Modeling, Simulation & Control of Induction Generators Used in Wind Energy Conversion

Transcription

1 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Chapte-4 Equvalent Ccut and Matheatcal Model of nducton Geneato 4. ntoducton: n peent-day pactce, two type of geneato uually fnd applcaton n WPP: nducton geneato and Synchonou geneato. nducton geneato coonly ued n wnd powe geneato becaue of t uggedne, elablty and plcty. 4. nducton Geneato: Thee-phae nducton geneato ha been wdely ued n WPP becaue of qualte uch a uggedne, elablty and plcty. A thee-phae nducton geneato ha thee dentcal wndng yetcally placed n the tato. The lanated oto cae ba connected to two hotng ng at both end n cae of a Squel Cage nducton Geneato (SCG); whle thee-phae balanced wndng ae connected to thee lp ng n Wound oto nducton Geneato (WG). A pe-phae ccut wll uffce, epectve of the delta o ta connecton of tato wndng fo a balanced opeaton. The equvalent ccut of an nducton geneato (hown n Fgue 4.) a vey ueful tool to analy and coputaton of t pefoance unde vaou conon. Th ecton llutate a ple pe phae equvalent electc ccut of a thee-phae nducton achne. A the SCG and DFG ue thee-phae tato wndng achne, the equvalent ccut qute la except that the oto voltage n SCG vey vey all a t oto hot-ccuted.

2 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Fgue 4. Equvalent ccut of nducton achne The tato and oto voltage equaton fo the equvalent ccut baed on Kchhoff law can be expeed a equaton (4.) and (4.) epectvely [8]. M (4.) M (4.) Equaton (4.) ay be expeed a; ( ) ( ) M M ( ) M l The tato voltage can be expeed a hown n equaton (4.). ( ) x x (4.) Slaly equaton (4.) can be odfed a; ( ) ( ) M M ( ) l Alo the oto voltage gven by equaton (4.4).

3 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon ( ) x x (4.4) 4. Powe Flow Baed on the geneal elaton between echancal toque and electcal powe, the echancal nput powe and tato powe output ae coputed a gven n equaton (4.5). P T P (4.5) T e The well known toque and powe balance gven by well known equaton (4.6). d T J D T e (4.6) Aung that the total oent of neta J (kg ), and otatonal and fcton loe to be neglgble, the echancal equaton (4.6) wll becoe a; d J T T e (4.7) Alo fo a lo-le geneato at teady tate T T e and P P P Theefoe the oto powe ae obtaned fo equaton (4.8) and (4.9) a follow, P P P (4.8) T T e T T P (4.9)

4 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Fo the equaton (4.9) t can be concluded that the oto powe only a facton of the tato powe becaue the lp vey low unde noal opeaton. Theefoe the powe electonc convete, connected n the oto of DFG fo the contol, wll have to handle le powe and ubequently the atng of the convete wll be le, whch an potant advantage of DFG. The decton of the oto powe flow dependent on the lp gn.e. upe- ynchonou o ub-ynchonou conon. The oto wll nect the eal powe nto the yte though the convete at upe-ynchonou peed and wll abob the eal powe fo the yte though the convete unde ub-ynchonou peed [0]. Thee no gnfcant net powe ntechange between oto and yte at ynchonou peed and the voltage on the oto DC Matheatcal Model t well known that a DC dve ha excellent dynac pefoance, a t poble to decouple the tato agnetc flux and electoagnetc toque of the dve. The vecto contol, alo known a Feld Oentaton Contol (FOC), of nducton achne eulate the DC dve contol. ecto contol (.e. decouplng contol) chee fo ac oto dve have been wdely accepted n hgh-pefoance vaable peed applcaton by ceatng ndependent contol of toque and flux contol [8, 56]. n a la anne, vecto contol tatege have been popoed fo contollng the actve and eactve powe of the nducton geneato. n Secton 4.5 t ha been explaned how the thee-phae yte could be educed nto uncoupled two-phae yte ung the tong atheatcal tool. n th ecton a dynac odel of DFG and t contol have been peented ung the geneato conventon [5, 47]. The DFG odellng and contol have been caed out n the well known d -q coodnate yte ung Pak tanfoaton fo both thee-phae to two-phae and two-phae to thee-phae axe tanfoaton [, 6, 7, 8]. The tato and oto wndng of thee-phae nducton geneato ae epeented by two et of othogonal fcttou col. The odel baed on the ffth-ode two-ax epeentaton coonly known a Pak odel [, 5, 8]. Followng aupton ae ade to pepae the odel of DFG:

5 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon. Flux tanent ae neglected.. Magnetc atuaton neglected.. Flux buton nuodal. 4. The powe convete ae deal and lole. 5. The equaton ae deved n d -q ax epeentaton on the ynchonou efeence fae. 6. The q ax 0 90 ahead of d ax n the decton of otaton. The equvalent ccut of a DFG n an abtay efeence fae otatng at ynchonou peed hown n Fgue 4. [9, 8]. Fgue 4. Equvalent ccut of DFG n an abtay efeence fae otatng at N Accodng to the Fgue 4., the tato and oto fluxe equaton (4.0). ( l ) ( l ) and ae epeented by (4.0) The tato and oto voltage n efeence fae ae expeed by equaton (4.). d d ( ) (4.) The equvalent tato agnetng cuent defned a;

6 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Theefoe and ( ) Subttutng n gve Now ubttutng the value of, and n equaton (4.) gve ( ) d d d σ whee σ f tato voltage and ae aued to be contant, then 0 d and ( ) d d σ The above et of equaton fo tato and oto voltage nd -q coodnate can be wtten a hown n equaton (4.).

7 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon d q d q d q d q dd q dq d dd q d q d (4.) The ubcpt d and q ndcate the dect and quadatue ax coponent of the efeence fae, whee and epeent tato and oto quantte, epectvely. The decopoton nto d -q coodnate yte equed fo the contol. The flux lnkage can be futhe calculated ung the followng elaton hown n equaton (4.) d q d q ( l ) d d d d ( ) l q q q q ( ) ( ) l d d d d l q q q q (4.) The oto lp defned by equaton (4.4). (4.4) Alo the electoagnetc toque developed gven by equaton (4.5). T e p ( ) n (4.5) q d d q t can alo be wtten n te of oto cuent a T e n p ( ) d q q d The equaton fo actve and eactve powe n d and q axe ae expeed by equaton (4.6). P Q d d q d q q d q (4.6)

8 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Noally a edu to hgh powe geneato ued n wnd fa; theefoe the tato etance can be neglected. The tato voltage along d-q ax fo equaton (4.) wll educe to equaton (4.7). d q d q dd dq (4.7) n vecto contol ethod, whch ued to acheve ndependent contol of actve and eactve powe, the tato flux vecto algned wth d-ax whch gve the followng equaton (4.8) [68]. d q q d q d 0 (4.8) The tato voltage n DFG, whch a vaable-peed contant-fequency geneato, ean contant. Moeove the thee-phae nuodal voltage tanfoed nto d - q ynchonou efeence fae. Th gve the elaton a hown n equaton (4.9). 0 d q (4.9) Fo equaton (4.6), (4.8) and (4.9), the tato actve and eactve powe can be obtaned a hown n equaton (4.0) and (4.) epectvely. P q (4.0) Q d (4.) Fo equaton (4.0) and (4.), t can be concluded that the delveed powe depend dectly on the dandq coponent of oto cuent except that fo the eactve powe thee econd te, whch epeent powe needed to agnete the achne.

9 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Alo, the electoagnetc toque popotonal to the q a hown n equaton (4.). T e np q (4.) 4. 5 Axe Tanfoaton A t ha been entoned n ecton 4.4, a DFG utlze bac the pncple of feld oentaton contol. To undetand th pncple, t neceay to tudyd, q odel. The dynac pefoance of an ac achne oewhat coplex becaue the thee-phae oto wndng ove wth epect to thee-phae tato wndng a the couplng co-effcent between the two phae change contnuouly wth the change of oto poton. The achne odel can be decbed by dffeental equaton wth te-vayng utual nductance, but uch a odel tend to be vey coplex. The ft vectoal epeentaton of thee-phae yte wa ntoduced by Pak, Kon and Stanley [, 6,]. Pak popoed a atheatcal tool to eplace the vaable aocated wth tato wndng wth otatng fcttou wndng of oto. G. Kon popoed a tanfoaton of both tato and oto vaable to a ynchonouly otatng efeence fae that ove wth the otatng agnetc feld. The ue of efeence fae and tanfoaton theoy can plfy the analy of electcal achne and vecto contol of AC achne Tanfoaton fo thee-phae to two phae axe n th ecton t hown how a thee-phae otatng yte can be tanfoed nto a two-phae otatng yte []. t alo hown how the tatonay two-phae yte can be obtaned whch the bac pncple contol of DFG. The tanfoaton caed out baed on the pncple of nvaance of powe o that the powe n one et of vaable ae a powe n the new et of vaable. A yetcal -pole, thee-phae wndng on the oto epeented by thee col A, B and C each of N effectve tun and utually dplaced by 0 0 a hown n Fgue 4.. Maxu value of f F a, F b and

10 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Fc ae hown along the epectve phae-axe. The cobned effect of thee thee f eult n a contant agntude f, whch otate at a contant velocty dependng on the pole and fequency. Fgue 4. otatng -phae balanced wndng et the thee-phae cuent be gven by equaton (4.5). a b c Co( t) π Cot 4π Cot (4.5) Then thee cuent wll poduce an f of a contant agntude otatng wth epect to the thee-phae wndng at the te. n Fgue 4.4 a balanced two-phae wndng epeented by two othogonal wndng col α, on the oto. The axe of A and α ae taken to be concdent fo the convenence n tanfoaton.

11 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Fgue 4. 4 otatng -phae balanced wndng et the two- phae cuent be gven by equaton (4.6), α Cot π Cot Sn ( ) t (4.6) flow n the two-phae wndng, the eult wll be an f of contant agntude N evolvng wth epect to the two-phae wndng at the te fequency of the phae cuent. The f of thee-phae and two-phae yte can be equated n agntude to acheve the tanfoaton. Now both the agntude of cuent and nube of tun of two-phae yte ae changed to obtan dentcal tanfoaton fo voltage and cuent. et the nube of pe-phae tun n two-phae wndng be a te the pe-phae tun of the thee-phae wndng. Then fo equal f, α hould be equal to a whch can be poved by eolvng the -phae f along α -ax a hown n equaton (4.7).

12 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon [ ] ) (40 ) (0 ) ( Co Co Co N N c b a α c b a α (4.7) And laly gven by equaton (4.8). c b 0 (4.8) To obtan a quae atx a zeo equence cuent whch doe not poduce any otatng f can be added n a convenent fo and coplete eult can be epeented a hown n equaton (4.9). c b a 0 0 α (4.9) The above tanfoaton alo apple to voltage o flux Tanfoaton fo otatng axe to Statonay axe The otatng two-axe wth otatng phao and tatonay pace phao n tatonay axe ae hown n Fgue 4.5 and 4.6 epectvely. otatng axe α, ae algned along q d, axe by takng angle 0 at te t 0.

13 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Fgue 4. 5 otatng α, axe of -phae wndng Fgue 4. 6 Statonayd, q axe of -phae wndng

14 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon Aung the ae effectve nube of tun n α, and d,q axe, f α F and F can be eolved along d andq axe, t gve the elatonhp a follow: α Sn F Co F F d Theefoe cuent along d andq axe ae gven by equaton (4.0) and (4.). α Sn Co d (4.0) Slaly α Co Sn q (4.) The equaton (4.0) and (4.) n atx fo ae expeed a hown n equaton (4.). α Co Sn Sn Co q d (4.) The tanfoaton fo otatng thee-phae yte to two-phae otatng yte and two-phae otatng yte to two-phae tatonay yte can be caed out fo equaton (4.9) and (4.). Wth the help of thee elaton the tanfoaton fo thee-phae otatng yte to two-phae tatonay yte can be obtaned by ubttuton and takng the nvee tanfoaton wll gve the elaton a hown n equaton (4.) and (4.4). c b a q d Sn Sn Sn Co Co Co π π π π (4.) and

15 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon a b c Co π Co 4π Co Sn Sn Sn π 4π d q 0 (4.4) 4. 6 Powe Electonc Concept Wnd powe tochatc by t natue and t peed change vey often. A vaable-peed wnd geneato able to extact oe enegy copaed to contant peed achne. Howeve, the geneated powe, voltage and fequency of a vaable peed achne change wth the wnd peed. n uch cae, powe electonc offe a gnfcant contol. t can handle hghe cuent and voltage wth ega cale powe aplfcaton. The ao tak of powe convete n ecent applcaton to hape the output powe. Powe electonc can alo contol the actve and eactve powe flow and can be ued a a local eactve powe ouce n cae of weak gd [5]. t can pove the powe qualty by educng the flcke level and lt the hot-ccut powe. The developent n powe electonc ha not only nceaed n enegy conveon ate and qualty contol of an nducton geneato but educed cot too. Powe electonc vey ueful to contol the fequency n a vaable peed concept. Th featue eult n the advantage lke: () Optal enegy opeaton, () Wnd peed vaaton ae abobed by the oto peed change, hence thee le load on the gea and dve chn, () Powe electonc can elnate the gea and (v) t educe the noe patculaly at low wnd peed. The bac eleent of powe convete ae dode and wtchable thyto o tanto. Dode conduct cuent n fowad baed conon and wll block cuent n evee decton. The opeaton of a conventonal thyto o tanto can be contolled. The ot wdely known contollable devce ae gate tun off (GTO) thyto, ntegated gate coutated thyto (GCT), bpola uncton tanto (BJT), etal oxde econducto feld effect tanto (MOSFET) and nulated gate bpola tanto

16 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon (GBT). The only dadvantage wth the powe electonc ae the powe loe and oe cot. n th ecton, ot coonly powe convete topologe ued n wnd ll ae peented Soft State The oft tate uually cont of two ant paalleled connected thyto and ued n a fxed peed wnd geneato to enege the geneato once t opeatng peed eached [48]. t functon to buld up the agnetc flux lowly and hence nze tanent cuent dung enegaton and educe the n-uh cuent. The ooth connecton of the geneato to the gd acheved by adutng the fng angle of the thyto n the tatng and late on, the thyto ae bypaed to educe the loe n powe electonc devce Capacto Bank The capacto bank ued n SCG to upply eactve powe. n cae of the SCG connected to an olated load, t eental a thee no othe ouce to povde the eactve powe. When the SCG connected to the gd, the capacto bank wll nze the eactve powe abobed fo the gd [50]. The capacto bank ae connected o dconnected dependng on the aveage eactve powe deand of the geneato to acheve full load dynac copenaton. The bank ae uually ounted at the botto of the towe o to the nacelle ectfe and nvete The electonc devce can be ued n the ectfyng a well a n the nvetng ode. Dode vey coon devce to be ued n uncontolled ectfe, becaue of t

17 Modelng, Sulaton & Contol of nducton Geneato Ued n Wnd Enegy Conveon plcty, low cot and low loe. Howeve t non-lnea n natue hence geneate haonc cuent and allow only a undectonal powe flow. Back to back connected convete ae wdely ued n thee-phae fequency convete. The back to back convete a bdectonal powe convete contng of two pule-wh odulated (PWM) convete. The capacto connected n back to back aangeent decouple the contol of the two convete and antan the gd de DC lnk voltage contant. The bac concept of DFG contol that the oto fequency change wth the change n peed and the decton of oto powe flow change fo upe-ynchonou to ub-ynchonou peed. The powe electonc convete accoplh th vey convenently. The powe electonc convete copenate the dffeence between echancal and electcal fequence by nectng a oto cuent wth a vaable fequency, thu electcal and echancal fequence ae decoupled. Th featue eult n axu enegy extacton and noe educton at low wnd peed. Convete can alo wok a an actve eleent n powe yte akng actve and eactve powe flow contollable. t can be ued a a local eactve powe ouce n cae of weak gd and alo pove the powe qualty by educng the flcke level and lt the hot-ccut powe. The gd-de convete n DFG can pefo a Statc Copenato (STATCOM) to uppot T conon. n oden vaable peed wnd geneato yte nulated Gate Bpola Tanto (GBT) ae typcally ued Suay n th chapte a coplete atheatcal odel and equvalent ccut of a DFG ha been peented. ecto contol ethod, whch decouple the oto cuent nto d -q axe, ued to contol the back-to-back connected convete. Tanfoaton fo thee-phae to two-phae axe hghlghted hee. t ncluded the coplete decpton of behavou of the DFG unde teady-tate conon. The powe flow n tato and oto ccut of DFG unde ub-ynchonou and upe-ynchonou peed ae alo dcued hee. Th chapte ha povded bef nfoaton of powe electonc concept ued n wnd ll. t can be ad that powe electonc devce ae pong techncal tool and ae vey potant pat of the WPP whch ake the to wok fully autoatc.