TWO INDUCTION MOTORS ELECTRIC DRIVE WITH ROTATORY STATOR

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1 TWO INDUCTION MOTORS ELECTRIC DRIVE WITH ROTATORY STATOR Alexade PUGACHEV Electoic, Radioelectoic ad Electic Egieeig depatmet, Byak State Techical Uiveity Byak, Ruia Fedeatio, Adey KOSMODAMIANSKIY Tactio Rollig Stock depatmet, Mocow State Uiveity of Railway Egieeig (MIIT Mocow, Ruia Fedeatio Abtact: The bief uvey of techique to etict the tat cuet of a iductio moto i caied out. The electic dive coited of two idetical iductio moto oe of which ha otatoy tato i popoed a a alteative type of oft-tate. The piciple of it opeatio fom the theoetical backgoud i coideed. The equivalet cicuit of electic dive i developed ad mathematical model o it bae i deiged. The expeimetal etup to validate the mathematical model i decibed. The eult of both imulatio by Matlab ad expeimetal ivetigatio ae peeted. The aemet of powe loe i the popoed electic dive how a poibility to ue it a a adjutable electic dive i ome applicatio without tog equiemet to peed cotol. Key wod: iductio moto, oft tat, otatoy tato, equivalet cicuit, powe loe. Itoductio The uvey of tate-of-at electic dive how that thee ae a umbe of a diffeet techique ad appoache to cotol the peed of a iductio moto [,, ]. Motly, it eed a fequecy covete to feed a iductio moto ad implemet ome of cotol cheme that povide deiable quality idicato i tem of efficiecy, tability, accuacy, etc. But thee ae till a quite coideable umbe of applicatio that do ot have a tict equiemet o the wide age of peed, it accuacy, taiet time ad o o. Itead of it, the etictio of tat cuet ad toque, the ability of wok i evee eviometal opeatig coditio have to be fulfilled. The electic dive of thi kid ae ofte coected to ychoou geeato that povide upplyig. The typical example of uch applicatio ae the fa, ai compeo, wate ad oil pump, foge ad pe mechaim deiged fo quay, mie, Fa Noth coditio. The pectum of optio of fequecy covete ae ofte exceive to cove demad ove cotol of thee applicatio. Moeove, the ue of evee duty fequecy covete i liked to additioal paymet to buy it ad eceity of highkilled taff to maitai it thoughout it opeatio. A a eult, the mot pefeable way to avoid the complicatio i to itoduce a techique of oft tatig oly to etict tat cuet ad toque [4]. The hitoically fit method fo oft tat i implemetatio of oe o moe et of eito which, duig tat, ae coected i eie with the gid to the tato widig. Thee i a vey high powe diipatio i the eito, eultig i the equiemet fo vey high powe ated eito. Typically, the eito will diipate a much a 50% - 00% the powe atig of the moto fo the duatio of the tat. The igificat impovemet of efficiecy duig tat wa eached by ubtitutio of eito by eactace. It led to coideable educig of heat loe, but the poblem of o-dicete cotol wa till i place. Aothe appoache fo oft tatig ae the itoducig of auto tafome, the ue of ta delta tate, lip ig o woud oto moto with additioal eito coected to it. Each of appoache ha ome advatage ad hotcomig that limit it implicatio. Nowaday, the mot popula oft tate fo a iductio moto i the wide age of powe ae baed o thyito o IGBT cheme [5]. Thyito o IGBTbaed oft tate allow to iceae moothly the voltage applied to the tato widig that lead to epective chage of cuet ad toque. A a mai deficiecy of thee device, the eceity of peece of killed electoic taff ha to be highlighted fo maitaiig ad epaiig. Oe of feaible way to olve thi poblem i to employ the two iductio moto electic dive with otatoy tato. Thi electic dive doe ot cotet ay emicoducto witche o eitive elemet. It ha imple cheme fo electical coectio ad high eliability duig opeatio. The mai hotcomig of the dive i ome ophiticatio i mechaical deig. The popoed electic dive ae alo able to cotol peed i a mall age of it without igificat deatig of efficiecy. The eult of both theoetical ad expeimetal ivetigatio of the electic dive ae peeted i thi aticle.

2 . Piciple of opeatio The cheme of the electic dive coited of two the ame woud oto iductio moto oe of which ha a otatoy tato i how i Fig.. Fig.. Scheme of the electic dive The value of ated powe of each iductio moto, IM ad IM, i the ame ad it equal to half of ated powe eeded by electic dive. The tato widig ae coected to the ame voltage upply, v =v. The oto widig ae coected i eie with each othe. The haft of moto ae liked togethe. The tato of the IM i mouted o that it ca otate aoud the axle by ome auxiliay device, AD. The piciple of opeatio i decibed by Fig.. a b c d Fig.. Vecto diagam of the electic dive While the electic otatio agle of the IM tato φ =0 (Fig.,a, the EMF, E ad E, iduced i the oto widig of the IM ad IM, epectively, ae diected oppoite, it eultig value of EMF, E Σ, equal to ull. It lead to the oto cuet of I =0 ad the toque of T eσ =0. If the otatio agle of φ 0 (Fig.,b, the the E Σ 0, the cuet of I tat to flow i the oto widig ad T eσ 0 that lead to the movig of the moto haft. The active compoet of 0a of the oto cuet fo the IM ha a oppoite ig to the E. It mea that ude thi agle of φ the toque of the IM i egative to the eultig toque of two moto ad it peed ad it ha bakig effect. The active compoet of 0b of the oto cuet fo the IM ha the ame ig a the E that lead to the poitive toque. Futhe iceaig of the φ otate the E ad, coequetly, E Σ clockwie (Fig.,c. A a eult, the both Oa ad Ob ae diected the ame diectio a the epective EMF. The toque of IM ad IM have the ame diectio a the eultig toque ad peed. If φ =π (Fig.,d, E ad E coicide totally ad the E Σ equal to algebaic um of E ad E, i.e. E Σ =E +E. The I i placed the ame way to E ad E ad both IM ad IM have the ame toque T e =T e =T eσ /. Ude thee coditio the peed of the moto ha the maximum value that deped o the voltage upply fequecy a i diect o lie mode.. Mathematical model The ix diffeetial equatio elatig the tato ad oto voltage to the tato ad oto cuet ha bee educed to fou equatio by uig the famou pak tafomatio [6]. Thi tafomatio offe, beide implificatio, the advatage to elimiate completely the time vayig paamete. The equivalet cicuit fo the two iductio moto electic dive with otatoy tato i the tatioay fame i how i Fig.. I Fig., R, R deote the tato ad oto eitace; L l, L l do the tato ad oto leakage iductace; L m doe the magetizig iductace; R i doe the eitace epeetig the io loe i the tato due to eddy cuet ad to hyteei cuet; ω, ω do the electic peed of the both oto haft ad the tato of IM; i, i do the cuet flowig though the tato ad oto widig; i m, i i do the cuet flowig though the iductace of L m ad eitace of R i ; λ, λ, λ m do the tato, oto ad magetizig flux likage, epectively. Subcipt of ad effe all the vaiable ad paamete to the IM ad IM, epectively. Accodig to the equivalet cicuit, the tato ad oto voltage equatio i the tatioay fame i the vecto fom ae the follow: dλ dλm v = R i + + ( dλ dλm v= R i + + jω ( λ + λm ( Fig.. Equivalet cicuit fo the two iductio moto electic dive with otatoy tato

3 dλ dλ dλm dλ 0 = R i jω ( λ + λ + λ + λ jω λ m m m m ( dλm Ri ii = (4 dλm Ri ii = + ωλm (5 i + i = i + i (6 m i i m + ii = i + i (7 The actual ig of λ m i the equatio of ( deped o the diectio of cuet flowig though the magetically coupled iductace ad it will be extacted futhe i thi ectio. Fom the ectio oe ca coclude that the pace poitio of the two tato i ot coicided i geeal. Sice that, it i eceay to itoduce two tatioay fame liked to epective tato. Lettig tatioay fame of β lik to the tato of IM ad tatioay fame of β lik to the tato of IM, we obtai pace poitio of all the widig, a how i Fig. 4. Fig. 4. Space poitio of the widig It i obviou that two iductio moto have the haed haft ad oto cicuit ad do ot have ay magetic lik. To decide the equatio of ( - (7, it eed to employ the depedace betwee flux likage a epective cuet: λ = Lli (8 λ = L i (9 l λ m = Lmim (0 Geeally, the pace poitio of the widig i chagig duig electic dive wokig. The fame ha bee chooe o that the oto widig of both IM ad IM (all iductace of L l i the Fig. 4, the tato widig of the IM (iductace of L l with cuet of i ad i β flowig though ad the magetizig widig of the IM (iductace of L m with cuet of i m ad i mβ flowig though wee aliged to fame of β. Thu, the oly widig that otate with the fame of β, i.e. with the tato of the IM, ae the tato widig of the IM (iductace of L l with cuet of i ad i β flowig though ad the magetizig widig of the IM (iductace of L m with cuet of i m ad i mβ flowig though. The oto widig coected i eie ad decibed by equatio of ( caue the eceity of tafomig of the IM magetizig flux likage fom the β to the β. Sice the coodiate of the cuet ad flux likage complete the whole age of chagig duig the electical agle of φ =π the the ext equatio follow with egad to diectio of the cuet of i, i β, i m, i mβ flowig though the magetically coupled iductace of the IM ad otatio agle how i the Fig. 4: λm = λm coϕ + λmβ iϕ ( λmβ = λm iϕ λmβ coϕ ( Thu, takig (8 - ( ito accout, the equatio of ( - (7 i tafomed below to olve it elatively to the 6 ukow cuet ad 4 flux likage. The tato voltage equatio: di dλm v = R i + Ll + ( diβ dλmβ vβ= R iβ + Ll + (4 di dλm v = R i + Ll + + (5 + ω ( L i + λ l β mβ diβ dλmβ vβ = R iβ + Ll + ω ( Lli + λm The oto voltage equatio: di dλm dλm 0 = R i + Ll + dλmβ coϕ + iϕ + ω (Lli + λm + ( ω + ω ( λ iϕ λ coϕ m mβ diβ dλmβ dλm 0 = R iβ + Ll + dλmβ iϕ coϕ ω (Lli + λm ( ω + ω ( λ coϕ + λ iϕ m mβ β + (6 (7 (8 The magetizig ad io loe cotou equatio: dλm Ri ii = (9 dλmβ Ri iiβ = (0

4 dλm R i ii = + ωλm ( dλmβ Ri ii β = ωλmβ ( To omit all the i i fom (9-(, it eed to ue the cuet equatio. The cuet equatio of the IM: i + i = i + i ( m i i + i = i + i (4 mβ iβ β β To wite cuet equatio of the IM, it eed to tafom the oto cuet fom fame of β to fame of β: i = i co ϕ + iβ iϕ (5 iβ = i i ϕ + iβ coϕ (6 The, the cuet equatio of the IM: im + ii = i + i co ϕ + i iϕ (7 i m β ii β = iβ i i + iβ + ϕ coϕ (8 The implemetatio of equatio of (-(8 allow u to calculate all eeded cuet ad flux likage i the tatioay fame liked to two tato. The tato ad io loe cuet ad magetizig flux likage of the IM ae obtaied i the fame of β but to tafom it to β hould ot be a iue. Alo, it hould be oticed that the tato otatio peed of ω i much malle tha the oto peed of ω. A a eult, all compoet of equatio of (5-(8 ad (, (, cotetig of ω, become eglectable. The geeal expeio fo toque of a iductio moto: β β λ T = i λ = i (9 e = = ϕ ϕ The toque i the eult of iteactio of magetically coupled iductace. Fo the IM all iductace place otgoal axe while iductace of the IM place o axe mutual poitio of that deped o otatio agle of φ. The expeio fo toque of each iductio moto: T T p [( L i + λ λ ( L i + λ λ ] e = l µ µ β l β Ll e = p L l β µ β [( L i λ coϕ + λ iϕ l m mβ ( λm iϕ λmβ coϕ + ( Lliβ λm λ coϕ ( λ coϕ + λ iϕ ] µ iϕ mβ m mβ The total toque of both IM ad IM: T eσ = Te + Te (0 The iductio moto with otatoy tato i a electic moto havig two movig uit which ae tato ad oto. Thu, the equatio of mechaic movig ae the ext: J p Σ dω = Te Σ T L ( J Σ dω = Te TL ( p whee J Σ, J Σ deote the total momet of ietia of the otatoy tato of IM ad the oto haft of IM ad IM with the mechaical uit coupled to them, epectively, p deote the umbe of the tato widig pole pai, T L, T L deote the load toque applied to the otatoy tato ad the oto haft, epectively. 4. Reult of imulatio Simulatio of the electic dive wa caied out by uig of Matlab. The load device i imulatio wa a cetifugal fa with quae depedece of load toque fom peed. The ated paamete of iductio moto of IM ad IM ae the ext: P at =. kw, V,at =0 V, f,at =50 Hz, p =, R =.6 Ω, R =4.9 Ω, L l =0.008 H, L l =0.06 H, L m =0. H, R i =4 Ω, whee P at, V,at ad f,at deote the output powe, tato voltage ad it fequecy, epectively. The imulatio wa eplicated with the tato cuet fequecy of f 50 Hz. The depedace of the R i fom the f wa take ito accout by the ext empical equatio [7]: R i = f f The depedace of the L m fom the magetiig cuet, I m, wa take ito accout by the ext equatio [7]: L = 0.00I I 0.6I I.87I + 0.4I +.4 whee L = Lm / Lm, at, I = I m / I m, at Some eult of imulatio ae how i Fig. 5, 6. a b Fig. 5. Reult of imulatio (V = 0 V, f = 50 Hz, φ = π ad 4

5 5. Expeimetal etup ad eult The pefomace of the uggeted electic dive i expeimetally validated by eult obtaied by expeimetal etup, the block diagam of which how i Fig.. The expeimetal etup itelf i how i Fig. 7. a b Fig. 6. Reult of imulatio πt / 0 ad, t 0 (V = 0 V, f = 50 Hz, ϕ = π ad, t > 0 A it could be ee fom Fig. 5 ad 6, the oft chagig of φ fom 0 to π lead to deceaig of total tato cuet ad toque. It hould be oticed that the φ = π povide the equality of the tato cuet of both IM ad IM. While φ =0, the tato cuet alo equal to each othe ad oughly to o-load cuet. While 0<φ <π, the tato cuet have diffeet value. Alo, the eult of imulatio how that eve fo zeo agle betwee the two tato thee i quite a high value of the hot-tem peak taiet tato cuet due to witchig of the tato widig, i.e. RL cicuit, to the full voltage of the gid. Thi peak value i eticted oly by the tato eitace, electical ietia of the tato iductace ad level of the magetic atuatio, o fo the toge etictio of the taiet cuet it could be ecommeded to put a hot-duty eitace eie to the tato widig. Aothe way to avoid the high peak cuet i to employ a ychoou geeato that dimiihe the cuet due to it ow eactace (ychoou geeato i alo ued fo the expeimetal ivetigatio i the ext Sectio. Thi i feaible epecially fo vehicle that upply all electical load by a geeato. It hould be oticed that the atio of the peak cuet to the ated oe iceae with iceaig of the powe of electic dive. Fo a mall ad medium powe dive (o moe tha a few te of kw, the peak value of the cuet doe ot exceed the ated cuet ad doe ot lead to ay dageou coequece. Thu, the poblem of the peak cuet eed caeful coideatio fo the lage dive whee employmet of the additioal hot-duty device o ychoou geeato could educe the peak cuet ad povide deiable oft tat. Fig. 7. The expeimetal etup The detail of IM ad IM coectio ae decibed i Sectio, the paamete of the iductio moto ae peeted i Sectio 4. Afte uvey beig caied out, the DC moto fed by IGBT-baed H-bidge cicuit i decided to be ued a the auxiliy device, AD, fo the pupoe of otatio of the IM tato. The DC moto peed ad agle i cotolled by mea of pulewih modulatio of the amatue voltage. The powe of DC moto ha to be eough to otate the IM tato ad hold it i the poitio eeded. The load toque of the DC moto i the toque of the IM, T e. The tafe uit betwee the DC moto ad the tato i a wom eductio uit liked to the tato by teel ope. The ated electical paamete of the DC moto ae the follow: the amatue voltage i 0 V, the amatue cuet i. A. The cetifugal fa coupled to the IM ad IM haft by cada haft i the load device of the electic dive. ACS7 cuet eo, maufactued by Allego Micoytem, ae ued fo cuet meauemet. E40S6 icemetal ecode, maufactued by Autoic, ae ued fo the IM ad IM oto peed ad DC moto peed ad agle meauemet.the igal fom all cuet eo ad ecode ae coected to the multi-fuctio boad of aalog-todigital coveio of the LA-USB, maufactued by Rudev-Shilyaev, ad fom it to the peoal compute. The tato widig of the IM ad IM ae upplied by voltage comig fom yhcoou geeato that povide it iuoidal hape ad, a it wa teed befoe i Sectio 4, educig of the peak taiet cuet. Fig. 8 ad 9 how the both expeimetal ad imulatio eult. 5

6 a b ( i u i u P = + β β (5 The total active electic powe of the electic dive: P Σ = P + P (6 Accodig to the Fig., the total powe loe of the electic dive coit of loe i the coppe of the two tato widig ad two oto widig ad loe i the io of the two tato yoke. The total powe loe ca be foud fom the equatio of powe balace: Plo = P Σ Pmech (7 The depedece of atio of the total powe loe to the ated mechaical powe of the electic dive, P at,σ = =P at, + P at, =P at, fom the otatio agle i how i Fig. 0. c Fig. 8. Reult of expeimetal (olid ad imulatio (dahed ivetigatio of taiet mode (V = 50 V, f = 7.5 Hz, φ = π/ ad Fig. 9. Reult of expeimetal (olid ad imulatio (dahed ivetigatio of teady tate (V = 0 V, f = 50 Hz 6. Aemet of efficiecy A it could be ee fom the Fig. 9, two iductio moto electic dive ha a ability to cotol peed ove ome age. It idicate to the fact that thi electic dive could be implemeted ot oly a oft-tate but alo a a adjutable dive. To ae thi poibility, it eed to calculate the feaible age of peed i which the electic dive ha the appopiate efficiecy ad powe loe. The ext equatio wee employed to etimate the powe loe. The mechaical powe o the moto haft: P mech = TeΣω / p ( The active electic powe of each moto: P = ( i u + iβuβ (4 Fig. 0. Ratio of the powe loe to the ated powe v. otatio agle (V = 0 V, f = 50 Hz It hould be oticed that, with the φ =π, the powe loe coicide with it ated value. A it could be ee fom the Fig. 0, the cuve of the powe loe ha the clea poit of miimum with value of the otatio agle malle tha π (thi cae φ =0.86π. Sice the diffeece of peed caued by chagig of φ fom π to 0.86π i vey mall (Fig. 9 the it could be ecommeded to adjut the otatio agle i the poitio that povide the miimum of loe. The coideable deceae of the φ lead to exceive aiig of the loe. So, beide the oft tat, implemetatio of two iductio moto electic dive give the othe impotat advatage that i ability to vay peed i a mall age leadig to the eductio of powe loe with hiftig agle φ. 7. Appoximate compaative aemet of the electic dive Itoducig of the ew kid of electic dive o the ew techique of oft tat/top equie ome ecoomic calculatio to pove it pactical feaibility. Baed o uvey of Iteet eouce, the Table ummaize the cot of the clue equipmet of electic dive. The obeved fequecy covete povide V/f ad ome kid of vecto cotol, the oft tate ae baed o emicoducto device ad povide the oft tat ad top. The both covete ad tate have ecloue atig IP0. The iductio moto ae totally ecloed fa cooled (TEFC quiel cage foot mouted oe. 6

7 Table Compaative aemet of equipmet of the diffeet electic dive Equipmet Fequecy covete Soft tate Iductio moto Powe 7.5 kw 55 kw 0 kw 7.5 kw 55 kw 0 kw 7.5 kw 55 kw 0 kw Pice, $ To calculate appoximately cot of the whole dive, it eed to add the pice of a iductio moto ad pice of fequecy covete o oft tate depedig o the type of electic dive. The cot of the two iductio moto electic dive i detemied motly by the pice of the two TEFC lipig moto with the halved powe of each oe. Pice of the two moto i $ fo the 7 kw ( x.5 kw, $ fo the 60 kw ( x 0 kw, $ fo the 0 kw ( x 55 kw. The all coideed moto have 4 pole. The cot of additioal device to otate the tato deped o the type of thi device. The evo dive with AC o DC buhle moto i ecommeded to be ued. It powe detemie the cot ad the peed of the tato otatio. Geeally, the powe of evo moto i the ext: Pad = Te ω = Te dϕ / (8 The moe powe, the highe peed of the tato otatio ad the fate toque epoe of the whole dive could be deliveed. The age of geometical agle of otatio fo the 4 pole moto i φ =π/. Thu, evo dive ha to give the miimal taiet time of thi mall otatio. It hould be oticed that fo the fa thee ae o tog equiemet o the fat toque epoe ad taiet mode o the evo dive could be choe fo the taiet time of the tato otatio of at leat a few ecod to povide oft tat, top ad the peed vayig i the mall age. The holdig of the tato i the till poitio duig teady tate could be doe by wom gea box eductio o ay mechaical bake peetig the mai compoet of tamiio betwee the evo moto ad the tato. The calculatio of equatio (8 how that the output toque of tamiio vaie about 0 to 65 Nm fo the two kw 4 pole moto. The powe of evo dive (without powe loe i the tamiio fo the 5 ec taiet time i W. So, the powe ad eegy coumptio of evo dive could be eglected elatively to the powe of the whole dive. The cot of buhle evo dive with poitio cotol fo the coideed age of powe i $. The cot of tamiio i $. So, the total cot of the popoed electic dive vaie $ fo the 7.5 kw to $ fo the 0 kw. Aalyzig the Table allow to coclude that elevace of the two iductio moto electic dive iceae with iceaig powe of dive. It ha fewe cot elatively to fequecy covete - iductio moto dive ad compaable cot to emicoducto oft tate - iductio moto dive ice a few te of kw. 8. Cocluio The electic dive popoed i thi aticle ha the two idetical lipig iductio moto oe of which ha otatoy tato that allow to etict the tat cuet. The electic dive equie moe complicated mechaical moutig tha the idutial oe but it doe ot have ay emicoducto i the tato o oto cicuit. The poblem of the hot-tem peak taiet cuet appeaig fo the lage dive could be olvig by puttig the hot-duty eie eitace o upplyig fom ychoou geeato a it happe o vehicle. The geat advatage of the coideed dive befoe the idutial oft tate i ability to vay peed i a mall age leadig to the eductio of powe loe with hiftig agle of otatio. The toque epoe i quite a low ad deped o powe of evo dive otatig the tato. The electic dive i appopiate fo the fa whee thee i o tog equiemet o taiet time. The electic dive ha ecoomic gai o it cot befoe ivete fed moto ice a few te of kw. Refeece. Thaga Raj, C, Sivatava, S.P,. Agawal, P. Eegy efficiet cotol of thee-phae iductio moto - a eview. I: Iteatioal Joual of Compute ad Electical Egieeig, Vol., No., Apil 009. p Thoe, O.V., Dalva, M. A uvey of the eliability with a aalai of fault o vaiable fequecy dive with i iduty. I: EPE 95, Spai, 995, p Abdel-Halim, Fiet, A.M., Al-Ahma, M.A., Elfaakouy, M.E., Mahmoud E.M. A ovel appoach fo the aalyi of a thyito- cotolled iductio moto. I: Joual of Electical Egieeig, Vol. 5, 05, Editio, p Siddiqui, U.F., Vema, A., Soi, S. Compaative Pefomace Aalyi of Iductio Moto Uig Semicoducto Device i Tem of Fiig Agle. I: Iteatioal Joual of Emegig Techology ad Advaced Egieeig, Vol 4, Iue, Febuay, 04, p Riyaz, A., Iqbal, A., Moioddi, S., MoiAhmed, S., Abu-Rub, H. Compaative pefomace aalyi of Thyito ad IGBT baed iductio moto oft tate. I: Iteatioal Joual of Egieeig, Sciece ad Techology, Vol., No., 009, p Nowoty, D., Lipo, T. Vecto Cotol ad Dyamic of AC dive. Claedo Pe, Oxfod, UK, Komodamiakii, A.S., Klyachko L.M., Voobiev V.I., Pugachev, A.A. Cotol ytem of a tactive dive with tempeatue cotol of themally loaded elemet. I: Ruia Electical Egieeig, Vol. 85, No. 8, 04, p