A Modified Approach to Induction Motor Stator Voltage and Frequency Control.

Transcription

1 A Modiied Appoach to nduction Moto Stato oltage and Fequency Contol. C.U. Ogbuka, M.Eng. and M.U. Agu, Ph.D. Depatent o Electical Engineeing, Unieity o Nigeia, Nukka, Enugu State. E-ail: ucogbuka@yahoo.co dacelagu@yahoo.co.uk ABSRAC An inete-ed thee phae quiel cage induction oto die yte with ipoed echanical chaacteitic i peented. A detailed analytical eiew o the ideal contant lux contol ethod and the baic contol tategy wee undetaken beoe an ipoed contol ethod, which utilize a low equency boot-oltage, wa deeloped. hi ethod, unlike the baic contol ethod, poide a boot-oltage at low equencie theeby copenating o the tato ipedance dop, oeing contant lux opeation with axiu otoing toque o zeo to ated peed. (Keywod: induction oto, contant olt/hetz /, contant lux, oto toque and peed) NRODUCON nduction achine ae oe o the ot equently ued in induty becaue o thei obutne, eliability, low cot, high eiciency and good el-tating capability [1,, 3, 4]. he induction oto, paticulaly with a quiel cage oto, i the ot widely ued ouce o echanical powe ed o an AC powe yte. t low enitiity to ditubance duing opeation ake the quiel cage oto the it choice when electing a oto o a paticula application [5]. n pite o thi populaity, the induction oto ha two inheent liitation: (1) the tandad oto i not a tue contant-peed achine, it ull-load lip aie o le than 1% (in highhoe powe oto) to oe than 5% (in actional-hoepowe oto) and () t i not, inheently, capable o poiding aiable peed opeation [6, 7]. hee liitation can be oled though the ue o adjutable peed contolle [8, 9]. he baic contol action inoled in adjutable peed contol o induction oto i to apply a aiable equency aiable agnitude AC oltage to the oto to achiee the ai o aiable peed opeation [10]. he ot coon AC die today ae baed on inuoidal pule-width odulation SPWM. Howee, oltage ouce inete with contant olt/hetz ae oe popula, epecially o application without poition contol equieent, o whee the need o high accuacy o peed contol i not cucial [11]. Howee, ince the intoduction o ieldoiented contol theoy, alot all eeach ha been concentated in thi aea and little ha been publihed about contant opeation. t application at low equencie i till challenging due to the inluence o the tato eitance and the neceay oto lip to poduce toque [1]. n addition, the nonlinea behaio o pule-width odulated oltage inete in the low oltage ange ake it diicult to ue contant die at equencie below 3Hz [13]. CONSAN FLUX CONROL: PRNCPLES AND MOOR PERFORMANCE he ideal o the aiable equency, aiable oltage contol ethod i the contant lux contol whee the agnetizing cuent i kept contant [10, 14]. A the equency aie, all the eactance ay, accodingly. aking the he Paciic Jounal o Science and echnology 44

2 opeating equency a ω and ω b o ω a the bae (ated) equency at which the eactance, x, and x ae deteined, then the x l ailia equialent cicuit o the teady tate analyi o quiel cage induction oto odiie a hown in Figue 1 below. he axiu and iniu toque,, ae deteined by etting ax/ in which ax/ in d e 0 to ind d ; whee ae alue o lip at ax/ in ax/ in occu. heeoe, l ae a ax/ in ± ax (5) Subtituting ax/ in o in Equation 4, ax/ in ± 4ω E x a (6) Figue 1: Steady State Equialent Cicuit o a Squiel Cage nduction Moto o Contant Flux Contol (a 1). he pe unit equency a i deined a, a ω ω (1) ated ωb ω Whee E a e. Fo contant, E ax E x a, i the ated induced oltage o back E ae a () Next, the oto opeation o thi contant lux contol i exained. Unde thi opeating condition, the oto eeed cuent i aea Ea (3) ( ) + ( ax) ( ) + ( x) a he eect o the te a i obiou in Equation 3 and 4. t i een that i a i aintained contant, then and e ae aintained contant analogou to aatue oltage contol o dc oto up to ated peed. Fo Equation 6, it can be een that i independent o a and that in in agnitude. ax able 1: Saple Machine Data. ax/ in i equal to Rated oltage 400 Winding Connection Sta Rated Fequency 50H z Nube o Pole 6 Rated Speed 960p Stato Reitance 0.4Ω Roto Reeed Reitance 0.Ω Stato Reactance 1.5Ω Roto Reeed Reactance 1.5Ω Magnetizing Reactance 30Ω Figue how the oque-pe Unit Fequency Cue o the Saple Moto o able One unde Contant Flux Contol, at a 1. he eulting oto toque i: e ( aω Ea ω a ( ) + ( x ) a ) (4) hi contol tategy applie up to the ated tato oltage at the ated equency. Aboe the ated equency, a>1, contant at ut be kept to aoid daage to inulation. he Paciic Jounal o Science and echnology 45

3 Fo analyi, ax/ in 4aω ( ± + a x L ) (9) Figue 4 how the oque-pe Unit Fequency Cue o the Saple Moto o able 1 o contol aboe ated peed (a 1). Figue : oque-pe Unit Fequency Cue o Contant Flux Contol (a 1). Fo contol aboe bae peed, whee a >1, i no longe contant but deceaing with inceae in equency. hi iplie inceaed agnetizing eactance and continuou deceae in agnetizing cuent. he appoxiate equialent cicuit i, theeoe, ued o analyi in thi egion o opeation. he agnetizing eactance i taneed to the input teinal a hown in Figue 3. Figue 3: Appoxiate Equialent Cicuit o Contol aboe Rated Speed (a 1). Unde thi opeating condition, the oto eeed cuent and the oto toque ae, epectiely, a hown below. (7) ( + ) + a xl l Figue 4: oque-pe Unit Fequency Cue o Contol aboe Rated Speed (a 1). he poble with diect ipleentation o contant lux die i that lux (epecially agnetizing lux o cuent) cannot be diectly eaued due to the luped natue o winding paaete. Die enginee hae tied to ole thi poble by uing the contant contol tategy which peit the indiect contol o lux. BASC CONROL: PRNCPLES AND MOOR PERFORMANCE he appoxiate equialent cicuit i adopted o the baic contol analyi a hown in Figue e (8) ω a ( + ) + a xl 5. he Paciic Jounal o Science and echnology 46

4 a l ax / in a ± (13) ( ) + ( xl + x ) a Finally, the axiu and iniu toque o opeation at a 1 i obtained a: Figue 5: Appoxiate Equialent Cicuit o Baic Contol (a 1). n the equialent cicuit, the opeating equency to ated equency atio ated teinal oltage eactance. Whee, ated ated t i deduced o Figue 5, that: a ultiplie the and all inductie, i the ated equency. ax/in (14) 4 ω ( ± ( ) + ( xl + x ) ) a a he + ign i o axiu toque while the ign i o iniu toque. Figue 6 how the oque-pe Unit Fequency Cue o the Saple Moto o able One unde Baic Contol at a 1. (10) ( + ) + a ( x l + x ) a Fo thi, the opeating toque e i deied a: e a (11) a ω ( + ) + a ( xl + x) o obtain the lip ax/ in at which axiu/iniu toque occu, the it lip deiatie o the opeating toque, e, i equated to zeo. d e 0 d (1) t i obtained, theeoe, that Figue 6: oque-pe Unit Fequency Cue o Baic Contol (a 1) With thi appoach, o 0 a 1, the agnetizing cuent i a o being contant at low peed becaue o lage dop in the tato ipedance when copaed to a. Hence the need o odiication to copenate o thi tato ipedance dop at low equencie [10]. he Paciic Jounal o Science and echnology 47

5 MODFED CONROL SRAEGY AND EXAMPLE MOOR PERFORMANCES o ake ull ue o the oto toque capability at the tat and at low peed, the atio i inceaed to utain agnetizing lux at it ated alue theeby copenating o the tato eitance dop at low equencie aociated with the baic contol. he tato oltage i adjuted accoding to Equation 15. a a Whee + ( + ) (17) heeoe, je x ae + jea Ea aea + ( + l)( + ) (18) x + x a Equation 18 i plotted a a aie in the ange 0.1 a 1. he eult i hown in Figue 8 below. 0 + Ka (15) hi tato oltage i copoed o two coponent. One i a contant te which i an o-et oltage and the othe i a equency dependent coponent. Whee een at zeo equency, o copenate o the dop in tato eie ipedance to ake the agnetizing cuent equal to it ated alue. Whee, a, i the pe-unit equency and o i the tato oltage choen to gie ated agnetizing cuent at zeo peed. Now, to deteine o and K, the oltage elationhip in the exact equialent cicuit o Figue 7 i analyzed. l ae a Figue 8: Look-Up Plot o Modiied Contol. he contant, K, in Equation 15 i the lope o Figue 8 while 0 i obtained by extapolating the taight line and deteining the point o inteection at a0. he lope, K, i obtained a and obtained a (though extapolation at a 0) hen, Equation 15 odiie to a (19) Figue 7: Steady State Equialent Cicuit o a Squiel Cage nduction Moto o aiable oltage and Fequency Contol. Fo Figue 7, ae + ( + )( + ) (16) a l t i een that een at zeo equency (a0), the low equency boot-oltage copenate o the tato ipedance dop. Unde thi condition, the contol chaacteitic ae exained a a aie o 0.1 to uing the appoxiate equialent cicuit o Figue 9. he Paciic Jounal o Science and echnology 48

6 + l a _ PERFORMANCE COMPARSM BEWEEN HE BASC AND HE MODFED CONROL SRAEGES Due to the tato ipedance dop at low equencie aociated with the baic contol, Figue 9: Appoxiate Equialent Cicuit o Modiied Contol Stategy. Fo Figue 9, and ae obtained a ollow: e (0) ( + ) + a xl (1) ω a ( + ) + a xl e the agnetizing lux and cuent gadually inceae to ated alue a equency tend to ated. hi lead to a coeponding gadual inceae in the oto deeloped toque up to ated alue at ated equency. he coplete die tategy, a pogaed in MALAB, i hown in Figue 11. Fo the odiied contol tategy whee the low equency boot oltage i injected to utain the agnetizing lux theeby copenating o the tato eitance dop, at the axiu peiible cuent the die opeate eentially at a contant lux, poiding contant toque opeation o zeo to ated peed [10]. he coplete die tategy, a pogaed in MALAB, i hown in Figue 1. Whee, x x + x L l Figue 10 how the oque-pe Unit Fequency Cue o the aple oto o able One unde the Modiied Contol. Figue 11: he Coplete Die Stategy o Baic Contol. Fo both the baic and the odiied die Figue 10: Coplete oque-pe Unit Fequency Cue o Modiied Contol. tategie, the oto i dien beyond bae peed by inceaing the equency uthe. Howee the oltage applied cannot be inceaed beyond ated alue to aoid inulation beakdown. he Paciic Jounal o Science and echnology 49

7 allow the contant contol to opeate up to the ated peed beyond which the oto teinal oltage i kept contant at it ated alue to aoid daage to oto inulation. A copaion o the coplete die tategie o the baic and the odiied contol ethod, which decibe the opeation o the achine in a wide equency ange, wee undetaken and the eult, a hown in Figue 11 and Figue 1, coni the odiied contol a a ey good appoxiation to the idealitic contant lux contol. Figue 1: he Coplete Die Stategy o Modiied Contol. hee ae oe application, like taction, in which peed contol in a wide ange i equied and the toque deand in the high-peed ange i low. Fo uch application, contol beyond the contant powe ange i equied. o peent the powe o exceeding beakdown toque, the achine i opeated at a contant lip peed and the achine cuent and powe ae allowed to deceae a hown in Figue 11 and 1. Now, the oto cuent and toque deceae ineely with the peed. hi chaacteitic i oten called the eie oto chaacteitic. Fo peed below ated, the oltage and equency ae educed with peed to aintain the deied atio o contant lux, and to keep the opeation on the potion o the peed-toque cue with a negatie lope. CONCLUSON he odiied contol tategy, the cental thee o which i the injection o low equency boot-oltage, oe the oppotunity to ealize axiu toque o zeo to ated peed, theeby copenating o the low equency tato ipedance dop aociated with the baic contol. he contol tategy geneally REFERENCES 1. Leonhad, W Contolled AC Die, A Succeul ane o dea to ndutial Pactice. CE 95. Bazil, pp Okoo, O Dynaic Modelling and Siulation o Squiel-Cage Aynchonou Machine with Non-Linea Eect. Jounal o ASM ntenational. (6): Daniel, L. and. K. Philip. 00. Contol o nduction Machine Die. CRC pe LLC, llinoi. 4. MacDonald, M.L. and P.C. Sen Contol Loop Study o nduction Moto Die Uing D-Q Model. EEE anaction on ndutial Electonic and Contol ntuentation. 6(4): Otoic, Copute-Aided Analyi o Electic Machine. Pentice Hall ntenational (UK) Ltd.: London, UK. 6. Okoo, O MALAB Siulation o nduction Machine with Satuable Leakage and Magnetizing nductance, Botwana Jounal o echnology. 13(): Fitzgeald, A.E Electic Machiney. 5th Edition, McGaw-Hill nc.: New Yok, NY. 8. Maino, R., S. Peeada, and P. aligi Adaptie nput-output Lineaizing Contol o nduction Moto. EEE anaction on Autoatic Contol, 38(): Zhou, K. and D. Wang. 00. Relationhip Caie-Baed ecto Modulation and hee Phae Caie-baed PWM: A Copaatie Analyi. EEE an. ndutial Electonic. 49(1): he Paciic Jounal o Science and echnology 50

8 10. Boe, B.K Powe Electonic and aiable Fequency Die. EEE Pe, New Yok, NY. 11. Huein, S. and R. a poing Mechanical Chaacteitic o nete-nduction Moto Die Syte. Aeican Jounal o Applied Science.3(8): Aedo, M.G.,. Lipo and D.W. Nootny A New nduction Moto /F Contol Method Capable o High-Peoance Regulation at Low Speed, EEE an. nd. Application. 34(4): Sepe, S. and L. Lang nete Non- Lineaitie and Dicete-ie ecto Cuent Contol. EEE an. nd. Application. 30(1): Agu, M.U. 007/008 Seion. Electic Machine Die. Unpublihed Coue Note o EE 614, Depatent o Electical Engineeing, Unieity o Nigeia, Nukka. etal (elting, cating, oging, oing, annealing, hadening), Renewable Enegy Souce (epecially in the aea o woking with ola photo oltaic cell and panel to ealize ola lighting, heating, battey chaging and wate puping), Powe Syte Ditibution o Reidential, Coecial and ndutial Aea. SUGGESED CAON Ogbuka, C.U. and M.U. Agu A Modiied Appoach to nduction Moto Stato oltage and Fequency Contol. Paciic Jounal o Science and echnology. 10(1): Paciic Jounal o Science and echnology ABOU HE AUHORS Eng. Ogbuka, Coa Uchenna eceied hi B.Eng. (Fit Cla Hono) and M.Eng. degee in 004 and 008, epectiely, in the Depatent o Electical Engineeing Unieity o Nigeia, Nukka whee he peently wok a a Lectue/Reeach Student. Hi eeach inteet ae in Adjutable Speed Die o Electical Machine: (DC and AC Electic Machine oque/speed Contol with Conete and nete) and Powe Electonic. Eng. Po. Agu, Macel U. obtained hi B.Sc. in Electical Engineeing in 1974 in the Unieity o Nigeia, Nukka. He alo eceied hi M.A.Sc. and Ph.D. in 1978 and 198, epectiely, in Powe Electonic o the Unieity o oonto, Canada. He i a Poeo o Powe Electonic in the Depatent o Electical Engineeing Unieity o Nigeia, Nukka. Hi eeach inteet ae in, but not liited to, Powe Electonic Cicuit (Solid State AC/DC and DC/DC Conete, nete Cicuit and Cycloconete/inete cicuit), Static Electic Moto Die (DC and AC Electic Machine oque/speed Contol with Conete and nete), Analogue, digital and icopoceobaed electonic contol cicuit, Static nduction Heating Powe Supplie o heat teatent o he Paciic Jounal o Science and echnology 51