Speed Control of A Doubly Fed Induction Motor using Integral Plus Proportional Controller

Transcription

1 Jounal of owe Electonic & owe Syte SSN: X (Online), SSN: (int) Volue 7, ue 3 Speed Contol of A Doubly Fed nduction Moto uing ntegal lu opotional Contolle Al-Mayhedee Zubai, *, Mohaad Abdul Mannan, Md. Kaul Haan, Junji Taua 2 Depatent of Electical and Electonic Engineeing, Aeican ntenational Univeity- angladeh, Dhaka, angladeh 2 Depatent of Electical and Electonic Engineeing, Kitai ntitute of Technology, Japan Abtact Conventionally, the peed contol anipulate of Doubly-Fed nduction Moto (DFM) ha been developed piaily which i baed on taditional opotional-lu-ntegal () contolle due to it iple contuction and ipleentation. The teady-tate eo iniization, ovehoot eoval and ditubance ejection ae not poible in which the benefit of contolle ae choen though tial and eo appoach. The teady-tate eo and ditubance ejection ay be viable, if the benefit of opotional-lu-ntegal contolle ae choen though ight on the pole. ut the ovehoot eliination i not poible whee the opotional-lu-ntegal baed contolle i deigned. n thi pape, ntegal- lu-opotional () contolle i popoed to deign fo peed contol of the Doubly-Fed nduction Moto. The ntegal-lu-opotional contolle i well uited to iniize the ovehoot poble that i aien in opotional-lu-ntegal contolle. The pefoance of popoed ntegal-lu-opotional contolle fo peed contol of Doubly-Fed nduction Moto yte ha been analyzed and invetigated though the iulation wok. The outcoe of iulation wok ae illutated to how the effectivene of ecoend ntegal-lu- opotional contolle in copaion with taditional opotional-lu-ntegal contolle. The popoed ntegal-lu-opotional contolle how the uch bette pefoance ove opotional-lu-ntegal contolle in phae of iniization of ovehoot. Keywod: DFM, vecto contol, contolle, contolle *Autho fo Coepondence E-ail: azubai25@gail.co NTRODUCTON Known eeing that 899 [], the doubly fed induction oto (DFM) i a wound oto aynchonou achine povided though the tato and the oto fo two extenal upply voltage. Thi achine i vey deiable fo vaiable peed function uch a the electic autoobile and the poduction of electical enegy [2 4]. Conequently, it cove all enegy ange. Obviouly, the equeted vaiable peed aea and the pefeed pefoance ely on the utility ot [5 7]. The ue of DFM affod the chance to odulate enegy dift into and out of the oto winding in ode to have, at the ae tie, a vaiable velocity in the chaacteized upe ynchonou o ub ynchonou ode in oto o in geneato egie. Two ode can be elated to lip enegy ecovey: ub ynchonou otoing and upe ynchonou geneating opeation. n geneal, while the oto i fed though a cycloconvete, the enegy ange can obtain the MW ode which povide the dienion of enegy fequently eeved to the ynchonou achine [7 0]. The DFM ha oe aweoe benefit in contat to the taditional quiel-cage achine. The DFM can be contolled fo the tato o oto via oe than a few viable cobination. The dawback of two ued convete fo tato and oto offeing can be copenated though the quality contol pefoance of the poweed yte. ndeed, the ente intuction ae caied out with the aid of kill of fou paticula tage of anipulate feedo elative to the quiel cage induction achine whee it anipulate appea quite iple. The flux oientation tategy can tanfo the non-linea and coupled DFM-atheatical annequin into a linea odel leading to one captivating olution fo poducing o otoing opeation JoES (207) STM Jounal 207. All Right Reeved age 38

2 Speed Contol of a Doubly Fed nduction Moto Zubai et al. [0 4]. t i known that the oto diven yte account fo about 65% of the electicity fed on in the wold. pleenting exceive efficiency oto diven yte, o enhancing cuent one, ought to ave ove 200 billion kwh of electical enegy pe yea. Thi touble ha eeged a vey ipotant, pecifically following the econoic cii due to the aplify in oil pice a uch, innovative enegy aving technologie ae appeaing and ceating wiftly in thi centuy [5 8]. n thi faewok, the DFM continue to be of exteely good patie owing to the beginning of the thinking of double flux oientation [9, 20]. Seveal technique of contol ae ued to contol the induction oto aongt which the vecto contol o aea oientation anipulate that peit a decoupling between the toque and the flux, in ode to achieve an ipatial contol of toque and the flux like DC oto. Theefoe, decoupling the contol chee i equied via copenation of the coupling effect between d-axi and q-axi cuent dynaic. With the field oientation contol (FOC) ethod, induction achine dive ae tuning into a ajo candidate in highpefoance oveent anipulate application, whee evo quality opeation i equied. Fat tanient epone i ade viable with the aid of decoupled toque and flux contol. The ot boadly ued contol technique i poibly the popotional integal contol (). t i effotle to deign and ipleent, howeve it ha poble in dealing with paaete vaiation, and load ditubance. n ode to ipove the oveall pefoance of contolle of extaodinay electical oto ha been deigned in [22 25]. n thi pape, the peed contol of DFM baed on contol chee i popoed conideing it can effotlely deign and ipleent. The popoed contolle i capable to ovecoe the teady tate eo and ovehoot iue and to eject the ditubance. The oveall pefoance of peed contol baed on the popoed contolle i invetigated by uing iulation eult, which had been caied out though Matlab/Siulink oftwae. Fo the iulation wok, it i obeved that the contolle give highe pefoance though ability of ovehoot and teady-tate eo. DYNAMC MODENG OF DOUY FED NDUCTON MOTOR Figue how the typical configuation of oveall contol yte of DFM. Two invete ae ued to tanit cuent fo dc ouce to the tato winding and the oto winding. The witching action of invete i pefoed baed on the injecting the contollable voltage in to the tato and the oto to obtain the deied voltage with deied fequency of both tato and oto fo vaiable peed opeation. Fig. : Oveall lock Diaga of DFM Dive Syte. JoES (207) STM Jounal 207. All Right Reeved age 39

3 Jounal of owe Electonic & owe Syte Volue 7, ue 3 SSN: X (Online), SSN: (int) Fig. 2: Coplex Synchonouly Rotating dq-axe Refeence Fae Equivalent Cicuit of DFM. Though the two invete hae the ae dc bu, they can be opeated epaately, eaning that both tato and oto winding can be contolled independently. Figue 2 how the equivalent cicuit diaga of a DFM in coplex vecto fo in a ynchonouly otating dq-axe efeence fae. n thi Figue 2 ubcipt and efe to the tato and oto winding vaiable, epectively. v = v d +jv q and v = v d +jv q ae the tato and oto voltage vecto; i = i d +ji q and i = i d +ji q denote tato and oto cuent vecto; R and R ae the tato and oto eitance;, l, l ae the agnetizing, tato leakage and oto leakage inductance, epectively; = d +j q and = d +j q ae the tato and oto flux vecto; i the tato winding electical angula velocity and i the oto winding electical angula velocity. Uing the fundaental law of oh law and faaday law, the expeion of tato and oto voltage with the cuent and fluxe in ynchonouly otating fae can be given a follow [2]: vd Rid pd q () vq Riq pq d (2) vd Rid pd q (3) vq Riq pq d (4) d id id (5) q iq iq (6) d id id (7) q iq iq (8) n the above equation ubcipt d and q ae epeented fo d-axi quantitie and q-axi quantitie, epectively, and p i epeented d/dt. The electoagnetic toque and the echanical dynaic can be given by: i Te Kt q d idq (9) J T p T (0) e n n whee, K n, J t i inetia, i fiction coefficient and n i the nube of pole pai. Uing the above equation () to (0), the tate-pace equation of a DFM can be witten a follow: pi K i K i d 2 d 4 d q pi K i K i K K v K v q 2 q 4 q d 3 q d 3 d () K K v K v 3 d q 3 q (2) p K i K v (3) d 6 d 5 d q d p K i K v (4) q 6 q 5 q d q p K K i K i K T 7 9 q d 9 d q 8 (5) whee, K, 2 2 R R K, 2 2 K K 3 K K, 6 5 KR, 3 K4, K 5 R, JoES (207) STM Jounal 207. All Right Reeved age 40

4 Speed Contol of a Doubly Fed nduction Moto Zubai et al. K J 7. K 8 n J, K K K 9 8 VECTOR CONTRO OF DFM A vecto contolled doubly fed induction achine i a captivating olution fo exceive liited peed ange electic poweed foce and ea application, it conit in guiding an electoagnetic flux of the DFM along the axi d o q [5]. n thi pape, we elect the diection of efeence (d, q) in accodance to the diect tato flux vecto d, o the odel of teady-tate DFM will be iplified a follow: V d R d q (6) V q R q d (7) V d R d q (8) V q R q d (9) whee, The agnetization of achine i cetain by way of the oto diect cuent, o the tato cuent in the d axi i taken to zeo (i d = 0). The cuent and voltage in the tato ae then in phae: V q = V and q =. n thi cae we acquie a unity powe facto at the tato, o the tato eactive electicity i zeo i.e. Q = 0. Vecto contol conit in oienting the tato flux. Thu, it eult the containt given below in (20). The tato flux i oiented on the q axi. d 0 q t (20) Uing the containt of vecto contol of Eq. (5), the developed toque of Eq. (9) can iply be witten a follow: T (2) e n q Accoding to the peviou atheatical deivation, the efeence fo tato cuent and oto cuent can be obtained. aed on the vecto contol tategy thee efeence ae uaized in Table. Table : Contol Stategy to the DFM Model. Objective Refeence d ef n i d n / q 0 ef iq ( / ) iqef Q 0,(co ) ef i d 0 ef ef ef Te T e iq T e / KTe DESGN OF CONTROER SYSTEM n ode to deign the cuent contolle, we have the following expeion by eaanging the Eq. () to (4): pid Rid ud Cd v cd (22) piq Riq uq Cq v cq (23) pid Rid ud Cd v cd (24) piq Riq u q Cq v cq (25) The decoupling copenation te C d, C q, C d, and C q, and the inteediate voltage u d, u q, u d, and u q, in Eq. (7 20) ae given a follow: R C d id q q (27) R C q iq d d (28) Cd Cq R i d R i q d d d q d q (29) (30) u v v (3) u v v (32) q q q u v v (33) d d d u v v (34) q q q With the containt of vecto contol of Eq. (5), the echanical dynaic of Eq. (0) with Eq. (6) can be witten a follow: d JoES (207) STM Jounal 207. All Right Reeved age 4

5 Jounal of owe Electonic & owe Syte Volue 7, ue 3 SSN: X (Online), SSN: (int) p T T (35) n n e J J J t i evident fo Eq. (29) that the peed of a DFM can be contol by contolling the electoagnetic toque of DFM. Then the efeence fo tato q-axi cuent can be geneated fo the efeence of electoagnetic toque which i the output of peed contolle. Uing Eq. (7 20) and - doain of aplace tanfoation, the openloop tanfe function fo fou diffeent cuent contolle can be given a follow: T T (36) d q A T T (37) d q A Conideing the load toque T a a tep function the open-loop tanfe function fo peed contolle fo Eq. (29) i obtained a follow: T (38) A ( ) ( ) n Eq. (30) to (32) d q T, T, T d () () T e ( ) d T, A V ( ) cd, q A d, n (a) J V ( ) cd, T ( ) q T,, V ( ) cq q V ( ) cq, T R, T R, T, T. J R R (b) Fig. 3: lock Diaga of Stato Cuent Contolle. (a) d-axi cuent contolle, (b) q- axi cuent contolle (a) (b) Fig. 4: lock Diaga of Roto Cuent Contolle. (a) d-axi Cuent Contolle, (b) q-axi Cuent Contolle Fig. 5: lock Diaga of Speed Contolle of a DFM. To obtain the d-axi and q-axi tato and oto voltage with the ipleentation of vecto contol and baed on the Eq. (7) to (28), the block diaga of tato and oto cuent contolle ae hown in Figue 3 and 4. Siilaly, the peed contolle baed on and the calculation pocedue of efeence tato q- axi cuent i hown in Figue 5. The geneic fo of open-loop tanfe function Eq. (30 32) fo peed and cuent contolle can be witten a follow: G o A (39) The tanfe function of contolle and contolle ae given a follow: K G ( ) K e( ) (40) K G ( ) e( ) K a( ) (4) whee, e() = ()-a(), a() i actual value, () i efeence value, K i popotional gain and K i the integal gain. Cobining the open-loop tanfe function and contolle tanfe function the cloed-loop tanfe function can be witten a follow: JoES (207) STM Jounal 207. All Right Reeved age 42

6 Speed Contol of a Doubly Fed nduction Moto Zubai et al. G G c c () () K K 2 ( A K ) K K 2 ( A K ) K (42) (43) Conideing two pole and 2 (and they ae choen a = 2 ) in the left-half of coplex plane the gain of and contolle can be calculated a follow: 2 A K 2 (44) K t ha been een fo thee cloed-loop tanfe function of Eq. (36) fo contolle that a zeo i placed in the left-half plane. The ovehoot poble of contolle i aied due to the zeo and the ovehoot i inceaed a the popotional gain inceaed. On the othe hand, the zeo of contolle can be eliinated by changing the tuctue which becoe a contolle. The ovehoot poble can be iniized by uing contolle intead of contolle. SMUATON AND RESUT At fit the odeling of DFM i done by uing Eq. ( 5) have been developed in Matlab/Siulink oftwae. The ued DFM ating and paaete ae given in Appendix. The contolle of DFM with vecto contol tategy baed on contolle a hown in Figue 3 5 and contolle ha been pefoed fo tep change of peed to pefo iulation wok fo contolle, jut the contolle of Figue 3 5 eplaced by contolle. n the iulation wok, the gain ae choen ae value fo both contolle and contolle. The pole fo peed contolle i choen 50 and fo the fou cuent contolle the value of pole i choen of 500. Since the pole of cloed-loop yte ae placed in the left-half plane, the contolle pefoance i table unde the vaiation of load toque. Figue 6 and 7 how the tanient pefoance of peed contol yte of a DFM baed on the deigned contolle and contolle. n iulation wok, the vaiation of efeence peed ha been conideed a follow: (i) the peed tep-up fo 0 p to 600 p at tating condition i.e. t=0, the peed tep-up fo 600 p to 200 p at t =2, the peed tep-down fo 200 p to 600 p at t =4, the peed tep-down fo 600 p to 0 p at t =2, the peed tepdown fo 600 p to 0 p at t =6. Figue 6(a) and Figue 7(a) how the pefoance of peed fo contolle and contolle. The pefoance of both contolle i alot iila at teady-tate condition. ut it i clea fo thee figue that the ovehoot poble i totally vanihed in the pefoance of contolle. Figue 6(b) and Figue 7(b) evident that the tato d-axi cuent eaining zeo at teady tate condition and vey all change in tanient condition. Fo thee Figue, it ha been een that the vaiation of tato cuent baed on contolle at tanient condition i bette a copaed with that of contolle. Figue 6(c) and Figue 7(c) how that the tato d- axi flux i eaining contant which i the equieent of vecto contol tategy. Figue 6(d) and Figue 7(d) how the pefoance of electoagnetic toque with applied load toque. Since the ovehoot i occued in contolle the change of electoagnetic toque i lage a copaed with the ae pefoance in cae of contolle. CONCUSON Thi pape peent the deign of an contolle fo peed contol of a DFM. The iulation outcoe got on a DFM the uage of the contolle ae peented in thi pape. The oveall pefoance of contolle ued to be copaed with that of taditional contolled yte. Fo the copaative iulation outcoe of each and contolle, it can be concluded that the two contolle pefoance unde teady-tate condition ae alot ae. The ot neceay advantage to educe the ovehoot can be obtained by the ue of the popoed contolle. The two contolle againt yte paaete vaiant ae alo veified. t i evident fo the iulation outcoe that the pefoance of each and i alot iila when the paaete ae vaied. JoES (207) STM Jounal 207. All Right Reeved age 43

7 Jounal of owe Electonic & owe Syte Volue 7, ue 3 SSN: X (Online), SSN: (int) Contuctionally, thee i little diffeence between and contolle and each ipleentation will be eay and iple fo that eaon the ue of contolle can be oe pefeable than contolle fo pactical application. Fig. 6: Tanient efoance of Speed Contolle aed on. Fig. 7: Tanient efoance of Speed Contolle aed on. JoES (207) STM Jounal 207. All Right Reeved age 44

8 Speed Contol of a Doubly Fed nduction Moto Zubai et al. AENDX The DFM ating and paaete ae given a follow: Rating 75 kw, 2 pole, 500 p aaete R =35.52, R = 20.92, = 5.45 H, = 5.45 H, = 5. H, J = 0.00 Kg- 2, = 0.07 N/(ad/) REFERENCES. Michael S, Vicato, John A, Tegopoulo. A Doubly-Fed nduction Machine Diffeential Dive Model fo Autoobile. EEE Tan. on Enegy Conveion.2003; 8(2): p. 2. Akagi H, Sato H. Contol and efoance of a Flywheel Enegy Stoage Syte aed on a Doubly-Fed nduction Geneato- Moto. EEE owe Electonic Specialit Confeence.999; 27: 32 39p. 3. anda D, enedict E, Venkataaana G, Thoa A. ipo A Novel Contol Stategy of the Roto Side Contol of a Doubly-Fed nduction Machine. EEE. 200; p. 4. eonhad W. Contol Electical Dive. Geany, Spingie velag elin Heidelbeg; Wang S, Ding Y. Stability Analyi of Field Oiented Doubly Fed induction Machine Dive aed on Coputed Siulation. Taylo & Fanci Electical Machine and owe Syte Moel, Godfoid H, Mizaian A, Kauffann JM. Double-fed induction achine: convete optiiation and field oiented contol without poition eno. EEE oc. Elect. owe Appl. 998; 45(4): p. 7. Hopfenpege, Atkinon DJ, akin RA. Stato flux oiented contol of a cacaded doubly fed induction achine. EEE oc. Elect. owe Appl. 999; 46(6). 8. Hopfenpege, Atkinon DJ, akin RA. Stato flux oiented contol of a cacaded doubly fed induction achine with and without poition encode, EE oc. Elect. owe Appl. 999; 47(4): p. 9. Metwally HM. et al. Optiu pefoance chaacteitic of doubly fed induction oto uing field oiented contol. Elevie Science Enegy Conveion and Manageent. 2002; 43: 3 3p. 0. Akagi H, Sato H. Contol and efoance of a Doubly fed nduction Machine ntended fo a Flywheel Enegy Stoage Syte. EEE Tan. on owe Electonic. 2002; 7().. Djuovic M et al. Double Fed nduction Geneato with Two ai of ole. EMDC Confeence of Electical Machine and Dive EEE. 995; 42: 3p. 2. eonhad W. Adjutable-Speed AC Dive nvited ape. oceeding of the EEE. 988; 76(4): p. 3. ongya Xu, Wei Cheng Toque,Reactive owe contol of a Doubly Fed nduction Machine by oition oition Senole Schee. EEE Tanaction on nduty Application.995; 3(3): p. 4. eeada S, Tilli A, Tonielli A. ndiect Stato Flux-Oiented Output Feedback Contol of a Doubly Fed nduction Machine. EEE Tan. On contol Syte Technology. 2003; p. 5. Wang DH, Cheng KWE. Geneal Dicuion on Enegy Saving owe Electonic Syte and Application. oceeding 2004 Fit ntenational Confeence. 2004; p. 6. i Zang, Haan K H. Neual Netwok Aided Enegy Efficiency Contol fo a Field Oientation nduction Machine Dive. oceeding of Ninth ntenational Confeence on Electical Machine and Dive. EEE Confeence ublication. 999; David E. Rice. A Suggeted Enegy-Saving Evaluation Method fo AC Adjutable- Speed Dive Application. EEE Tan. on nduty Application.988; 24(6): 07 7p. 8. Jaie Rodiguez et al. Optial Vecto Contol of uping and Ventilation nduction Moto Dive. EEE Tan. on Electonic nduty. 2002; 49(4): p. 9. Did S, Nait-Said MS, Tadjine M. Double flux oiented contol fo the doubly fed induction oto Electic owe Coponent and Syte Jounal. 2005: 33(0). 20. Did, Said, Makouf, Abdela, Nait-Said, Mohaed-Said,Tadjine, Mohaed. Highly Efficient Contol of the Doubly Fed nduction Moto. Jounal of Electical Engineeing and Technology. 2007; p. JoES (207) STM Jounal 207. All Right Reeved age 45

9 Jounal of owe Electonic & owe Syte Volue 7, ue 3 SSN: X (Online), SSN: (int) 2. ete Va.Vecto Contol of AC Machine. Claendon e; New Yok: Oxfod Univeity e iaw CM, in FJ, Kung YS. Deign and pleentation of Highpefoance nduction Moto Sevo Dive. EEE oc.-.993; 40: p. 23. Mannan MA, Muata T, Taua J. Enegy Model aed Diect ToqueContol of nduction Moto Uing Contolle. Jounal of ntenational Confeence on Electical Machine and Syte. 202; : 9 5p. 24. Mannan MA. ntegal lu opotional Contolle aed Speed Contol of Diect Toque Contolled MSM. Aeican Acadeic and Scholaly Reeach Jounal. 203; 5: 80 90p. 25. Riadh RR, an MA, Shobial AM, Shahjalal M, Mannan MA. SpeedContol of An nvete Fed Thee-hae nduction Moto Uing Contolle Conideing Coe o and Stay oad o. Tend in Electical Engineeing. 205; 5: 28 35p. Cite thi Aticle Al-Mayhedee Zubai, Mohaad Abdul Mannan, Md. Kaul Haan et al. Speed Contol of A Doubly Fed nduction Moto uing ntegal lu opotional Contolle. Jounal of owe Electonic & owe Syte. 207; 7(3): 38 46p. JoES (207) STM Jounal 207. All Right Reeved age 46