Modeling and Field-Oriented Control of the Dual Stator Winding Induction Motor in the EMTP-Type Environment

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1 Modelng and Feld-Oented Contol of the Dual Stato Wndng Inducton Moto n the EMP-ype Envonent hban hbungu Abtact--he dual tato wndng nducton oto uppled by edundant Vaable Fequency Dve (VFD) fnd t applcaton n hp populon, locootve tacton, and aeopace. he edundancy of VFD lead to elablty and afety fo a contnuou avalablty of the yte even when one VFD ha faled. h pape popoe the odelng n an abtay efeence fae of dual tato wndng (wth an abtay dplaceent between the two thee-phae wndng et) nducton oto wth atuaton of the an flux fo the EMP-type oluton. he Indect Feld Oented Contol baed on the two ax d-q odel of the dual tato wndng nducton oto nvetgated and can be extended to any nube of phae, whch ae a ultple of thee. he contol can be pleented ung two VFD bult a an Actve Font End (AFE) Rectfe followed by Voltage-Souced Invete (VSI) baed nuodal PWM o cuent hytee contolle. he popoed odelng and contol wa ulated by ung the Engneeng Sute V6 oftwae and the ulaton eult how the plcty of the contol chee. Keywod: Dual Stato Inducton Moto (DSIM), Indect Feld Oented Contol (IFOC), Vaable Fequency Dve, AFE Rectfe. I. INRODUCION HE concept of ultphae (oe than thee-phae) achne odelng and dve not new. hee ae aleady lot of exaple n lteatue decbng ultphae achne [] [4], whch ae jut a epeentatve aple. Recently, oe attenton ha been gven to odelng and contol of a ultphae oto, epecally ultphae nducton oto. Geneally, a ultphae nducton oto dve ha any advantage ove the conventonal thee-phae dve uch a hgh powe capablty by dvdng powe between ultple phae, educed toque pulaton and hghe elablty. In patcula, wth the lo of one o oe tato wndng et, a ultphae nducton oto can contnue to opeate. he odelng and dve of a ultphae nducton oto can ue a vaety of tanfoaton. he yetcal coponent theoy and the atx theoy eve a theoetcal foundaton fo thee tanfoaton. A an advantage, by egentng equally the appled powe n ultphae nducton, t poble to upply hban hbungu wth Sat echnologe, Inc., Place du Coece, Boad (Québec), Canada, J4W 3B3. Engneeng Sute V6 a tadea of Sat echnologe, Inc. one o oe wndng unde balanced conon f fo any eaon oe of the cannot be uppled. he an focu of th pape to develop a dynac odel of the DSIM fo any abtay angle of dplaceent between the two wndng et fo the EMP-type oluton. he d-q odel n an abtay efeence fae odel ha been developed and can be ued to analyze the behavo of an nducton oto n any efeence fae. A ple IFOC chee contol fo an unatuated DSIM pleented ung two VFD bult a Actve Font End (AFE) Rectfe followed by VSI baed hytee cuent contolle. Snce the DSIM not avalable n tandad lbay of ot electcal oftwae, the valdaton and popoed contol of the Engneeng Sute V6 oftwae odel (ethe n teady tate o tanent) wee copaed wth the odel bult n the MALAB/SIMULINK envonent. Howeve, only the eult obtaned fo the Engneeng Sute V6 ae peented. A. Aupton II. MODELING OF DSIM he DSIM degned a an electoechancal yte copoed on the tato de by two wye thee-phae wndng, whch ae gounded though two epaate neutal pedance, efeed to a tato 1 and tato and on the oto de by a coon quel cage. he quel cage eplaced by an equvalent thee-phae wndng. he DSIM depcted n Fgue 1. he odelng of th oto ue the followng aupton: Stato wndng ae nuodally buted aound the a gap, he two et of tato wndng ae patally hfted by an electcal angle α, he yety of the wndng and only the atuaton of the an flux ae condeed, he agnetc couplng between tato wndng 1 and condeed though the an flux; the couplng of thee wndng though the leaage flux neglected, All the electoagnetc vaable and paaete of the oto ae efeed to the tato de. Pape ubtted to the Intenatonal Confeence on Powe Syte anent (IPS015) n Cavtat, Coata June 15-18, 015

2 unat unat d L d1 L d L d d (16) b b1 b a a α a1, d q d-q agnetzng flux coecton te R, L Neutal etance and nductance n n he echancal equaton gven a follow: c1 c Fg. 1. Wndng of DSIM B. DSIM equaton n dq0 Refeence Fae he odelng of the DSIM tat wth the clacal appoach of odelng the thee-phae nducton oto. he DSIM condeed a two ndependent thee-phae oto coupled though a coon oto wndng. he Pa tanfoaton tanfo abc efeence fae voltage and flux equaton nto an abtay dq0 efeence fae. ang nto account the an flux lnage atuaton by addng the d-q agnetzng flux coecton te [10] to the an flux, the voltage and flux equaton nto an abtay dq0 efeence fae ae a follow: dq1 vq1 Rq1 ωd1 (1) dd1 vd1 Rd1 ωq1 () d01 v01 ( R 3 Rn ) 01 (3) dq vq Rq ωd (4) dd vd Rd ωq (5) d0 v0 ( R 3 Rn ) 0 (6) dd vd Rd ( ω ω ) q (7) dq vq Rq ( ω ω ) d (8) unat unat q1 Lq1 L q L q q c (9) unat unat d1 Ld1 L d L d d (10) ( l 3 L ) (11) 01 σ n 01 unat unat q Lq L q1 L q q (1) unat unat d Ld L d1 L d d (13) ( l 3 L ) (14) 0 σ n 0 unat unat q L q1 L q Lq q (15) dω J e dω load (17) ( 1 ) ( 1 ) 3 p L e d q q q d d L (18) ω ω (19) p ω, ω p, d load, e Mechancal and electcal peed ad/ Nube of poleand dapng facto N /ad Load and electoagnetc toque C. anent Modelng Snce v d 0 and v q 0, equaton (15) and (16) nto (7) and (8) and applyng the tapezodal ule, the atx fo of oto d-q cuent n an abtay efeence fae a follow: d 1 d q1 htd ( t ) [ C] q ht ( ) d q t q ( ) ( ) ht t, ht t Roto d-q htoy te d q Saple te [ C ] -by-4 atx (0) Replacng (9) to (14) nto (1) to (6) and applyng the tapezodal ule, we have: d 1 vd 1 q1 htd 1 ( t ) vq1 ht q1 ( t d ) [ Z ] vd ( t ) q t htd ( t ) vq htq ( t d ) q (1)

3 ( ) ( ) v0 1 t R t ht0 1 t v0 t 0 R 0 0 t ht0 t ( lσ 3 Ln ) R0 ( R 3 Rn ) Z 4-by-6 etance atx [ ] ( ) ht t () Stato dq0 htoy te fo d1, d, q1, q,01,0 he eleent n atce [ C] and [ Z ] ae a functon of the oto paaete and the peed devaton. Snce the peed change lowly, n copaon wth the electcal quantte, and peed at te t unnown, the equaton (0) and (1) ae lneazed by ung the pedcto coecto ethod [8]. he followng pedcton ued: ( t ) ( t ) ω ω ω (3) he tato and oto d-q htoy te ae not only dependent on pevou d-q cuent and peed devaton but alo on pevou and actual d-q agnetzng flux coecton te. Snce d-q agnetzng flux coecton te at te t ae unnown, the thee-pont pedcto foula wll be ued (ee atuaton odelng). Replacng (0) nto (1), we have: vd 1 t d 1 t ed1( t ) v t t e ( t ) q1 q1 q1 R dq v e d ( t ) d t d t v t t eq ( t ) q q R dq 4-by-4 etance atx (4) Applyng Pa nvee tanfoaton (ee appendx), the voltage equaton n abc efeence fae ae a follow: vabc1 t Zabcabc1 t Zabc1 abc t eabc1 (5) vabc t Zabc1abc1 t Zabc abc t eabc (6) conductance equaton fo a follow: abc 1 t vabc 1 t h 1 t [ G] abc t vabc t h t 1 [ ] Gabc Gabc1 Zabc Zabc1 G Gabc1 Gabc Zabc1 Zabc 6-by-6 conductance atx (7) h 1 t eabc 1 t h [ G] 6-by-1 cuent htoy h t eabc t he odelng n a oto, fo a ynchonou and tatonay efeence fae, ae obtaned epectvely by ettng: ω ω, ω ω, ω 0 Gven a powe yte netwo decbed by the followng nodal equaton: t G v t hn n abcn (8) Hee, ouce, hn n epeent the netwo htoy cuent G denote the oveall conductance atx wthout ncopoatng the DSIM conductance atx and vabcn epeent the nodal voltage. A ngle DSIM ntefaced wth the above powe yte netwo by olvng (7) fo the tato cuent and then ubttutng the nto (8). he fnal lnea yte of equaton n te of nodal voltage ha the followng tandad fo: h t Geq vabcn t (9) Fgue llutate the foulaton of (9) whee t hown that G n and hn t ae odfed by ncludng the 6-by-6 h 6-by-1 oto cuent htoy te to the coepondng oto node. oto equvalent conductance [ G ] and [ Zabc ] [ Z ] [ Z ] e abc1 abc1 abc1 abc Self-etance atx, Mutual etance atce, e Voltage behnd etance D. Intefacng DSIM wth EMP-type netwo oluton he coplete odel of the DSIM fo the EMP-type oluton obtaned afte cobnng (5) and (6) n the Fg.. Contbuton of the DSIM to the netwo nodal equaton.

4 E. Satuaton Modelng he chaactetc of nonlnea nductance cuent dependent can be epeented a a ult pecewe lnea nductance wth oe lope. Let aue that the flux veu agnetzng cuent povded (Fg. 3.), whch only the ft quadant hown, and uppoed to be yetcal. unat L unat L unat d d (36) unat q q (37) 3. Detene the appopate pece of atuated lne ung and calculate the agnetzng flux coecton te: unat t L b (38) 4. Calculate d-q agnetzng flux coecton te a follow: he agnetzng flux gven a follow: Fg. 3. Magnetzng Flux v cuent of the DSIM unat L at fo a gven agnetzng cuent (30) < 0 the agnetzng flux coecton te. unat d d (39) at unat q q (40) at III. INDIREC FIELD ORIENED CONROL Neglectng atuaton and f we chooe a new d-q ax otatng at a ynchonou peed and algned wth the oto feld, that ean q 0, and the electoagnetc toque wll be: Snce the agnetzng flux veu cuent can be appoxated at t L t a a ult pecewe lnea cuve a, whee the nee pont flux, the teatve algoth fo calculatng the d-q flux atuaton effect a follow: e 3 p L L dq q q1 q (41) 1. Calculate the agnetzng cuent ung the thee-pont pedcto foula: ( t ) ( t ) ( t 3 ) (31) 4 4 t t t t (3) 1 d d d d t t t t (33) q q1 q q t d t q t, Repeent d-q agnetzng cu ent d q May be,,,,, d1 d q1 q d q (34). Calculate the unatuated flux (a gap taght lne), d and q utual flux ung the pedcted d-q cuent: unat L unat (35) If contant, whch ple that 0, the d electoagnetc toque wll depend only on q equaton (8), (15) and (16) gve: Rq ω Ld d. Hence, ω (4) d d L (43) d d1 d If the agntude d ha to be changed, (7), (16) and nowng that q 0, we have: L d d (44) 1 τ L τ R

5 A. VSI Baed Hytee Cuent Contolle Snce the nvete contolled by a hytee cuent contolle, only the peed and flux contolle hould be degned. 1) Flux PI Contolle Degn he followng contolle wll output the d ax cuent (efeence) d gven a follow: L and pf pf ( 1 τ ). Ung (44), the open loop tanfe functon ( 1 ) (45) ae epectvely the te contant and popotonal gan of the flux contolle. Fo a gven α, te contant of the flux cloed loop tanfe functon, the flux contolle paaete ae calculated ung the Intenal Model Contol (IMC) and the tanfe functon gven a follow: G c ( ) τ 1 L α L α (46) Snce both tato ut have equal d ax cuent, d ax cuent (efeence) fo each tato obtaned a follow: d1 d d (47) ) Speed PI Contolle Degn he followng contolle wll output a efeence toque e. Ung (17) and (41), the open loop tanfe functon gven a: p ( 1 ) ( ) (48) 1 τ an d p ae epectvely te contant and popotonal gan of the peed contolle. 3 p L t J,, τ L t d d d By ung the pole placeent ethod, one can place pole at p 1 and p, and t wll be aued that p1 the donant pole. hu, the peed contolle paaete ae calculated a follow: p ( p p ) τ 1 1 p τ p p 1 he u of tato q ax cuent obtaned by ung (41), whee toque and flux ae epectvely the output of peed and flux contolle. Fo both tato havng equal q ax cuent, we have: q1 q q (49) B. Vaable Fequency Dve and Contol Fgue 3, 4 and 5 uaze the pleentaton of the two VFD dve DSIM. Paaete of the DSIM and load odel ae gven n the appendx. VFD have been degned n Engneeng Sute V6 wth unty powe facto AFE ectfe. DC voltage contol ae baed on hytee cuent contolle and voltage contolle ae degned ung abc Refeence Fae ethod. vabc d abc 0 q θ abc Fg. 4. Daga bloc of an AFE ectfe DC voltage contol IV. SIMULAION PARAMEERS A. AFE Rectfe Contolle and Degn fo Unty Powe Facto wo epaate 3-phae voltage ouce 460 V, 60 Hz, R 0.15 Ω,L 8 H upply two AFE ectfe that feed the nvete. he DC efeence voltage et to 1000 Volt. he IGB (odeled by deal wtch n paallel wth a dode) tggeed by a hytee contol whch et to h ±0.1 A. he dode nubbe RC ae C n 0.1 µf and R n 500 Ω.he capacto ntally chaged at 1000 Volt and C 5000 µf. pv ABLE I AFE RECIFIER VOLAGE CONROLLER PARAMEER pv v Voltage contolle and v ae epectvely the popotonal and ntegal of the ectfe voltage contolle.

6 Fg. 5. Daga of VFD dve DSIM e q q abc d 3 p L L abc L 1 τ d d d q1 d1 abc1 abc d α abc1 abc1 q Fg. 6. Daga bloc of the DSIM peed contol wth IFOC B. DSIM Contolle and Degn he two nvete that contol the DSIM ae contolled by a hytee cuent contolle. he hytee contol et to h ± 0.5 A. Ung the foula developed fo peed and flux contolle, the followng table uaze the PI Contolle paaete. p and ABLE II DSIM FLUX AND SPEED CONROLLER PARAMEERS Flux contolle Speed contolle ae epectvely the popotonal and ntegal of the flux o peed contolle. V. SIMULAION RESULS he ft cenao wa caed out to copae onlne tatup of the atuated (blac colo) and unatuated (blue colo) p oto dvng load odel 1. Fgue 7 and 8 how the peed (ad/) and electoagnetc toque (N) of the atuated and unatuated oto ung the odel pleented n the Engneeng Sute V6. Fgue 9 and 10 how the tato cuent (A) of both tato (cae of unatuated oto). he econd cenao wa caed out ung VFD to dve the DSIM connected to the load odel. A efeence peed of 10 ad/ and -10 ad/ ae appled epectvely at t 0 and t 1.6. Fgue 11 and 1 how contol of electoagnetc toque and peed. oque lted to 500 N a equeted. Fgue 13 and 14 how tanent and teady tate of both tato cuent (A). Both cuent ae equal n agntude nce d-q cuent contol ae equally haed between both tato. Fgue 15 how contol of the flux (Wb) veu t efeence. he thd cenao tude the behavo of long one of the nvete when the yte connected to load odel. A efeence peed of 10 ad/ appled and nvete lot at t 1.4. Fgue 16 and 17 how peed (ad/) and electoagnetc toque (N). A expected at t 1.4 when nvete dconnected, peed and toque dop. he toque fall to half of the teady tate value befoe nceang to the deed value equeted by the peed contolle n ode to

7 eet the efeence peed. A a conequence, Fgue 18 and 19 how tanent and teady tate of both tato cuent (A), whee tato 1 cuent double the teady tate value. Fgue 0 how the tanent of flux (Wb). Fg. 7. Speed fo unatuated v atuated oto Fg. 8. oque fo unatuated v atuated oto Fg. 9. Stato 1 cuent fo unatuated oto Fg. 10. Stato cuent fo unatuated oto Fg. 11. Electoagnetc v Load toque Fg. 1. Speed v efeence Fg. 13. anent-dsim tato 1 cuent Fg. 14. anent-dsim tato cuent Fg. 15. Magnetzng flux v efeence Fg. 16. Speed v efeence Fg. 17. Electoagnetc v Load toque Fg. 18. anent-dsim tato 1 cuent

8 Fg. 19. anent-dsim tato cuent Fg. 0. Magnetzng flux v efeence VI. CONCLUSIONS he odelng of the DSIM fo the EMP-type oluton and a ple appoach to the IFOC ha been peented. he valy of the odel and contol wa vefed by eveal nfoatve ulaton. he odelng and contol of the DSIM ae baed on a two axe d-q odel, and can be ealy extended to any nube of phae, whch ae a ultple of thee. he DSIM can be odeled n any efeence fae and any abtay angle dplaceent between the two thee-phae wndng et. he edundancy of the VFD pove elablty and avalablty of the yte even when one VFD ha faled. Wthn the acceptable lt fo the DSIM cuent, the ple IFOC peented allow contol of the DSIM unde balanced conon and equed toque even when one of the nvete out of evce. VII. APPENDIX Load Model 0.5 ω, gn ω ω load1 load Pa nvee tanfoaton nγ coγ 1 f n ( π ) co( π abc γ γ ) 1 f 3 3 dq0 n ( γ π ) co ( γ π ) Fo the oto γ θ θ, fo the tato 1 γ θ and the tato γ θ α. f : Voltage o cuent θ : Angle between tato and oto dentcal phae θ : Angle between q ax and tato phae A he DSIM a 460 V, 60 Hz, 4 pole and α 30. he axu toque allow 500 N and the oto ungounded though an pedance R 1e5 Ω, L 0 H. he DSIM paaete ae gven n table III. Stato etance Roto etance ABLE III n DSIM PARAMEERS Roto leaage nductance Stato leaage nductance Magnetzng nductance R R n Ω 0.8 Ω l σ 0.8 H l σ 0.8 H L 34.7 H Moent of Ineta J 1.66 g Rated flux 1 Wb d Satuaton cuve ( Wb) Fo 8.9A ( Wb) Fo > 8.9A 0 VIII. REFERENCES [1] Alf Kae Adnae, Mate Electcal Intallaton and Deel Electc Populon, ABB AS Mane, Olo, Apl 003. [] Sngh G. K., Na K. and L S. K., A ple ndect feld-oented contol chee fo ultphae nducton oto, IEEE an. Ind. Elec., vol.5, Aug [3] A. Munoz and. A. Lpo, Dual tato wndng nducton achne dve, IEEE an. Ind. Appl., vol.36, Sept/Oct [4]. A. Lpo, A d-q odel fo x phae nducton achne, Poc. Int. Conf. Electc Machne, Athen, Geece, [5] D. W. Novotny and. A. Lpo, Vecto Contol and Dynac of AC Dve. Oxfod, U.K. Claendon, [6] Zhao Y. and. A. Lpo, Space Vecto PWM Contol of Dual hee- Phae Inducton Machne Ung Vecto Space Decopoton, IEEE an. Ind. Appl., vol.31, [7] G.K. Sngh, Mult-phae nducton achne dve eeach- A uvey, Elect. Powe Syt. Re., vol. 6, 00. [8] Doel, H. W., EMP heoy boo, Mcotan Powe Syte Analy Copoaton, Vancouve, [9] Hubet Raz, Handboo of Aynchonou Machne wth Vaable Speed. 1 t Eon, Wley, 011. [10] P. C. Kaue, O. Waynczu, S.D. Sudhoff, Analy of Electc Machney and Dve Syte. nd Eon, IEEE Pe, Wley- Intecence, 00. [11] M. P. Kazeow, F. Blaabjeg, R. Khnan, Contol In Powe Electonc. Selected Poble. Acadec Pe, 00. [1] Gaha C. Goodwn, Stefan F. Gaebe, Mao E. Salgado, Contol Syte Degn. 1 t Eon, Pentce Hall, 000.