %. The acctive power injjected in the ppower grid varries according to the wiind speed, whhich is only poossible if the voltage across tthe dc linnk remains constant. Besiddes, the curreent remains nearly n sinnusoidal as deesired. Fig. 16. Phase currennt (5 A/div., 5 ms/div.) and phase voltage (100 V/ddiv., 5 ms/ddiv.).

Figg. 14. Currents injected in the ppower grid withoout filtering (5 A/div., A 5 mss/div.).

The self-conntrol strategy is able to prrovide power factor coorrection and keep the phaase currents nnearly sinusoiddal as seeen in Fig. 188, where the rms phase current c is 5 A and TH HDI=2.6%. Besides, it cann be seen thaat the rms innduced cuurrent and rmss induced voltaage in the PMS SG are 5 A annd 220 V in Fig. 19, w while the inputt power is neaarly 3.3 kW annd the inpput power facctor is 0.942.

Fig. 17. Behavior off the dc-link voltaage (100 V/div., 5 ms V/div.) and phase p and negattive load steps. currrent (10 A/div., 5 ms/div.) during positive

Since the dc--link voltage remains r consttant at Vdc=4000 V, the efficiency cuurves for the rrectifier, inverrter and the whole w WE ECS have beenn obtained acccording to Fig.. 20. It can be seen thatt the rectifier presents highher efficiencyy than the invverter for the entire opeerating range. This fact can bbe explained since s the switching loosses in the semiconducttors of the ddc-ac

coonverter are higher than thoose regarding the rectifier. If the dcc-link voltage is increased to 700 V annd the input power p asssumes 6 kW W, efficiency regarding thee rectifier annd the inverter are suppposed to incrrease up to 98.67% and 966.94% acccording to thheoretical calculations assoociated to thee real chharacteristics oof the semiconnductors used in the experim mental prrototype. Connsidering thhe analyzed scenario, ooverall effficiency is higgher than 90% % when the inpput power is hhigher than about 1.3 kkW.

B. Simulation Reesults on The M Mechanical Power P Controll According to the characterristic curve of the turbine shhown in F Fig. 6, in ordeer to extract thhe maximum ppower at 6 m/ss, the shaaft angular sppeed must bbe =17.2 raad/s, resultingg in Pmeec(max)=1.132 kW. Analoogously, =22.9 rad/s and Pmeec(max)=3.111 W at 8 m/s annd =28.6 radd/s and Pmec(mmax)=6 kW W at 10 m/s. M MPPT is achhieved satisfacctorily in Fig. 21, wheere the maxim mum power iss extracted as defined in Fig. 6 for distinct wind speeds. Besiddes, it can be seen that the poower coeefficient is maxximum and eqqual to 0.41 ovver the entire w wind speeed range. When the winnd speed increeases, the torqque imposed byy the turbbine becomes higher than tthe resistant toorque, causingg the anggular speed of the wind tuurbine to incrrease. The M MPPT algoorithm is respponsible for increasing thhe resistant toorque undder this condiition, which ccauses the geenerator currennt to incrrease as seen in Fig. 22. T The peak curreent increases from 4.28 A to 6.63 A, A while the rm ms voltage inccreases from 342.5 3 V tto 431.7 V sinnce Ei(peak)=k., while thee power proceessed by the converteer increases from 2.83 kW k to 5.80 kW windings. Bessides, connsidering the I2R loss in the PMSG w pow wer factor is 0.997 and TH HDI=1.65% under u rated poower conndition.

Figg. 18. PMSG phaase currents (5 A//div., 5 ms/div.).

In order to vverify the perfformance of tthe control syystem represented in F Fig. 8, the WE ECS operationn above the rrated winnd speed is eevaluated as shown in Fig. 23. At 8 m/s, maxximum pow wer is suppoosed to be extracted, and connsequently ki= =ki(mppt) since ki(mppt)