İSTANBUL TECHNICAL UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY MODELING AND CONTROL OF VARIABLE-SPEED DIRECT-DRIVE WIND POWER PLANT

Transcription

1 İSTANBU TECHNICA UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOOGY MODEING AND CONTRO OF VARIABE-SPEED DIRECT-DRIVE WIND POWER PANT M.S. The by Yuuf GÜRKAYNAK Department : Programme: Electrcal Engneerng Control an Automaton Engneerng AUGUST 6

2 İSTANBU TECHNICA UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOOGY MODEING AND CONTRO OF VARIABE-SPEED DIRECT-DRIVE WIND POWER PANT M.S. The by Yuuf GÜRKAYNAK (5449) Date of ubmon : 4 Augut 6 Date of efence examnaton: 6 Augut 6 Supervor (Charman): Member of the Examnng Commttee At. Prof. Dr. Denz YIDIRIM At. Prof. Dr. event OVACIK At. Prof. Dr. Tarık DURU (KÜ.) AUGUST 6

3 PREFACE The power wthout control not a power. Thee wor whch come from an avertement for a tre traemark are my tuy phloophy on my acaemc tue. Power all aroun u n fferent form an they are meanngle wthout coner. Takng power uner control wll make power ueful for human. By workng on th the my am wa to make one more tep to control the wn power or energy, an make th energy more relable for the human. I woul lke to ay thank you to my famly an to my fren who alway upporte me, to my profeor who eucate me n my 6 year of unverty lfe. Specal thank to my upervor Atant Prof. Dr. Denz YIDIRIM, who helpe me to acheve th the n a lmte tme. atly I woul lke to ay thank to TUBİTAK-BAYG for ther cholarhp urng my grauate tuy. Augut-9 Yuuf GÜRKAYNAK

4 CONTENTS PREFACE ABBREVIATIONS IST OF FIGURES IST OF SYMBOS ÖZET SUMMARY. INTRODUCTION. Generator an Topologe.. Synchronou Generator... Woun Fel Synchronou Generator (WFSG)... Permanent-Magnet Synchronou Generator.. Inucton Generator... Doubly Fe Inucton Generator (DFIG)... Squrrel Cage Inucton Generator (SCIG). Varou Type of MPPT for Dfferent Topologe.. Mappng Power Technque.. Hll Clmbng.. Varyng Duty Rato Metho. The Selecte Topology. MODEING OF THE SEECTED TOPOOGY. Introucton.. Whte Box Moelng.. Black Box Moelng.. Grey Box Moelng. Wn Turbne Moelng.. Wn Stream Power.. Mechancal Power Extracte From the Wn.. Drve Tran (Shaft) Moel (Dynamc Moel)..4 Relaton Between Statc an Dynamc Moel of Wn Turbne. Moelng of Permanent Magnet Synchronou Machne.. Wnng Inuctance an Voltage equaton.. The Permanent Magnet nkage.. The Torque Equaton..4 Reference-Frame Theory v v v x x

5 ..5 Retve Element..6 Inuctance Element..7 Magnet Element..8 Iea to Fn Out the Parameter of Voltage Equaton..8. Determnng the Permanent magnet flux..8. Determnng the Retance, Quaratc an Drect Axe Inuctance.4 Moelng of Uncontrolle Rectfer.4. Introucton.4. Iealze Crcut wth Zero Source Inuctance.4. Effect of On Current Commutaton.5 Inverter Moel. CONTRO OF THE SEECTED TOPOOGY. The Tak of the Control Sytem. Hytere Current Controller.. Varable Swtchng Frequency Controller.. Contant Swtchng Frequency Controller. MPPT.. The Wn Turbne Stable Workng Pont.. Some Control Scenaro... If Wn Spee Up... If Wn Slow Down.. The Flow Dagram of The MPPT..4Calculaton of the New Current Reference..4. Steepet Decent Algorthm a a ne Search Metho..4. Steepet Decent Algorthm n MPPT 4. SIMUATION RESUTS an COMMENTS 4. Frt Scenaro 4. Secon Scenaro 4. General Smulaton Reult 5. CONCUSION REFERENCE RESUME v

6 ABBREVIATIONS AEP ARMA CC DFIG EMI FOC MPPT PCC PMSG PRBS PWM-VSI SCIG SG WECS WFSG WTS : Annual Energy Proucton : Auto Regreve Mean Average : Current Controller : Doubly Fe Inucton Generator : Electromagnetc Interference : Fel Orentaton Control : Maxmum Power Pont Tracker : Pont of Common Couplng : Permanent Magnet Synchronou Generator : Peuo Bnary Sequence Sgnal : Pule Wth Moulaton Voltage Source Inverter : Squrrel Cage Inucton Generator : Synchronou Generator : Wn Energy Converon Scheme : Woun Fel Synchronou Generator : Wn Turbne Sytem v

7 FIGURE IST Fgure. Fgure. Fgure. Fgure.4 Fgure.5 Fgure.6 Fgure.7 Fgure.8 Fgure.9 Fgure. Fgure. Fgure. Fgure. Fgure.4 Fgure.5 Fgure.6 Fgure.7 Fgure.8 Fgure. Fgure. Fgure. Fgure.4 Fgure.5 Fgure.6 Fgure.7 Fgure.8 Fgure.9 Fgure. Fgure. Fgure. Fgure. Fgure.4 Fgure.5 Fgure.6 Fgure.7 : Conventonal Danh Concept Wn Power Plant.. : The Torque-pee curve of Inucton Machne.. : The Gr Connecton of a Squrrel Cage Inucton Generator... : Woun Fel Synchronou Generator.. : Permanent-Magnet Synchronou Generator wth boot converter : Permanent-Magnet Synchronou Generator wth 4 quarant converter... : Doubly Fe Inucton Generator (DFIG). : Doubly fe full-controlle nucton generator Page No : Squrrel Cage Inucton Generator (SCIG)... : Block Dagram of the Senorle WECS Controlle Sytem.. : Precte Caharactertc (c power-tator frequency) of the WECS : Precte Caharactertc (c power-c voltage) of the WECS : Rotor Power P veru Rotor Spee n : The Flowchart of MPPT Whch Ue Hll Clmbng Technque.. : The Propoe Sytem for Varyng Duty Rato Technque : General Wn Turbne Charactertc... : Maxmum Power Trackng Control Metho. : Selecte Topology. : Wn pee before an after wn turbne.. : Power Coeffcent-pee rato.. : Wn Turbne Blae. : Turbne Curve for fferent type of wn turbne : Cp-λ curve for fferent blae angle... : An example of a turbne charactertc an fferent wn pee wth tall control. : The ynamc moel of the rve tran.. : Bac Structure of a Two Pole PMSG... : The abc an q frame.. : General Crcut Dagram of Rectfer... : Iealze Crcut Dagram : Dc bu voltage... : Phae current : Rectfer Crcut Dagram wth Current Commutaton : Curret Commutaton.. : Crcut Moel of Uncontrolle Rectfer... : The Bac Structure of the Phae Inverter v

8 Fgure. Fgure. Fgure. Fgure.4 Fgure.5 Fgure.6 Fgure.7 Fgure 4. Fgure 4. Fgure 4. Fgure 4.4 Fgure 4.5 Fgure 4.6 Fgure 4.7 Fgure 4.8 Fgure 4.9 Fgure 4. Fgure 4. Fgure 4. Fgure 4. Fgure 4.4 Fgure 4.5 Fgure 4.6 Fgure 4.7 Fgure 4.8 Fgure 4.9 Fgure 4. Fgure 4. Fgure 4. Fgure 4. Fgure 4.4 Fgure 4.5 Fgure 4.6 Fgure 4.7 : Hytere Control Crcut Dagram.. : Hytere Ban an Current waveform... : The nterecton of power reference wth the turbne curve. : The change of workng pont n the cae of pee up of the wn : The change of workng pont n the cae of low own of the wn... : The flow chart of MPPT... : An example of teepet algorthm mnmum earch. : Matlab Moel of the Topology. : Turbne Moel n Matlab.. : Graph of Power Coeffcent.. : Graph of Torque Coeffcent. : Matlab Moel of the Sytem Wth the Controller. : Wn Spee Change over tme.. : Mechancal Power Curve for m/ wn pee.. : Mechancal Power Curve for 4 m/ wn pee.. : Reference Current over Tme : Mechancal Power of the Generator over tme. : Delta Value Calculate by the MPPT.. : Actve Power n Electrcal Se : DC nk Voltage... : Rotor Spee over Tme. : Wn Spee Change over tme. : Mechancal Power Curve for m/ Wn Spee : Mechancal Power Curve for 9 m/ Wn Spee.. : DC nk Voltage over Tme. : Dervatve of DC nk Voltage. : Reference Current Calculate by MPPT... : Mechancal Power of the Turbne. : Delta Value over Tme : Actve Power of Electrcal Se : The Rotor Spee of the Generator : An Example Phae Voltage an Current. : FFT Analy of Phae Current wth Contant Swtchng Frequency.. : FFT Analy of Phae Current wth Varable Swtchng Frequency v

9 IST OF SYMBOS α B β C p,c Г g I ref K l j l λ λ f λ N p P t r R R c R S T e g r t ω g ω r ω t v,v V V V : earnng coeffcent : Dampng factor of haft : Blae angle : Power an torque coeffcent : Ar gap length : th phae current : Reference current : Stffne of the haft : Rotor length : Self nuctance of the th phae wnng : Mutual nuctance between th an j th phae wnng : nkage nuctance : Source nuctance : Tp pee rato : Maxmum value of the permanent magnet flux lnkage : Stator th phae total flux lnkage : Number of turn n a tator phae wnng : Number of par of pole : Turbne mechancal power : Rotor rau : Blae length : Rectfer equvalent crcut retance : Stator phae retance : th wtch logc poton : Inuce torque : Generator angular poton : Rotor angular poton : Turbne angular poton : Generator angular velocty : Rotor angular velocty : Turbne angular velocty : Wn pee before an after wn turbne : Rectfer equvalent crcut output voltage : Rectfer equvalent crcut average voltage : ne to lne phae voltage v

10 DOĞRUDAN SÜRÜŞÜ, DEĞİŞKEN HIZI RÜZGAR ENERJİ SANTRAİNİN MODEENMESİ VE KONTROÜ ÖZET Günümüze en öneml problem ve tab k en büyüğü enerjye olan htyaçtır. Bu htyacı karşılayacak br çok yöntem varken, araştırmacılar günümüze yenleblr enerj kaynaklarını çeren çözümlere ağırlık vermştr. Bunun ebeb bu kaynakları ınırız olmaı ve oğaya herhang br zararının olmamaıır. Bu tezn amacı bu kaynaklaran br olan rüzgaran makmum enerjy alma yöntemlernen brn ncelemek ve gerçekleneblrlğn relemektr. Bu bağlama lk kııma gelenekel rüzgar türbnlerne ve günümüze kullanılan eğşken hızlı rüzgar türbnlerne genel bakış yapılmış ve lteratüre geçen bazı MPPT yapıları anlatılmıştır. İncelenmek üzere bat yapılı, eğşken hızlara çalışablme özellğne ahp ve şl kutuuna htyaç uymayan br topoloj eçlmştr. Bu topoloje generatör olarak oluk genşlğ, kutup ayıını artırablmek çn uygun olan, fırçaız olmaınan olayı bakımı az olan abt mıknatılı enkron makne eçl. İknc kııma e eçlen bu topolojek kontrolüz tam alga oğrultucu, türbn, enkron makne ve evrcye at moeller beyaz kutu moelleme yöntemyle moellenmştr. Üçüncü kııma bu temn optmum şekle çalışmaı çn br MPPT algortmaı önerlmştr. Bu algortma br en yleme yöntem olan baamakal artım (tepeet ecent) yöntemn ve an hız eğşmlerne göre karar verecek alları barınırmaktaır. Evrcy enetlemek çn, br akım enetleyc olan hterez enetleyc eçlmştr. Bu enetleyc gerekl emrler MPPT en alacak ve bu emr evrcy kullanarak teme uygulayacak şekle çalışır. Bu enetleycnn özellkler ayanıklı olmaı, avranışının tem katayılarınan bağımız olmaı, geçc hal avranışı götermeme ve güç faktörünü bağımız olarak eğştreblmer. Son kııma e eçlen topoloj, önerlen enetleyc temyle beraber br benzeteç programına (Matlab-Smulnk) kurulu. Farklı rüzgar eğşm enaryoları çn benzeteç programı koşturulu. Çıkan onuçlaran enetleme temn tenlen bçme çalıştığı, tem her halükara kararlı tuttuğu, en yükek güç noktaını küçük br hatayla yakalaığı gözlen. Bu hatanın en büyük eğer KW turbn gücü çn 4 W oluğu görülü. Son kııma, önerlen bu enetleme temn yleştrmek ve gelştrmek çn gereken yöntemler anlatılı. x

11 MODEING AND CONTRO OF VARIABE-SPEED DIRECT-DRIVE WIND POWER PANTS SUMMARY Nowaay the mot mportant problem an alo the bgget one the nee of energy. Although there are everal oluton to th problem, reearcher heae towar workng on the oluton wth renewable ource, becaue thee kn of ource are harmle to the envronment an they are lmtle. The am of th the to nvetgate the wn energy whch a renewable ource, an to examne one of the way or metho to harvet the maxmum energy from the wn. On th way, n the frt part an overvew gven for conventonal wn turbne an for everal varable pee wn power plant whch are currently n ue, then ome MPPT technque are ntrouce. After that, a topology whch ha bac tructure, ha the ablty of workng uner varable rotor pee an oe not employ gearbox, electe. For th topology PMSG electe a the generator whoe mantenance cot are low, becaue of t bruhle tructure. At the econ part, the component of th topology manly uncontrolle rectfer, wn turbne, PMSG an nverter are moele by whte box approach. At the thr part an algorthm (MPPT) whch rect the ytem to work at the optmum pont, uggete. Th algorthm cont of teepet ecent optmzaton algorthm an ome part whch wll keep the ytem table uner uen change n wn pee. Hytere controller electe a the current controller for the control of the nverter. The beneft of th controller that, t robut, t behavor nepenent from ytem parameter an t can control the power factor nepenently. At lat part the electe topology wth the propoe control ytem bult on the mulator (Matlab-Smulnk) an ome cenaro of uen wn change are nvetgate. It oberve that for each cenaro, control ytem worke properly, kept the ytem table an MPPT foun the optmum pont each tme. The maxmum error of the MPPT 4 W for KW turbne power. At lat ecton, to mprove the control ytem, new metho an new approache are ntrouce. x

12 . INTRODUCTION Global warmng ha been attrbute to the ncreae of the greenhoue ga concentraton prouce by the burnng of fol fuel. Wn power generaton an mportant alternatve to mtgate th problem manly ue to t maller envronmental mpact an t renewable charactertc that contrbute for a utanable evelopment. Three factor have mae wn power generaton cotcompettve, thee are: () The tate ncentve () The wn nutry that have mprove the aeroynamc effcency of wn turbne () The evoluton of power emconuctor an new control methoology for the varable-pee wn turbne that allow the optmzaton of turbne performance. Nowaay, varou wn turbne ytem (WTS) compete n the market. They can be gathere n two man group. ()Danh concept wn power plant ()Varable-pee wn power plant The frt group operate wth almot contant pee Danh concept []. In th Danh concept cae, the output of generator rectly connecte to utlty. The man component can be ummarze a follow []. Anemometer: Meaure the wn pee an tranmt wn pee ata to the controller. Blae: Mot turbne have ether two or three blae. Wn blowng over the blae caue the blae to "lft" an rotate. Brake: A c brake whch can be apple mechancally, electrcally, or hyraulcally to top the rotor n emergency tuaton.

13 Controller: The controller tart up the machne at wn pee of about. to 6.6 meter per econ [m/] an hut off the machne at about m/. Turbne cannot operate at wn pee above about m/ becaue ther generator coul overheat. Fgure.: Conventonal anh concept wn power plant [] Gear box: Gear connect the low-pee haft to the hgh-pee haft an ncreae the rotatonal pee from about to 6 revoluton per mnute (rpm) to about to 5 rpm whch the rotatonal pee requre by mot nucton generator to prouce electrcty. The gear box a cotly (an heavy) part of the wn turbne an engneer are explorng "rect-rve" generator that operate at lower operatonal pee that o not requre gear boxe. Generator: An off-the-helf nucton generator that prouce 5-cycle AC electrcty uually employe. The pee-torque curve gven n Fgure.. The ntermttent ahe lne whch eparate the generator an motor regon, how the operatng pont of the generator. Hgh-pee haft: The part of the rve tran connecte to the generator. ow-pee haft: The rotor turn the low-pee haft at about to 6 rpm.

14 Nacelle: The rotor attache to the nacelle, whch t atop the tower an nclue the gear box, low- an hgh-pee haft, generator, controller, an mechancal (k) brake. A cover protect the component ne the nacelle. Some nacelle are large enough for a techncan to tan ne whle workng. Ptch: Blae are turne, or ptche, out of the wn to keep the rotor from turnng n wn pee that are too hgh or too low to prouce electrcty. Rotor: The blae an the hub together are calle the rotor. Fgure.: The torque-pee curve of nucton machne [] Tower: Tower are mae from tubular teel or teel lattce. Becaue wn pee ncreae wth heght, taller tower enable turbne to capture more energy an generate more electrcty. Wn recton: Th an "upwn" turbne, o-calle becaue t operate facng nto the wn. Other turbne are egne to run "ownwn", facng away from the wn. Wn vane: Meaure wn recton an communcate wth the yaw rve to orent the turbne properly wth repect to the wn.

15 Yaw rve: Upwn turbne face nto the wn; the yaw rve ue to keep the rotor facng nto the wn a the wn recton change. Downwn turbne o not requre a yaw rve, the wn blow the rotor ownwn. Yaw motor: Power the yaw rve. Fgure.: The Gr Connecton of a Squrrel Cage Inucton Generator [] The econ one operate wth varable pee; In th cae, the generator oe not rectly couple the rve tran to gr. Thereby, the rotor permtte to rotate at any pee by ntroucng power electronc converter between the generator an the gr. The contant pee confguraton characterze by tff power tran ynamc ue to the fact that electrcal generator locke to the gr; a a reult, jut a mall varaton of the rotor haft pee allowe. The contructon an performance of th ytem are very much epenent on the mechancal charactertc of the mechancal ubytem, ptch control tme contant, etc. In aton, the turbulence an tower haow nuce raply fluctuatng loa that appear a varaton n the power. Thee varaton are unere for gr-connecte wn turbne, nce they reult n mechancal tree that ecreae the lfetme of wn turbne an ecreae the power qualty. Furthermore, wth contant pee there only one wn velocty that reult n an optmum tp-pee rato. Therefore, the wn turbne often operate off t optmum performance, an t generally oe not extract the maxmum power from the wn. Alternatvely, varable pee confguraton prove the ablty to control the rotor pee []. Th allow the wn turbne ytem to operate contantly near to t optmum tp-pee rato. The followng avantage of varable-pee over contantpee can be hghlghte: 4

16 () The Annual Energy Proucton (AEP) ncreae becaue the turbne pee can be ajute a a functon of wn pee to maxmze output power. Depenng on the turbne aeroynamc an wn regme, the turbne wll on average collect up to % more annual energy [] () The mechancal tree are reuce ue to the complance to the power tran. The turbulence an wn hear can be aborbe,.e., the energy tore n the mechancal nerta of the turbne, creatng a complance that reuce the torque pulaton () The output power varaton omewhat ecouple from the ntantaneou conton preent n the wn an mechancal ytem. When a gut of the wn arrve at the turbne, the electrcal ytem can contnue elverng contant power to the network whle the nerta of mechancal ytem aborb the urplu energy by ncreang rotor pee. (v) Power qualty can be mprove by reucng the power pulaton. The reucton of the power pulaton reult n lower voltage evaton from t rate value n the pont of common couplng (PCC). (v) The ptch control complexty can be reuce. Th becaue the ptch control tme contant can be longer wth varable pee (v) Acoutc noe are reuce. The acoutc noe may be an mportant factor when ntallng new wn farm near populate area. Although the man avantage of the varable-pee confguraton are the atonal cot an the complexty of power converter requre to nterface the generator an the gr, t ue ha been ncreang tealy ue to the above mentone avantage.. Generator an Topologe.. Synchronou Generator A ynchronou generator uually cont of a tator holng a et of three-phae wnng, whch upple the external loa, an a rotor that prove a ource of magnetc fel. The rotor magnetc fel may be upple ether from permanent magnet or from a rect current flowng n a col []. 5

17 ... Woun Fel Synchronou Generator (WFSG) Fgure.4: Woun fel ynchronou generator [] The WPS wth woun fel ynchronou generator hown n Fgure.4. The tator wnng connecte to utlty through a four-quarant power converter compre of two back-to-back PWM-VSI. The tator e converter regulate the electromagnetc torque, whle the upply e converter regulate the real an reactve power elvere by the WPS to the utlty. The Woun Fel Synchronou Generator ha the followng avantage []: The effcency of th machne uually hgh, becaue t employ the whole tator current for the electromagnetc torque proucton The man beneft of the employment of woun fel ynchronou generator wth alent pole that t allow the rect control of the power factor of the machne, conequently the tator current may be mnmze out any operaton ntance. The pole ptch of th generator can be maller than that of nucton machne. Th coul be a very mportant charactertc n orer to obtan low pee multpole machne, elmnatng the gearbox. The extence of a fel wnng n the rotor may be a rawback a compare wth permanent magnet exctaton. In aton, to regulate the actve an reactve power generate, the converter mut be ze typcally. tme the WPS rate power. 6

18 ... Permanent-Magnet Synchronou Generator Fgure.5: Permanent-magnet ynchronou generator wth boot converter []. Fgure.5 how a WPS where a permanent magnet ynchronou generator connecte to a three-phae rectfer followe by a boot converter. In th cae, the boot converter control the electromagnetc torque. The upply e converter regulate the DC lnk voltage a well a control the nput power factor. One rawback of th confguraton the ue of oe rectfer that ncreae the current ampltue. A a reult th confguraton ha been conere for mall ze WPS (maller than 5 kw) []. Fgure.6: Permanent-magnet ynchronou generator wth four quarant converter []. 7

19 Other cheme ung PMSG hown n Fgure.6, where, the PWM rectfer place between the generator an the DC lnk, an PWM nverter connecte to the utlty. The avantage of th ytem regarng the ytem hown prevouly the ue of fel orentaton control (FOC) that wll allow the generator to operate near t optmal workng pont n orer to mnmze the loe n the generator an power electronc crcut. However, the performance epenent on the goo knowlege of the generator parameter that vare wth temperature an frequency. The man rawback, n the ue of PMSG, are the cot of permanent magnet that ncreae the prce of the machne, emagnetzaton of the permanent magnet an t not poble to control the power factor of the machne []... Inucton Generator The AC generator type that ha mot often been ue n wn turbne the nucton generator. There are two kn of nucton generator ue n wn turbne that are: qurrel cage an woun rotor [].... Doubly Fe Inucton Generator (DFIG) The wn power ytem hown n Fgure.7 cont of a oubly fe woun-rotor nucton generator (DFIG), where the tator wnng rectly connecte to the utlty an the rotor wnng connecte to the gr through a four quarant power converter compre of two back-to-back PWM-VSI. The SCR bae converter can alo be ue but they have lmte performance. Fgure.7: Doubly fe nucton generator (DFIG) []. 8

20 Uually, the controller of the rotor e converter regulate the electromagnetc torque an upple part of the reactve power to mantan the magnetzaton of the machne. On the other han, the controller of the upply e converter regulate the DC lnk. Compare to ynchronou generator, th DFIG offer the followng avantage []: Reuce nverter cot, becaue nverter ratng typcally 5% of the total ytem power. Th becaue the converter only nee to control the lp power of the rotor Reuce cot of the nverter flter an EMI flter, becaue flter rate for.5 p.u. total ytem power, an nverter harmonc repreent a maller fracton of total ytem harmonc Robutne an table repone of th machne facng agant external turbance. One rawback of DFIG the ue of lp rng that requre peroc mantenance, epecally at ea hore te. The WPS of Fgure.8 how a oubly fe fully-controlle nucton generator, wth a c-tranmon lnk. Th type of WPS allow controllng the voltage an frequence of the rotor an tator, conequently th ytem prove a hgher flexblty on the control ytem than the conventonal oubly-fe nucton generator hown n prevou Fgure.7. In aton, th WPS ha been conere for offhore te, whch are connectng to lan by ubmarne cable. There are other metho of nterface the DFIG to the gr. Among them, are: () Cycloconverter () Matrx converter However they have ome avantage over the one preente n Fgure.7, thoe are: poor lne power factor, hgh harmonc torton n lne an machne current for a cycloconverter an for a matrx converter, epte elmnaton of the c capactor, th converter more complex an t technology le mature. 9

21 Fgure.8: Doubly fe full-controlle nucton generator [].... Squrrel Cage Inucton Generator (SCIG) Fgure.9: Squrrel cage nucton generator (SCIG) []. A WPS wth qurrel cage nucton generator hown n Fgure.9. The tator wnng connecte to utlty through a four-quarant power converter compre of two PWM VSI connect back-to-back trough a DC lnk. The control ytem of the tator e converter regulate the electromagnetc torque an upple the reactve power to mantan the machne magnetze. The upply e converter regulate the real an reactve power elvere from the ytem to the utlty an regulate the DC lnk. The ue of qurrel cage nucton generator have ome avantage []: The qurrel cage nucton machne extremely rugge; bruhle, relable, economcal an unverally popular, Fat tranent repone for pee poble,

22 The nverter can be operate a a VAR/harmonc compenator when pare capacty avalable, Among the rawback are: Complex ytem control (FOC) whoe performance epenent on the goo knowlege of the generator parameter that vare wth temperature an frequency. The tator e converter mut be overze -5% wth repect to rate power, n orer to upply the magnetzng requrement of the machne [].. Varou Type of MPPT for Dfferent Topologe MPPT (maxmum power pont tracker) an algorthm that egne to control the power flow n the wn power plant uch a way that, the generate power houl be a hgh a poble at every wn pee. In bac, MPPT a block that ha nput from the ytem meaurement (rotor pee, frequency, c voltage, c current ) an ha an output of new reference of the ytem (ytem workng pont). By ung the meaurement, t calculate or fn out the new operatng pont for the ytem. The algorthm ne the MPPT epen on the topology of the plant. In the followng, ome example of propoe MPPT tructure for fferent wn power plant wll be ntrouce... Mappng Power Technque Th bae on the look up table, that MPPT etermne the workng pont of the ytem by ung the prevouly prepare table ntea of makng calculaton, jut lke an explorer who fn h way by ung a map. An example for th technque gven below n Fgure.. Th topology cont of wn turbne, PMSG, uncontrolle rectfer an nverter. Inverter controlle to keep the c voltage value equal to the operatng voltage. The block agram hown n Fgure., the prelmnary egn of the enorle WECS controlle ytem. In the prelmnary egn tage, the ytem oe not nclue the mnmum c lnk voltage lmtaton, cut-n an cutout wn pee control feature. The control ytem cont of two gnal-trackng loop, namely the power-mappng" loop an generator frequency ervatve loop. The trackng gnal

23 requre for both loop are the output power from the WECS that tranferre to the c lnk an PMSG tator frequency [4]. Fgure.: Block agram of the enorle WECS controlle ytem [4] Increae n wn pee Fgure.: Precte charactertc (c power-tator frequency) of the WECS [4]. It recognze that the nverter ha the flexblty to operate over a we range of DC nput voltage. At a gven wn pee, the output DC lnk power ue to etmate the optmal DC operatng voltage from the "power-mappng" maxmum power v. DC voltage curve hown n Fgure.. Due to the entvty of P c to the change n V c for the PMSG, the P c an thev c wll contnue to ncreae or

24 ecreae tll the nterecton of Pc an V c at the maxmum power for the gven wn pee [4]. Increae n wn pee Fgure.: Precte charactertc (c power-c voltage) of the WECS [4] The tator frequency wll alo be changng (ncreang or ecreang) urng the change of the operatng c voltage. In the alternator frequency ervatve loop, the ervatve control acton prove a mean of obtanng the controller wth hgher entvty. Th ervatve control repon to the rate of change of the tator frequency (Fgure.) an can prouce a gnfcant correcton to the operatng DC voltage. The gan value from frequency ervatve loop wll become zero when the operatng c voltage optmal one whch lea to the maxmum power pont. Ung the reult etermne by both loop, the controller allow the DC bu voltage to vary to value correponng to the maxmum power operatng pont [4]... The Hll Clmbng Metho Th metho bae on changng the operatng pont of the ytem tep by tep. MPPT oberve the change on generate power an rotor pee. Accorng to thee change, t etermne whether to ncreae or ecreae the value of the et operatng pont of the plant at each amplng pero. The changng value of the reference can be a contant value or calculate value. An example for th kn of MPPT whch bae on the Fgure., gven below [5]:

25 The et pont nput of the pee control mut ncreae f, The rotor power P ncreae an the rotor pee ω act contant or ncreae, Both P an ω act ecreae. On the other han, the et pont nput mut ecreae f The rotor power P ecreae an the rotor pee ω act contant or ncreae, P ncreae an ω act ecreae. Fgure.: Rotor power P veru rotor pee n [5]. The flow chart of th kn of MPPT technque gven n Fgure.4. A een from the chart, lope (change n reference) ha a contant value of [5]. Th technque oe not nee any prevou knowlege about the ytem. So that, the preparaton of a look up table or map not requre. On the other han, t requre meaurement of the rotor pee an contnuouly earche for the optmum pont wth a contant tep. If the ytem far away from the optmum operatng pont, t wll take o many tme to reach the optmum pont. Proce can be hortene by ung varable lope ntea of a contant one. 4

26 Fgure.4: The flow chart of MPPT whch ue hll clmbng technque [6]... Varyng Duty Rato Metho Th a pecal metho that t can only be ue for the topologe whch ue DC chopper behn the uncontrolle rectfer. It bae on applyng varable uty rato to the DC chopper whch control the pee of the generator by changng the effectve value of nput voltage of the uncontrolle rectfer. MPPT earche the optmum operatng pont by obervng ytem repone to the varyng uty rato. An example of th ytem gven n Fgure.5 [6]. Fgure.5: The Propoe Sytem for Varyng Duty Rato Technque [6] 5

27 The output power charactertc of wn turbne hown n Fgure.6. Thee charactertc curve are ve nto recton A an B by otte lne (maxmum power lne) Fgure.6: General Wn Turbne Charactertc [6] For example, when the operatng pont at a (when the uty at th pont) the uty rato change n the range between an contnuouly an lowly for earchng the maxmum power pont. In practcal, the uty of th chopper change lke n the Fgure.6 [6]. Fgure.7: Maxmum power trackng control metho [6]. 6

28 = m nωt (.) m = (.) = If operatng pont ext n the area A a hown n Fgure.6, the relatonhp of P > P atfe. If th pont n recton B P P > atfe. Then we etect the pont P an P, an etermne by the followng equaton [6]: = K p ( P P )t (.) In practce, the value of (the DC bu current) etecte an ample hol correponng to a an a from current tranformer. Fnally, the uty of the chopper obtane a follow: ( I I ) = K t (.4) In orer to realze an approprate experment, =. 5 an ω = 4π [ra/] are electe [6]. Th metho better than the other technque, becaue t oe not requre many meaurement, epecally there are no mechancal meaurement an t oe nee any nformaton or any knowlege about the ytem. On the other han, the control ytem too entve to meaurement error, o that a proper flter an hghly accurate current tranformer houl be choen. m. The Selecte Topology The electe topology for the wn power ytem gven n Fgure.7. The ytem connecte to the gr wth a ere of converter whch mean that ytem can work at fferent wn pee an alo mean that a MPPT algorthm whch comman the ytem to run at the optmum angular pee can be mplemente. The haft of the PMSG connecte rectly to wn turbne wthout a gearbox. Th wll elmnate the noe an the loe caue by the gearbox. The generator choen a a permanent magnet ynchronou generator, whch mean that the mantenance cot wll be low. The reactve power n the machne can not be controlle. Electronc e 7

29 cont of an uncontrolle rectfer, C flter whch wll flter the harmonc on the c bu an IGBT nverter whch can control the ampltue an the phae hft of the lne current meanng that nverter rectly control the actve an reactve power tranferre to the gr at contant lne voltage. Wn Turbne ~ PMSG C Uncontrolle Rectfer IGBT Inverter Gr Fgure.8: The electe topology for varable-pee wn turbne 8

30 . Moelng of the Selecte Topology. Introucton The mathematcal moelng of the real phycal ytem an mportant concept n many engneerng an cence cplne. The erve moel can be ue n mulaton, controller egn, an egn of a new proce wthout any phycal work. There three man group n moelng [4]: ) Whte box approach ) Black box approach ) Grey box approach.. Whte Box Moelng Conventonally moelng to unertan the nature an the behavor of the ytem an to tate them mathematcally. Th approach calle whte box moelng. For whte box moelng, phycal an chemcal law are ue. A an example n moelng of a electromechancal ytem, electrcal law (Krchoff voltage an current law, Faraay law, Ampere law, ), mechancal law (the contnuty of pace, Dalembert law, Newton law, ) an the conervaton of energy law are ue. For nonlnear an complex ytem, th type of moelng har an ometme mpoble. In general for complex ytem, ome aumpton can be one to reuce of the complexty [4]... Black Box Moelng It ue for phycally unknown ytem. The only mlarty between the moel an the phycal ytem the behavor of them for the ame nput, but nteror behavor almot fferent. Fuzzy an artfcal neural network moelng are an example for the black box [4]. 9

31 .. Grey Box Moelng Th the combnaton of both whte box an the black box moelng. The phycally well known or em-known part are moele lke whte box an unknown part are moele by black box. The common metho for grey box moelng are ytem entfcaton metho [4]. For moelng the electe topology, whte box approach wll be ue, but for etermnng the parameter or the coeffcent of the moel, ytem entfcaton experment can be one. It requre to make ome aumpton to reuce the complexty of the ytem. For electrcal converter e (nverter an rectfer) t aume that the emconuctor wtche are lole an wtchng are ntantaneou. For turbne e, t aume that the ma of nerta focue on a ngle pont (lumpe parameter moel). For generator e t aume that, the wnng n tator are trbute n a way that the flux n the ar gap n a nuoal form; there are no any aturaton, lot effect, hytere an kn effect; magnetc permeablty of the generator core nfnte an wnng retance an nuctance value are nepenent from temperature. The alency effect of the permanent magnet are neglecte an t aume that a ngle large magnet locate n rotor of the generator.. Wn Turbne Moelng.. Wn Stream Power The Knetc energy of ar a an object of ma m [kg] movng wth pee v [m/] equal to[5]: mv E = (.) The power of the movng ar (aumng contant wn velocty) equal to: P wn E = = mv (.) t

32 where m [kg/] the ma flow rate per econ. When the ar pae acro an area A [m ] (for example: the area wept by the rotor blae), the power of the wn can be compute a [5]: Pwn ρ Av = (.) where ρ (kg/m ) the ar enty whch epen on the ar temperature an ar preure. Accorng to ga law: p ρ = m m (.4) RT 5 m atm Where p [atm] the preure, R (8.57x ) mol K the ga contant, T [K] the temperature of ar an m m [kg/mol] molar ma of the ar [5]. The ar enty.55 kg/m uner the conton of atm ar preure an 5 o C ambent temperature... Mechancal Power Extracte From the Wn The wn energy a ecrbe can not be tranferre nto another type of energy wth % converon effcency by any energy converter. In fact, the power extracte from the ar tream by any energy converter wll be alo le than the wn power P wn becaue the power acheve by the energy converter P ww can be compute a the fference between the power n the movng ar before an after the converter [5] The ar tream cro-ecton area of movng ar before turbne A maller than the one after turbne A. P ww = Pwn Pwn = ρ ( Av Av ) (.5) From the Fgure. v the pee of the wn before the wn turbne, an v the pee of the wn after the wn turbne. Full converon of wn power requre that ar velocty after converter v become zero, whch phycally, make no ene, becaue t contran the ar to be tll an further t requre the ar velocty before the converter v to be equal to zero alo.

33 Fgure.: Wn pee before an after wn turbne [] The real energy converter mut be conere a a type of bulkhea. Then the flowng ar exert a force on the converter. The reult of beng that, the preure before the converter ncreae an multaneouly the ar velocty n front of the wn converter (v ' ) ecreae [5]. The force [N] exerte on the converter can be foun from the change of momentum. F m( v v ) = (.6) The extracte mechancal power by th force equal to: P WW = Fv ' ' = m( v v ) v (.7) Aumng that the ma flow rate contant, t can be een that the ar velocty through the converter equal to average of v an v. ' v = ( v v ) (.8) Then the mechancal power (P WW ) extracte from the ar tream by the energy converter equal to P WW = ρ A( v v )( v v ) (.9) 4 an t le than the power n the ar tream before the converter P wn. The equaton (.9) can alo be wrtten a follow:

34 P WW = C P C Av p wn = p ρ (.) where the coeffcent C p < (efnng the rato of the mechancal power extracte by the converter to the power n the ar tream) calle the power coeffcent (Betz factor). Th coeffcent equal to [5]: v v C p = (.) v v Fgure.: Power Coeffcent-Spee Rato From the Fgure., or by mply takng ervatve of C p wth repect to v /v an equatng t to zero, wll ncate a maxmum value of C p nearly.59. At th maxmum value, pee rato equal to v /v =/. Then n front of an behn the ' energy converter the wn pee equal to v = v /, v = / repectvely. v The power coeffcent of real converter C p acheve lower value than that of compute above, becaue of varou aeroynamc loe that epen on the rotor contructon (number an hape of blae, weght, tffne, etc.). The rotor power

35 coeffcent uually gven a a functon of two parameter: tp pee rato ( λ ) an the blae ptch angle ( β ). The blae ptch angle efne a the angle between the plane of rotaton an the blae cro-ecton chor (Fgure.). The tp pee rato λ efne a. u ωr λ = = (.) v v Fgure.: Wn turbne blae [] where u [m/] the tangental velocty of the blae tp, ω [ra/] the angular velocty of blae tp, R rotor rau or blae length. Fgure.4 can only be obtane by experment. A generc equaton ue to moel C p ( λ, β ). Th equaton bae on the moele turbne charactertc an gven a [6] c C (, ) p λ β = c cβ c λ.5 = λ λ.8β β 4 e c5 λ c λ 6 (.) 4

36 where c are the coeffcent whch epen on turbne type. For a three blae turbne the coeffcent c =.576, c = 6, c =.4, c 4 = 5, c 5 = an c 6 =.68 the C p - λ curve for fferent blae angle can be rawn lke n Fgure.5 [6]. In ome cae ptch control not ue, ntea the blae angle fxe to value zero (tall control). An example for a tall controlle wn turbne power agram gven n Fgure.6 [6]. Fgure.4: Turbne curve for fferent type of wn turbne [5] The moel of blae ptch control wll not be cue n th the. 5

37 Fgure.5: C p - λ curve for fferent blae angle [6] Fgure.6: An example of a turbne charactertc wth fferent wn pee wth tall control [6]. 6

38 .. Drve Tran (Shaft) Moel (Dynamc Moel) Wn turbne cont of many mechancal component. Each component ha t own ynamc behavor but the ynamc of the rve tran omnant to other part. Thu the ynamc moel of the rve tran can be a to be the ynamc moel of the whole turbne [5]. The rve tran of a wn turbne generator ytem n general cont of blae ptchng mechanm wth a pnner, a hub wth blae, a rotor haft an generator. The moment of nerta of the wn wheel (hub wth blae) about %9 of the rve tran total moment of nerta, whle the generator rotor moment of nerta equal to about 6-8%. The remanng part of the rve tran compre the ret (-4%) of the total moment of nerta [5]. The acceptable (an common) way to moel the WTGS rotor to treat the rotor a a number of crete mae connecte together by prng efne by ampng an tffne coeffcent. Therefore the equaton of the th ma moton can be ecrbe a follow [5]: J t δ T T T =,, B δ t (.4) where J the moment of nerta of th ma, δ (ra) toronal angle of th ma, T the external torque apple to th ma, T, an T, are the torque apple to th ma (from,(-) th an,() th haft repectvely), B the ampng coeffcent repreentng varou ampng effect. The torquet,, T can be wrtten a follow: T = K,, ) δ δ ( δ δ B, (.5) t t T = K,, ) δ δ ( δ δ B, (.6) t t where K,, K, are the tffne coeffcent of the haft ecton between ma,() th an,(-) th repectvely an B,, B, are the ampng coeffcent of the 7

39 haft ecton. By combnng thee equaton, equaton of moton of the th ma can be obtane [5]. δ J = t T K δ ( δ δ B, t, ) δ B t δ t K δ δ ( δ δ B, (.7) t t, ) For many type of analy, a et of frt-orer fferental equaton a ueful form of equaton becaue they can be wrtten n matrx form an can be olve ealy. Thu the equaton above take the form of thee two equaton: δ t = ω (.8) ω J = t T K B ( ω ω ), ( δ δ ), B ω (.9) K B ( ω ω ), ( δ δ ), Conerng the rve tran a contng of N crete mae, we obtan a et of N fferental equaton. It ffcult to olve thee equaton an alo to ugget a controller for the ytem. Therefore, lumpe parameter approach wll be ue to mplfy an to reuce the number of equaton. The mnmal realzaton of the rve tran moel utlze n the power ytem operaton analy bae on the aumpton of the two lumpe mae only. The tructure of the moel preente n Fgure.7. Tt ωt T K ωg Tg J t J g B Fgure.7: The ynamc moel of the rve tran t = ωt (.) t 8

40 9 g g t ω = (.) t J T T t t t ω = (.) t J T T g g g ω = (.) ) ( ) ( g t g t K B T ω ω = (.4) where g t, are the angular poton of turbne an generator haft, repectvely t ω g ω, are the angular pee of turbne an generator haft, repectvely, g t T T, are the torque that apple to haft by the turbne an generator, repectvely, T the net torque on the haft, B the ampng coeffcent of haft an K the tffne of the haft. By combnng thee equaton an wrtng them n tate pace, the followng matrx acheve: (.5) If we aume that the angular pee of generator an turbne equal, n general th equaton can be olve lke th: ( ) g g t g t T t J J T = ω (.6)..4 Relaton between Statc an Dynamc Moel of Wn Turbne In tatc moel of the turbne the relatonhp between the power of the turbne an pee of the turbne expree for a gven wn pee. A for ynamc moel, the relatonhp between the pee of the haft, the torque of the generator an the torque of the wn turbne erve. The relaton between torque an power of the turbne = g t g t g t g g g g t t t t g t g t T T J K J K J B J B J K J K J B J B t ω ω ω ω

41 whch houl be expree for a complete moel, mng. In general, the torque known a; T t P t = (.7) ω t From the power equaton of the turbne; T t.5c ρπr v.5c ρπr C p p p = = =.5ρπR v = CΓ ( λ).5ρπr v (.8) ω λv t λ R v In th equaton C Γ known a torque coeffcent whch a functon of tp pee rato for a contant blae angle [5]. A explane earler, there not an exact equaton for the power coeffcent. So that, many kn of mathematcal curve fttng technque are ue to reach uch an equaton from the meaurement of the experment. The kn of fttng equaton mportant for calculatng the torque coeffcent, becaue there zero over zero nefntene for the zero tp pee rato, an t a bg problem for the computer to calculate the torque coeffcent correctly. Thu, a polynomal wll be the bet choce to overcome th problem. The general polynomal form of the power coeffcent gven a flow; C n k = a λ (.9) p a k k = Where a are the coeffcent of the polynomal, an n the egree of the polynomal. For zero tp pee rato, C houl be zero. So that, a. From th p = equaton, the torque coeffcent can be calculate lke th. C n Γ = a k k = λ k (.) The wn velocty uually vare conerably, an ha tochatc character. Therefore, n general, the wn houl be moele a a tochatc proce, but for the analy of WTGS operaton n an electrc power ytem, the wn varaton can be

42 moele a a um of harmonc wth frequence n the range of.- Hz. Wn gut are uually alo nclue n the wn moel [5]. v( t) = v Ak n( ω kt) vg ( t) (.) k max ( ) = vg vg t 4(n( ω g ) ) (.) e t where v the mean value of the wn velocty, A k the ampltue of k th harmonc, ω the frequency (pulaton) of k th harmonc, v g (t) the pee of the k wn gut, v g max the gut ampltue an ω g the gut frequency. The gut ampltue vare up to m/ an the gut pero can be n the range of -5.. Moelng of Permanent Magnet Synchronou Machne.. Wnng Inuctance an Voltage equaton In a magnetcally lnear ytem the elf-nuctance of a wnng the rato of the flux lnke by a wnng to the current flowng n the wnng wth all other wnng current zero. Mutual nuctance the rato of flux lnke by one wnng ue to current flowng n a econ wnng wth all other wnng current zero nclung the wnng for whch the flux lnkage are etermne [7]. MMF efne a the lne ntegral of H (the magnetc ntenty) whch alo equal to multplcaton of number of turn (N) an the current (I) of the wnng. N = MMF = H l (.) In magnetc crcut, f t aume that the magnetc permeablty = µ µ ) of the ( µ r core nfnte, n the magnetc crcut the only reluctance caue by the ar gap, becaue the relatve magnetc permeablty of the ar one ( µ argap = µ ). So, from th approach MMF = µ H = µ (.4) g B

43 where B magnetc fel enty an g the ar gap length. The ar gap fel enty, ue to the current n the a wnng can be obtane by ettng the other current zero. For the Fgure.8, f t aume that the conuctor are locate to tator lot n uch a way that the number of turn of the conuctor n nuoal form through the ar gap, the ntantaneou MMF through the ar gap ha alo nuoal form. The trbuton of the a wnng may be wrtten [7] N = nφ φ π (.5) a N p N = nφ π φ π (.6) a N p where N p the maxmum turn or conuctor enty expree n turn per raan. If N repreent the number of turn of the equvalent nuoally trbute wnng then π N = N p nφ φ = N p (.7) b ax a c S b q ax ω r r a ax b N c c ax a ax Fgure.8: Bac tructure of a two pole PMSG. N not the total number of turn of the wnng whch woul re to ame funamental component a the actual wnng trbuton. Becaue of the rght han

44 rule, the angle between the current flow recton an magnetc fel recton 9 o. So that f the wnng trbuton n lke nuoal functon, the MMF functon wll be lke cone functon [7]. The MMF waveform of the equvalent a wnng MMF a N = a coφ (.8) In a mlar way: N π MMF b = b co φ (.9) N π MMF c = c co φ (.4) The total ar-gap MMF prouce by the tator current can be expree. Th can be obtane by ang the nvual MMF [8]. N π π MMF = a coφ b co φ c co φ (.4) The magnetc flux enty functon caue by each of the wnng can be foun. Thu the magnetc flux enty wth all other current are zero except a : N B = µ a coφ (.4) g Smlarly the flux enty functon wth all other current are zero except b : N π B = µ b co φ (.4) g An alo wth all current other than c zero. N π B = µ c co φ (.44) g

45 Flux lnkage of a ngle turn of a tator wnng whch pan π raan an whch locate at the angle φ can be conere [7]. In th cae the flux etermne by performng a urface ntegral over the open urface of the ngle turn. In partcular φ = π ) B( ξ ) φ Φ( φ rlξ (.45) where Φ the flux lnkng a ngle turn orente φ from the a ax, l the axal length of the ar gap of the machne, r the rau to the mean of the ar gap (eentally to the ne crcumference of the tator), an ξ a ummy varable of the ntegraton. In orer to obtan the flux lnkage of an entre wnng the flux lnke by each turn mut be umme. Snce the wnng are conere to be nuoally trbute an the magnetc ytem aume to be lnear, th ummaton may be accomplhe by ntegratng over all col e carryng current n the ame recton. Hence, computaton of the flux lnkage of an entre wnng nvolve a ouble ntegral [7]. A an example, n etermnng the total flux lnkage of the a wnng ue to current flowng only n the a wnng can be one lke th. λ a = l = l a a N N a a ( φ ) Φ( φ ) φ ( φ ) φ π φ B( ξ ) rlξ (.46) In Eq..46 l the tator leakage nuctance ue prmarly to leakage flux at the en turn. Generally th nuctance account for 5 to percent of the maxmum elf-nuctance [7]. λ π φ π N a = la nφ π φ = l a N πµ rl g N µ g a a coφ rl ξ φ (.47) The nterval of ntegraton taken from π to π o a to comply wth the conventon that potve flux lnkage are obtane n the recton of the potve a ax by crculaton of the aume potve current n the clockwe recton about 4

46 the col (rght han rule). The elf nuctance of the a wnng obtane by vng λ a by I a. aa N πµ rl = l (.48) g The mutual nuctance between the a an b wnng may etermne by the frt computng the flux lnkng the a wnng ue to current flowng only n the b wnng [7]. In th cae t aume that the magnetc couplng whch mght occur at the en turn of the wnng may be neglecte. Thu λ a = = N π π a ( φ ) φ π φ N nφ B( ξ ) rlξφ φ π φ N µ g b π co ξ rlξφ (.49) Therefore, the mutual nuctance between the a an b wnng etermne by vng λ a by I b. So th gve N π = µ rl (.5) g ab The other mutual an elf nuctance can be calculate n the ome manner. In general nuctance can be efne a A N πµ rl = (.5) g By ung th efnton the tator nuctance element can be expree lke th: = = = (.5) aa bb cc l A ab = ba = ca = ac = bc = cb = A (.5) The matrx form of the tator flux lnkage gven a: 5

47 6 I λ = = = c b a A l A A A A l A A A A l c b a λ λ λ (.54) Where the nuctance matrx an I the wnng current matrx... The permanent magnet lnkage PMSG ha permanent magnet tck whch are locate on the urface of the rotor wheel. In equvalent ytem t can be aume that the rotor cont of a ngle magnet whch can rotate aroun of t center. It alo aume that the conuctance of the magnet poor that the flux whch prouce by the tator current o not nuce a voltage on the magnet. So the mutual nuctance between tator an the magnet zero, or the magnet current zero. Th current wll not appear a a tate varable. Permanent magnet can be moele a a contant flux lnkage ource wth a contant value. The equvalent flux lnkage crcle by the phae wnng epen on the angle between the tator an the rotor magnetc ax r [7]. = = n n n π π λ λ λ λ r r r f rc rb ra r λ (.55) where f λ the maxmum value of magnet flux lnkage. So the total flux lnkage n the machne. = = n n n π π λ r r r f c b a A l A A A A l A A A A l λ λ r λ (.56) The voltage equaton for the PMSM

48 va λ V = v b = R I (.57) t v c R R = R (.58) R.. The Torque Equaton For a lnear magnetc ytem the torque nuce n ytem efne a the change of the energy n the magnetc couplng area accorng to poton of the rotor. Th mean that [8] T e W c = (.59) r W c = λ I (.6) So that, the torque equaton gven below. co r π Te = I co r λ f (.6) π co r ater th equaton wll equal tot g, whch efne n the ynamc behavor of the turbne...4 Reference-Frame Theory It can be clearly een that ome of the machne coeffcent of the fferental equaton (voltage equaton) whch ecrbe the behavor of th machne are tmevaryng except when the rotor talle. Change of varable ue to reuce the complexty of thee fferental equaton. There are everal change of varable whch are ue an t wa orgnally thought that each change of varable wa 7

49 8 fferent an therefore they were treate eparately. It wa later learne that all change of varable ue to tranform real varable are contane n one. Th general tranformaton refer machne varable to a frame of reference whch rotate at an arbtrary angular velocty. All known real tranformaton are obtane from th general tranformaton by mply agnng the pee of rotaton of the reference frame [7]. A change of varable whch formulate a tranformaton of the -phae varable of tatonary crcut element to the arbtrary reference frame may be expree abc q f K f = (.6) where K the tranformaton matrx between the frame, f abc the varable matrx whch are referre to abc frame an f q tranforme varable matrx whch are referre to q axe. The tranformaton matrx may have fferent form. The mot recently ue one gven below [7]. = n n n co co co π π π π K (.6) where the angle between q an a axe. If ω the angular pee of frame et: () ) ( ξ ξ ω = t (.6) The nvere of the tranformaton matrx gven below : = n co n co n co π π π π K (.65)

50 f b f q r f a f c f Fgure.9: The abc an q frame. A tranformaton matrx ha a contrant that the power n the abc frame houl be equal to the power on the q varable. Pabc P q = (.66) va a vbb vcc = ( vqq v v ) (.67) an for balance ytem whch mean that f a f b f c = the zero component of the q axe f = ( f a f b f c ) = (.68) 4 So that, the equaton for the zero component, wll rop. For the PMSM th mean that the number of equaton whch ecrbe the ynamc of the machne wll ecreae one. Th tranformaton wll be apple to voltage an torque equaton whch are erve below. λ V = RI = RI λ λ t t ( r ) (.69) I q K K V = K RK λr ( K λq ) K (.7) t t K λq V q = K RK I q K λq K K K t t λr t (.7) 9

51 4..5 Retve Element R RK K = (.7) Thu, the retance matrx aocate wth the arbtrary reference varable equal to the retance matrx aocate wth the actual varable f each phae of the actual crcut ha the ame retance, but f the retance are not balance the tranforme matrx wll be nclue nuoal functon. To overcome th problem, a fxe reference frame can be electe [7]...6 Inuctance Element Inuctance element are the element whch are relate wth tator flux lnkage. Frt fn the ervatve of the nvere tranformaton matrx. = co n co n co n π π π π ω t K (.7) Multplyng t wth the tranformaton matrx: = ω t K K (.74) Apply the reult to nuctance element part of the voltage equaton. = λ λ λ λ λ ω q q t t t q q λ K K λ K K (.75) The rect () an quaratc (q) flux lnkage that are ue n the above equaton can be foun by mply tranferrng the tator flux lnkage to q frame. I λ = (.76)

52 4 = = q l A l A l q q I K K λ (.77) The quaratc an rect nuctance of the machne can be efne. The agonal element of the nuctance matrx whch on q frame are the nuctance element of the gven axe. Becaue t aume that, there no alency nether on the rotor nor on the tator, the quaratc an rect nuctance value equal. The efnton are gven below [7].5 = = = = = = = q q q l A l q λ λ λ (.78) A een earler for a balance ytem the zero component of the varable are zero. In our machne wnng are wye connecte. So that, the ummaton of wnng current wll be zero an from the equaton above the zero component of the flux lnkage zero. The fnal form gven below: = q q q q q q t t ω λ λ λ λ λ ω (.79) Up to th pont, an arbtrary reference frame et ue, whch mean that the angle unaffecte on the reult of the retve an tator nuctve element. In the tranformaton of magnetc element an the torque equaton, we wll ee the mportance of the electon of reference frame an later we wll call th electon a park tranformaton [7]...7 Magnet Element The magnetc element gven a

53 4 t r λ K (.8) = co co co π π ω λ r r r r f t r λ (.8) Multplyng t wth tranformaton matrx. = co co co co n co n co n co co co co co co π π π π π π π π π π ω λ r r r r r r r r r r f t r λ K (.8) The equaton epen on the angle of the rotor an alo the angle between the frame. If the frame angle electe a equal to rotor magnetc angle r an ung the trgonometrc entte that are gven below, th epenence wll be elmnate [8]. α α α n co n = (.8) co co co = π α π α α (.84) The fnal form : = r f r w t K λ λ (.85) Combnng the part of the voltage equaton reach the fnal form of for the voltage equaton.

54 v v q = R q = R ω r ω r q q q t q t λ ω f r (.86) The voltage equaton are obtane wth tranformaton to q frame mpler an number of the equaton ecreae by one. In general for a p machne, the above equaton can be mofe [8]. v v q = R q = R pω r pω r q q q t q t pλ ω f r (.87) Where p the number of par of pole. Tranferre torque equaton gven below. T e λ = t r K I T q (.88) T =.5 pλ (.89) e f q..8 Iea to Fn Out the Parameter of Voltage Equaton..8. Determnng the Permanent Magnet Flux To etermne the flux, the generator connecte to a varable pee motor. The generator wnng are open crcute whch mean that no current wll flow. From the voltage equaton: λ vq = = π f co( r ) va co( r ) vb co( r π ) vc ω ω (.9) For fferent rotor pee, quaratc axe voltage calculate an then flux of magnet calculate from the above equaton. For a goo approxmaton the mean value of the calculate value taken. 4

55 ..8. Determnng the Retance, Quaratc an Drect Axe Inuctance Th tme generator rotor locke whch mean that rotor pee wll be zero. From the voltage equaton, when rotor pee zero the nonlnear element n the equaton wll be elmnate. near voltage equaton for zero pee are gven below: v = R (.9) v q q = R q (.9) The value can be foun by tep repone analy, but n real machne there hytere an kn effect whch affect thee value. So that ytem entfcaton metho can be ue to etermne an average value. Sytem entfcaton a crete proce, o the frequency oman equaton houl tranform to z oman wth a zero orer hol. v R T e = (.89) R T R( z e ) v q q q e = (.9) R( z e R T R T q ) where T the amplng pero. By applyng PRBS or ARMA gnal to voltage e of the ytem an takng meaurement from the current, the parameter can be calculate from lnear regreon [9]..4 Moelng of Uncontrolle Rectfer.4. Introucton Uncontrolle three phae full wave rectfer a brge that contan x oe (uncontrolle, elf commutate wtch) a hown the Fgure. [] where the ource nuctance, C the c e capactance whch flter DC component from the rectfe wave. The value of the ource nuctance an ource frequency 44

56 mportant becaue ource nuctance wll caue a voltage rop on the DC e whch proportonal to thee varable. There are many moelng type for converter whch ecrbe the nput-output relaton. For rectfer the nput varable the effectve value of the lne to lne phae voltage an the output varable the mean value of c lnk voltage[]. a a D D D5 n b c C v R loa D4 D6 D Fgure.: General crcut agram of rectfer.4. Iealze Crcut wth = For th approach the ource e can be aume to be voltage ource an DC e a current ource. The Fgure. gven for th approach. D D D 5 a a n b v I c D 4 D 6 D Fgure.: Iealze Crcut Dagram 45

57 Wth =, the current I flow through one oe from the top group an one from the bottom group at nay ntant. In the top group, the oe wth t anoe at the hghet potental wll conuct an the other two become revere bae. In the bottom group, the oe wth t cathoe at the lowet potental wll conuct an the other two become revere bae []. The voltage waveform n the crcut are hown n Fgure. where v Pn the voltage at the pont P (potve) wth repect to the AC voltage neutral pont n. Smlarly, v Nn the voltage at the negatve DC termnal N (negatve). Snce I flow contnuouly, at any tme, v Pn an v Nn can be obtane n the term of one of the AC nput voltage v an, v bn an v cn. Applyng KV n the crcut on a ntantaneou ba, the c e voltage. v = v v (.95) Pn Nn Fgure.: Rectfer Voltage Waveform []. The ntantaneou waveform of v cont of x egment per cycle of the lne frequency. Hence, th rectfer often terme a x-pule rectfer. Each egment belong to one of the x lne-to-lne voltage combnaton. Each oe conuct for o. Conerng the phae a current waveform 46

58 Fgure.: Phae Current [] I when oe conuctng a = I when oe 4 conuctng otherwe (.96) The commutaton of current from one oe to the next ntantaneou, bae on the aumpton of =. The oe are numbere n uch a way that they conuct n a equence,,, Next, we wll compute the average value of the output DC voltage an rm value of the lne current, where the ubcrpt o ae ue to aumpton of =. To obtan the average value of the output c voltage, t uffcent to coner only one of the x egment an obtan t average over a 6 o or π / - ra nterval. Arbtrarly, the tme orgn t = choen when the lne-to-lne voltage v ab at t maxmum []. Therefore, v = vab = V coωt π < ωt < π (.97) 6 6 where V the rm value of the lne-to-lne voltage. By ntegratng v ab, the voltecon area A gven by π / 6 A = V coωt( ωt) = π / 6 V (.98) 47

59 an therefore vng A by the π / nterval yel / 6 π V = V coωt( ωt) = V =. 5V (.99) π / π π / 6 Ung the efnton of rm current n the phae current waveform, the rm value of the lne current n the ealze cae I = I =. 86I (.) By mean of Fourer analy of t n th ealze cae, the funamental-frequency component ha an rm value I = 6I =. 78I π (.) The harmonc component I h can be expree n the term of the funamentalfrequency component a I h I = (.) h Where h = 6 k ± the even an trple harmonc are zero. Snce I n the phae wth t utlty phae voltage, the placement power factor DPF = co( φ) =. (.) where φ the phae angle between current I an phae voltage. Therefore the power factor pf = I I DPF = =.955 π (.4) Total harmonc torton can be wrtten a: I I I I THD = = = =.7% (.5) I I.78I 48

60 The voltage waveform wll be entcal f the loa on the c e repreente by a retance R loa ntea of a current ource I. The phae current wll alo flow urng entcal nterval. The only fference wll be that the current waveform wll not have a flat top []..4. Effect of On current Commutaton We wll nclue on the AC e an repreent the c e by a current ource = I a hown n Fgure.4. a a D D D5 n b c v I D4 D6 D Fgure.4: Rectfer Crcut Dagram wth Now the current commutaton wll not be ntantaneou. We wll look at only one of the current commutaton becaue all other are entcal n a balance crcut. Coner the commutaton of current from the oe 5 to oe, begnnng at t or ω t= (the tme orgn choen arbtrarly). Pror to th, the current I flowng through oe 5 an 6. The commutaton hown n Fgure.5. The current commutaton only nvolve phae a an c, an the commutaton voltage reponble v comm = v v. The two meh current I a an I are hown n Fgure an bn.5. The commutaton current u flow ue to a hort-crcut path prove by the conuctng oe 5. In term of meh current, the phae current are a = u (.6) an 49

61 c = I (.7) u u bul up from zero to I at the en of the commutaton nterval ω t u =u. In the crcut v a u = (.8) t t a = Fgure.5: Current commutaton [] an v c c u = = (.9) t t 5

62 Notng that c = I an therefore / t = ( I ) / t = t. Applyng u c u u / KV n the upper loop n the crcut an ung the above equaton yel v u = van vbn = va vc = (.) t comm Therefore from the above equaton, u t van vcn = (.) The commutaton nterval u can be obtane by multplyng both e by ω an ntegratng: ω I u u van vcn = ( ωt) (.) where the tme orgn aume to be at the begnnng of the current commutaton. Wth th choce of tme orgn, we can expre the lne to lne voltage ( v v ) a an cn v an v = V nωt (.) cn I V ( cou) ω = ω I = (.4) u or cou ω I = (.5) V If the current commutaton wa ntantaneou ue to zero, then the voltage v pn wll be equal to v an begnnng wth ω t=. However, wth a fnte, urng < ω t < ω t u v pn a van vcn = van = (.6) t 5

63 where the voltage acro (= ( u /t)) the rop n the voltage v pn urng the commutaton nterval hown n Fgure.5. The ntegral of th voltage rop the area A u whch A = ω I (.7) u Th area lot at every 6 o nterval. Therefore, the average DC voltage output reuce from t orgnal value, an the voltage rop ue to the commutaton ω I π / π V = = ω I (.8) Therefore, the average DC voltage n the preence of a fnte commutaton nterval V = V V =.5V ω I (.9) π Where V the average voltage wth an ntantaneou commutaton wth =. If we nee to ue the crcut moel of the rectfer [] for average value moel (voltage rpple neglecte) R = ω π (.) V =.5V (.) the crcut gven n Fgure.6. Fgure.6: Average crcut moel of uncontrolle rectfer 5

64 .5 The Inverter Moel v c S S S5 v a v b v c v S S S 4 6 Fgure.7: The Bac Structure of the Phae Inverter In general nverter a kn of converter that convert the c current nto ac current. A three phae nverter n Fgure.7 conte of x wtche locate on three arm for each phae. Thu each phae voltage controlle by two wtche. Inverter oe not have recurve equaton, o that t behavor can only be ecrbe by a ere of logc equaton. For th approach, S repreent the logc nput to each wtch an ther value etermne th wtche poton. If S logc, the wtch cloe an f t the wtch open. Th nformaton lea to a moel for nverter []. v a Svc S v = (.) v b Svc S 4v = (.) v c S5vc S6v = (.4) 5

65 . CONTRO OF THE SEECTED TOPOOGY. The Tak of the Control Sytem The mot mportant tak of the control ytem to force the mechanc ytem to run at the optmum angular pee at whch turbne wll harvet the maxmum power from the wn for fferent wn pee. The econ mportant tak to control the power factor of the power plant to cover the gr requrement. The power equaton for gr e are gven below. S = P Q (.) P = S coϕ Q = S nϕ (.) S = I V (.) Where S the apparent power, P the actve power, Q the reactve power, ϕ the phae angle an co ϕ the power factor. Actve power: The mean of the ntantaneou power over an ntegral number of pero gvng the mean rate of energy tranfer from ource to loa n watt (W). Reactve power: The maxmum rate of energy nterchange between ource an loa n reactve volt-ampere (VAR). The output voltage or n other wor gr voltage contant. So from the equaton.,.,. changng the lne current wll change the apparent power an changng phae angle wll change the actve an reactve power upple to the gr. Th mean that a current controller neee whch wll control the ampltue or the effectve value an phae hft of the current an IGBT rver whch wll prouce the gatng gnal for the wtche n the nverter. Hytere current controller choen whch contan both the controller an rver. 54

66 A MPPT algorthm wll be propoe whch wll prouce current reference for the current controller. Th algorthm wll watch out the angular pee, t change an wll calculate new current reference for the next cycle. Th a global optmzaton problem that algorthm wll alway track for the optmum pont an fn global maxmum pont for the power.. Hytere Current Controller Fgure.: Hytere Control Crcut Dagram [] Hytere control cheme are bae on a nonlnear feeback loop wth two level hytere comparator. The wtchng gnal S A, S B, S C are prouce rectly when the error excee an agne tolerance ban h []... Varable wtchng frequency controller: Among the man avantage of hytere current controller are mplcty, outtanng robutne, lack of trackng error, nepenence of loa parameter change, an extremely goo ynamc lmte only by wtchng pee an loa tme contant. However, th cla of cheme, alo known a free runnng hytere controller ha the followng avantage []. ) The converter wtchng frequency epen largely on the loa parameter an vare wth the ac voltage. 55

67 ) The operaton omewhat rough, ue to the nherent ranomne caue by the lmt cycle; therefore, protecton of the converter ffcult. It charactertc of the hytere current controller that the ntantaneou current kept exact n a tolerance ban, except for ytem where the ntantaneou error can reach ouble the value of the hytere ban Fgure.: Current waveform an Hytere Ban []. Th ue to the nteracton n the ytem wth three nepenent controller. The comparator tate change n one phae nfluence the voltage apple to the loa n two other phae (couplng). However, f all three current error are conere a pace vector, the nteracton effect can be compenate, an many varant of controller known a pace-vector bae can be create. Moreover, f three-level comparator wth a lookup table are ue, a conerable ecreae n the nverter wtchng frequency can be acheve. Th poble wth approprate electon of zero-voltage vector []. In the ynchronou rotatng q coornate, the error fel rectangular, an the controller offer the opportunty of nepenent harmonc electon by choong fferent hytere value for the an q component. Th can be ue for torquerpple mnmzaton n vector-controlle AC motor rve (the hytere ban for the torque current component et narrower than that for the flux current component) 56

68 Recent metho enable lmt cycle uppreon by ntroucng a utable offet gnal to ether current reference or the hytere ban... Contant wtchng frequency controller: A number of propoal have been put forwar to overcome varable wtchng frequency. The tolerance ban ampltue can be vare, accorng to the ac-e voltage, or by mean of a P control An approach whch elmnate the nterference, an t conequence, that of ecouplng error gnal by ubtractng an nterference gnal erve from the mean nverter voltage. Smlar reult are obtane n the cae of contnuou wtchng operaton, where ecouplng more ealy obtane wthout etmatng loa mpeance. Once ecouple, regular operaton obtane, an phae commutaton may (but nee not) be ealy ynchronze to a clock. Although the contant wtchng frequency cheme more complex an the man avantage of the bac hytere control namely, the mplcty lot, thee oluton guarantee very fat repone together wth lmte trackng error. Thu, contant frequency hytere control are well ute for hgh performance hghpee applcaton []. In the electe topology, for the ake of mplcty varable wtchng frequency concept electe. In front of the controller reference current are prouce by mply multplyng the reference prouce by the MPPT wth the moulaton gnal ( phae hfte nuoal functon). In realty a P neee to match the waveform of the current wth lne voltage. It can be ealy notce of that the phae hft between the lne voltage waveform an the moulaton gnal wll effect on the power factor of the ytem wth no change n apparent power.. MPPT.. The Wn Turbne Stable Workng Pont A explane earler the MPPT wll rectly act on the apparent power whch rawn from the power plant. A a reult of th tuaton the angular pee of the plant wll change. But for a gven power reference (calculate by MPPT), the curve 57

69 of the turbne gve two workng pont of whch the reference lne nterect wth the curve. Fgure.: The nterecton of power reference wth the turbne curve Sytem ha only one table pee. et u examne the pont an n the Fgure. above. Frt the ytem aume to be workng at the pont. If ytem low a lttle, power reference wll be larger than the turbne prouce, o that ytem wll tall. If ytem pee up a lttle, power reference wll be maller than that of the turbne, o that ytem wll pee up. A a reult pont not a table workng pont. Th tme ytem aume to be n pont. If ytem low a lttle, power reference wll be maller than the turbne gve, o that ytem wll pee up. If ytem pee up a lttle, power reference wll be larger that the turbne, o that ytem wll low own. In each cae the pee wll go to pont. A a reult th pont a table workng pont. So only the rght han e of the curve wll be eale. The Fgure. how another tuaton about the control. At the tart up of the ytem MPPT houl et the power ref zero or hutown the energy tranfer an keep t untl ytem pae to rght han e of the ytem. 58

70 .. Some Control Scenaro... If wn pee up: Fgure.4: The change of workng pont n the cae of pee up of the wn From the Fgure.4 above, f the wn pee ncreae whle ytem wa workng at the optmum pont (), ytem wll ntantaneouly jump to pont (). At the pont () turbne power bgger than power ref. The generator wll pee up to pont () an wll tay table but pont () not the optmum pont. So the MPPT houl contnue earchng the optmum pont from pont ().... If Wn Slow Down: In Fgure.5 ytem aume to be runnng at the optmum pont (). When pee reuce, the curve of the turbne wll narrow own. The workng wll jump to pont (). At th pont the power from the turbne lower than the reference power value. Becaue of that, ytem wll low own an tall. MPPT houl watch out th behavor an houl reet all the proce an tart from the begnnng. Becaue, the mechancal tme coeffcent are larger than electrcal one, the DC bu voltage wll reuce much raply. So watchng out the c bar voltage wll help to control th 59

71 behavor. MPPT only work at each amplng tme. So that MPPT nee ome help to etect the uen rop n DC voltage lnk. Fgure.5: The change of workng pont n the cae of low own of the wn.. The Flow Dagram of the MPPT Some cenaro can be tete from the flow chart gven below n Fgure.6. Uner contant wn pee, the algorthm tart. It frt wat for the ytem to reach the table pont. Then t et ntal value an apple t to the ytem. The rotor pee wll ecreae accorng to th ntal value. Then MPPT wll calculate the new tep ze. Th calculate tep ze compare wth a lmt value. If the tep ze larger than that value, t calculate the new reference to the ytem. If t maller, th mean that ytem near enough to optmum pont thu MPPT top trackng. A the wn pee ncreae, the rotor pee wll alo ncreae. Algorthm agan calculate the tep ze (elta). Becaue t ue the abolute value, t pae the tep ze control an tart agan trackng the optmum pont. 6

72 Fgure.6: The flow chart of MPPT Another cenaro the ecreae of the wn pee. When the wn pee ecreae, the c voltage wll rop raply. An external nterrupt proucer (uen change etector) en an nterrupt gnal to the MPPT. MPPT top trackng an reet telf whch mean that tartng from the begnnng...4 Calculaton of the new current reference..4. Steepet Decent Algorthm a a ne Search Metho The problem we are nterete n olvng : P : mnmze f(x).t. n x R 6

73 where f(x) fferentable. If lnear expanon x = x a gven pont, f(x) can be approxmate by t T f ( x ) f ( x) f ( x) (.4) f mall,.e., f mall. Now notce that f the approxmaton n the above expreon goo, then we want to chooe o that the nner prouct f ( x) T a mall a poble. et u normalze o that =. Then among all recton wth norm, = the recton ~ = f ( x) f ( x) (.5) make the mallet nner prouct wth the graent f (x). Th fact follow from the followng nequalte: ~ T T f ( x) f ( x) f ( x) f ( x) T = = f ( x) f ( x) (.6) For th reaon the un-normalze recton: ~ = f ( x) (.7) calle the recton of teepet ecent at the pont x ~ Note that = f ( x) a ecent recton a long a f ( x). To ee th, mply oberve that T T f ( x) = ( f ( x)) f ( x) < (.8) o long a f ( x). A natural conequence of th the followng algorthm, calle the teepet ecent algorthm. 6

74 Steepet Decent Algorthm: Step. Gven x,et k := Step. k := f (x k ). If k =, then top. Step. Solve mn α f (x k α k ) for the tep ze α k, perhap choen by an exact or nexact lne earch. Step. Set x k x k α k k,k k. Go to Step. Note from Step an the fact that k = f (x k ) a ecent recton, t follow that f(x k ) <f (x k ). Fgure.7: An example of teepet algorthm mnmum earch [] The Fgure.7 how the behavor of the teepet ecent algorthm. Each crcle the output of the equaton f(x).the output value ecreae a the algorthm earche for the mnmum value []. Convergence Theorem: Suppoe that n on the et S { x R f ( x) f ( x )} f (.) : R n R contnuouly fferentable =, an that S a cloe an boune et. Then every pont x that a cluter pont of the equence {x k } atfe f ( x) = []. 6

75 ..4. Steepet Decent Algorthm n MPPT A explane earler, a recurve equaton for the turbne varable, but we know that the curve contnuou. So that t fferentable over the varable. Becaue, t mpoble to calculate the ervatve of the turbne curve, we houl fn t out from the efnton of the ervatve. The curve ha only one nput varable whch the current reference an the out put varable the angular pee of rotor. So that the ervatve of the curve : f = ω( t) ω( t ) I ( t) I ( t ) ref ref (.9) where t the nex element. Now, we can fn out the teraton form for current reference. I ref ( t ) = I ( t) α f (.) ref It mpoble to calculate α for each tep. So a contant value electe. Selecton of th contant value mportant becaue, t wll etermne the pee of convergence. If t large, algorthm wll be fat, but f t bgger than a certan value (th certan value can only be foun by experment) t wll pa the optmum pont an t wll lot t tablty. Mot afety one to elect th value mall to keep the ytem table. Another approach to ue the abolute value of the Becaue when wn pee up the gn of f ntea of ung t rectly. f wll revere, but t tll requre that current reference houl ncreae. If the abolute value taken, MPPT wll not nee to watch the pee ncreae to change the gn of the f. I ref ( t ) = I ( t) α f (.) ref 64

76 4. Smulaton Reult an Comment Th ecton eal wth the mulaton reult of the propoe control ytem. A explane earler th control ytem egne for electe topology. To oberve the behavor of the controller, frt of all a moel of topology bult up n Matlab 7.. Smulnk program. Th moel gven n Fgure 4.. Fgure 4.: Matlab Moel of the Topology The turbne moel from the matlab toolbox recontructe by curve fttng technque an t gven n a polynomal form. For th proce matlab curve fttng toolbox ue. Followng equaton are obtane. C p =.89λ.65λ.λ.449λ.588λ.58λ (4.) C Γ 5 4 =.89λ.65λ.λ.449λ.588λ.58 (4.) 65

77 Fgure 4.: Turbne Moel n Matlab Fgure 4.: Graph of power coeffcent For the permanent magnet ynchronou generator, the parameter are R =. 85Ω (4.) q = =. 95mH (4.4) λ f =. 9Wb (4.5) 66

78 For the mechancal e J g =.8Kgm (4.6) B g =. Nm (4.7) Thee mechancal parameter are electe to keep the mechancal tme mall an alo to peeup the mulaton, becaue the amplng tme of MPPT epen to mechancal tme contant. In real applcaton the nerta much bgger than th value. The rate power of the generator kw an number of pole are 6. For the DC flter C = mf = mh (4.8) (4.9) Fgure 4.4: Graph of torque coeffcent The moel of the ytem wth control ytem gven n Fgure 4.5. Control ytem compoe of three man part. Frt one the MPPT. MPPT take the 67

79 meaurement of current an pee, an then t calculate the elta value (the tep ze) for the next tep. It alo take nformaton from other block, for ntalzaton an nterrupt. The econ man part uen change etector. Thee block watch the ervatve of the c lnk voltage. If the ervatve value maller than a gven value, one of them en an nterrupt to MPPT to nform t about the tuaton an the other uen change etector block take the control of reference current value for mall tme. Th tme epen on the amplng tme of the MPPT, becaue MPPT can not change the output value untl the next tep tme. At the next tep tme after the nterrupt gnal MPPT make calculaton to fx the problem. The thr part the current control an reference generator part. Sgnal generator whch prouce reference current wave form, take the reference current an generate three phae nuoal wave. Thee waveform are the reference nput for the current controller. Current controller meaure the current value an calculate the error wth the reference, then t prouce gate gnal for the nverter wtche. To oberve the behavor of the control ytem properly, two mulaton are carre out. Each mulaton eal wth fferent cenaro. Frt one ncreae of wn pee when the ytem operatng at a table pont an econ one ecreae of the wn pee when the ytem at a table pont. Fgure 4.6: Wn Spee Change over tme 68

80 enable Iref Iabc_ref Iref Reference Generator z Vabc Iabc A a B b c C Three-Phae V-I Meaurement Current Controller Iabc* Pule Iabc g A B - C Inverter C Wn - v rotor_pee wn_pee turbne_torque Wn Turbne - A B C Uncontrolle Rectfer Tm A B m C Permanent Magnet Synchronou Generator m _q v_q wm Machne Meaurement Mean In u/t c_voltage_er Iref Iref Suen change etecter Iref elta MPPT Iref_ Iref_ pee pee_ control check check z pee_ z Iref_ enable z Iref_ Mean In Average of Spee check In check Dervatve of c lnk voltage Suen Change Detecter Fgure 4.5: Matlab Moel of the Sytem Wth the Controller 69

81 4. Frt Scenaro In th cenaro, the followng tep functon n fgure apple to turbne moel. The mulaton tarte by m/ wn pee an after. the wn pee ncreae to 4 m/. For th wn pee the power curve of the turbne are gven below n Fgure 4.7 an 4.8. Fgure 4.7: Mechancal power curve of the turbne for m/ wn pee 7

82 Fgure 4.8: Mechancal power curve of the turbne for 4 m/ wn pee Fgure 4.9: Reference current over tme 7

83 Fgure 4.9 the reference current value of the ytem whch are generate by MPPT. From th fgure t can be een that after 5 ytem caught the optmum pont. After wn pee ncreae, control ytem etecte that an contnue to earch the optmum workng pont then foun t at nearly 4. Fgure 4.: Mechancal Power of the Generator over tme. The Fgure 4. above how that the control ytem track the optmum pont wth nearly 4 watt error. Th error caue by the afety gap. If the calculate abolute value of the elta (tep ze) of the ytem between.5 an, MPPT top earchng, keep the reference contant, untl wn pee change. The abolute value of the elta ue n teepet ecent algorthm, o that f the elta value get greater than when wn pee ncreae ytem oe not effecte an contnuou to earch the optmum pont. 7

84 Fgure 4.: Step ze value calculate by the MPPT Fgure 4.: Actve power upple to utlty 7

85 Actve power n Fgure 4. behave mlarly wth the mechancal power. The fference between electrcal an mechancal power the loe n the ytem. Reactve power of the ytem zero, becaue the current an voltage are n phae.the other reult are gven Fgure 4. an 4.4. Fgure 4.: DC lnk voltage Fgure 4.4: Rotor pee over tme 74

86 4. Secon Scenaro In th cenaro, the mulaton tarte by m/ wn pee an after. the wn pee ncreae to 4 m/ Fgure 4.5. Fgure 4.5: Wn pee change over tme The behavor of the ytem nearly ame wth the frt cenaro except the uen voltage rop when wn pee ecreae. When wn pee ecreae, becaue the ytem can not meet the power harvete by the gr, the c lnk voltage rop raply. When the ervatve of the Dc voltage fall uner a certan value at 5th econ, control ytem etecte t an reet ytem. After that, ytem contnuou earchng the optmum pont. Agan from the fgure t obvou that ytem track the optmum pont wth only a mall error. 75

87 Fgure 4.6: Mechancal power curve for m/ wn pee Fgure 4.7: Mechancal power curve for 9 m/ wn pee 76

88 Fgure 4.8: DC lnk voltage over tme The uen voltage rop can be oberve from the Fgure 4.8 Fgure 4.9: Dervatve of DC lnk voltage 77

89 Fgure 4.: Reference current calculate by MPPT Fgure 4.: Mechancal power of the turbne 78

90 Fgure 4.: Step ze value over tme From the Fgure 4. an 4., t can be oberve that a the tep ze approache to zero the actve power approache to t maxmum value. Fgure 4.: Actve Power of Electrcal Se 79

91 Fgure 4.4: The Rotor Spee of the Generator 4. General Smulaton Reult In th ecton, ome general mulaton reult are gven. Frtly n Fgure 4.5, t can be een that current an phae voltage are n the ame phae, o that the reactve power zero. Other fgure are about the compare of FFT analy of fferent wtchng cheme of nverter. Varable wtchng mean a mey FFT reult. Th mean the current nclue o many harmonc, but the THD value maller. Small hytere ban mean, mall THD. Becaue the hape of the current more lkely to be a pure ne. 8

92 Fgure 4.5: An Example Phae Voltage an Current Fgure 4.6: FFT Analy of Phae Current wth Contant Swtchng Frequency 8