Modelling of Axial Flux Induction Machines and it Application as Differential in Electrical Vehicles

Transcription

1 Volue 1 Issue 12 (Decebe 214) Modelling of Axial Flux Induction Machines and it Application as Diffeential in Electical Vehicles Pesai Neelia * Ms.Ch.Manjeea M.V Raesh Babu M.tech final yea Assistant pofesso Associate pofesso EEE.Dept,VNR VJIET EEE.Dept,VNR VJIET EEE.Dept,VNR VJIET Abstact This pape poposes the odelling of Single Ai gap Axial Flux Induction Machine and it is extended to Twin Roto Axial Flux Induction Machine. It is also poposed to use a Twin Roto Axial Flux induction Machine as a eplaceent fo existing conventional echanical diffeential. The possibility of having shote axial length and two independent otos in a single achine favous fo above application. These otos ae used as wheel otos and this also becoes one cedential fo using the in electic vehicle applications. Futheoe it is copact and has high powe density. The pesent wok is siulated in MATLAB envionent. Keywods Axial flux Induction achine, TRAFIM, odelling, Diffeential, MAT-LAB. I. INTRODUCTION TO AXIAL FLUX INDUCTION MACHINES Based on the flux diection in the ai gap, electoechanical enegy convesion achines ae classified into Radial Flux Machines and Axial Flux Machines. The woking pinciple involved in both the axial flux and adial flux achine ae sae but diffes in its constuction. In conventional adial flux achines the conductos ae placed in paallel and the diection of ai gap flux is adial to the shaft axis whee as in the axial flux achines the conductos ae placed in adial to the shaft and ai gap flux is paallel to the shaft. The ealiest achines wee AFMs though they wee eplaced by RFM afte a elatively shot peiod of tie. In 1821, Faaday invented a piitive disc oto which was in the fo of an AFM. Howeve, since 1837, when Davenpot claied the fist patent fo a RFM, it becae the accepted configuation fo electical achines. Since 198 the applicability of axial flux achines to low-speed, diect-dive electical dive applications has been studied. Liitations of Radial flux achines Bottle Neck fo the flux path at the oot of the oto slot. Cooling Poble. In efficient utilization of Roto Coe. Long oto length is equied because the toque is poduced at a fixed ai-gap diaete which is effectively salle than the axial field oto whee toque poducing diaete gows adially fo a fixed ai-gap length. These Liitations cannot be conveniently eployed unless thee is an alteation in the geoety of the RF achine which leads to a AF achine. Advantages of Axial flux achines Cooling is ipoved Lage axial length is not equied fo the poduction of high toque. Tooth flux density is constant. Efficient utilization of oto coe At a tie it can be opeated at diffeent speeds with ulti ai gap topology. In axial flux achines the stato has ing stuctue and oto is disc shaped. The adial length fo the stato inne adius to the oute adius is the active pat to poduce the toque and the axial length is dependent on the pope yoke design of the stato and the oto i.e., the flux density in the stato and oto yokes. Though the nube of poles inceases the active adial pat of the achine eains unchanged and the axial length depends on the flux density in stato and oto yokes. When the atio of oto oveall length to oto extenal diaete > 1 then adial flux type is pefeed and when it is <.3 axial flux type achine is pefeed. Thus the axial flux achine has the flexibility in having highe pole nube which let the achine to be an attactive altenative fo the low speed applications. Futheoe it has high efficiency, high powe and toque densities and low oto losses. Fig.1 shows the configuations of a conventional and an axial-field achine. Fo the conventional achine, the ain diensions ae the ai gap diaete and the effective length while fo the axial-field achine the ain diensions ae the oute and inne diaetes. 214, IJIRAE- All Rights Reseved Page -1

2 Volue 1 Issue 12 (Decebe 214) Fig. 1a Radial Flux Machine Fig. 1b Axial Flux Machine Usually these achines can have single o ultiple ai gaps. The ultiple ai gap axial flux achines have N statos and N+1 otos fo intenal stato extenal oto [ISER] type achines and N+1 statos and N otos fo extenal stato and intenal oto [ESIR] type achines. Because of its highe efficiency ISER type achine is pefeed. Based on the flux diection in the stato coe the two topologies can be deived fo ISER. One is Noth- Noth (NN) type topology and the othe is Noth-South (NS) type topology. Futheoe these topologies ae classified into Slotted type and Non Slotted type. In Non-Slotted type axial flux achine thee is only NN type topology which consists of stato with tape wound ion coe and windings wapped aound the coe with back to back connections whee as in Slotted type axial flux achine thee ae both NN type and NS type topologies. Based on the above classification diffeent types of peanent agnet synchonous achines and induction achines ae deived. Axial flux Induction [AFI] achines ae of slotted type. They can be eithe single ai gap o ultiple ai gaps. In single stato double oto type stuctue the otos can have (i) Two independent shafts diving two diffeent loads and hence two diffeent speeds can be obtained at a tie. (ii) Two otos can shae the sae shaft enhancing the toque/powe output. Futheoe two diffeent topologies ae deived fo slotted type based on the diection of ain flux in the stato coe as discussed ealie called Slotted NN-type AFI achine and Slotted NStype AFI achine which ae illustated in the Fig.2. Fig. 2 NS Topology NN Topology II. MODELLING OF AXIAL FLUX INDUCTION MACHINES A. Modelling of Single Ai gap Axial flux Induction achine The single ai gap axial flux induction achine consists of single stato and oto. The equations which descibe the pefoance of an induction achine ae independent of agnetic flux diection in the ai gap. The syste equations of an axial flux induction achine ae given below in the atix notation. 214, IJIRAE- All Rights Reseved Page

3 Intenational Jounal of Innovative Reseach in Advanced Engineeing (IJIRAE) ISSN: Volue 1 Issue 12 (Decebe 214) Vs Rs Is Ls Ls Is p V R I Ls L I. (1) The above equation is in the fo of V RI p LI.. (2) The genealized D-Q axes odels ae used fo analyses of achines. Any paticula efeence fae odel can be deived by substituting the appopiate fae speed and position in the genealized efeence odel. Refeence faes otating at an abitay speed ae called abitay efeence faes and othe faes ae paticula cases of this abitay efeence fae. Syste equations in abitay efeence fae can be epesented in the atix notation as R V R I p L I dqs dqs dqs Rs w sls wl s wl s s Rs wl s ws w L R ws w L w w L w w L R s s Ls s L L Whee p epesents the diffeential opeato.. (3)... (4)... (5) The tansfoation is done into synchonously otating efeence fae. This odel is useful whee the vaiables in the steady state need to be DC quantities. Soe high pefoance contol schees use this odel to estiate the contol inputs. This odel facilitates the siulation of vecto contol ethods of induction oto. In synchonously otating efeence fae odel, the speed of the efeence fae is ω. And equation (3) can be epesented in a state vaiable fo as d 1 1 I dqs L dqs V dqs L dqs R I dqs dt. (6) The above diffeential equation is solved by using Runge-kutta ethod in MATLAB to obtain the d-q axis cuents of both stato and oto. The siulation esults ae shown below. ids,iqs,id,iq D,Q axis stato and oto cuents x ids iqs id iq tie in secs Fig. 3 Stato and oto cuents in synchonous efeence fae odel The electoagnetic toque is obtained by equation (7) and the siulation esult is shown in Fig.4. 3 p T e L i d i q s i d s i q. (7) , IJIRAE- All Rights Reseved Page -3

4 Volue 1 Issue 12 (Decebe 214) steady state toque in synchonous efeence fae x Te -4 B. Modelling of Twin Roto Axial flux Induction Machine tie in secs Fig. 4. Steady state toque in synchonous efeence fae The axial flux induction achine consists of single stato sandwiched between two otos. Since the achine consideed hee fo the odelling is NN type AFIM, the flux path is in paallel with the shaft axis in the ai gap and paallel and pependicula to the shaft axis in the stato coe. The d-q axis voltage and flux linkage equations of twin oto AFIM in synchonously otating efeence fae ae given below. V = R i + pλ + ωλ λ = L i + L i + L i V = R i + pλ + ωλ λ = L i + L i + L i V = R i + pλ (ω ω )λ λ = L i + L i + L i V = R i + pλ + (ω ω )λ λ = L i + L i + L i V = R i + pλ (ω ω )λ λ = L i + L i + L i V = R i + pλ + (ω ω )λ.. (8) λ = L i + L i + L i.. (9) The atix notation of the above set of voltage equations is given below V = [R]I + p[l]i... (1) Whee esistance atix is and inductance atix ae given below Rs wls wl wl wls Rs wl wl ( w w ) L R ( ww ) L ( w w ) L R ( ww ) L ( w w ) L R ( w w ) L ( w w ) L ( w w ) L R ( w w ) L ( ww ) L ( w w ) L ( w w ) L R (11) L L s s L L (12) To obtain the d,q axis cuents of stato and oto, equation (1) ust be epesented in the state vaiable fo and siulate in the envionent of MATLAB. The siulation esults ae shown below. 214, IJIRAE- All Rights Reseved Page -4

5 Volue 1 Issue 12 (Decebe 214) D,Q axis stato and oto1 cuents x ids,iqs,id1,iq ids iqs id1 iq tie in secs Fig. 5 Stato and oto1 d,q cuents of double aigap Induction achine D,Q axis stato and oto2 cuents x ids,iqs,id2,iq ids iqs id2 iq tie in secs Fig. 6 Stato and oto2 d,q cuents of double aigap Induction achine The electoagnetic toque fo the twin oto axial flux induction achine is obtained by siulating equation (13). The siulation esult is shown in Fig.7. 3 p Te L i d1 id 2 iqs ids iq1 iq 2. (13) 2 2 Te steady state toque in synchonous efeence fae x tie in secs Fig. 7 Steady state toque in synchonous efeence fae Theefoe the twin oto axial flux achine is designed and toque coesponding to the otos is obtained and this lets to investigate the diffeential opeation in electical hybid vehicles and the toque is found to be doubled than with single oto. And this analysis lets to investigate on the possibility of eplacing the RFIG in the VSWECS with the ediu speed TRAFIG so as to educe the gea box atio and enhance the powe output in wind enegy convesion systes. III. APPLICATION OF AXIAL FLUX INDUCTION MACHINE AS DIFFERENTIAL IN ELECTRIC VEHICLES The pobles associated with vehicle eissions have long been a cause fo concen, patly due to aibone pollutants, and oe ecently elating to cliate change due to geenhouse gas eissions. Accoding to the US Envionental Potection Agency (EPA), in addition to up to 4% of geenhouse gas eissions, conventional Intenal Cobustion Engine (ICE) vehicles contibute 4-5% of ozone, 8-9% of cabon onoxide and 5-6% of ai toxins found in uban aeas and with vehicle nubes foecast to incease fo 7 illion to 2.5 billion in the next half centuy, the need fo sustainable tanspot solutions is clea. So ecent yeas have seen a suge of inteest in zeo eission tanspot solutions. The leading contende to eplace petol poweed vehicles at pesent is Battey-poweed Electic Vehicles (BEVs), since they ae the ost efficient solution which can be poweed (echaged) entiely fo enewable enegy souces. 214, IJIRAE- All Rights Reseved Page -5

6 Volue 1 Issue 12 (Decebe 214) A. Woking of a TRAFIM as a Diffeential Fo electic vehicle applications, wheels oto dives epesented a new attactive possible solution fo thei lightness and copactness. The wheels ae diectly diven by the electic oto and the geas ae not necessay anyoe. Because axial flux otos can find thei advantageous applications in the low speed, high toque electical dives. Fo axial flux oto applied in electic vehicle ust be ealized: high powe/weight and toque/weight atio, high efficiency and suitable shape to atch the constains space. Twin oto axial flux induction oto has one stato coe with two polyphase windings and two otos with two diffeent shafts which ay otate independently. All the thee agnetic coes (the stato and the two otos) ae in the fo of discs with slots fo the stato windings and the oto cages. The achine can be classified as a twin oto axial flux oto. Fig. 8 Two independent otos diving two diffeent speeds In siple tes, the achine opeates as follows. When the vehicle is steeed staight ahead, both diving wheels un at the sae speed, and theefoe at the sae slip. Conditions in the achine ae syetical and both otos poduce equal aatue eaction. Thus all flux, except leakage, linking the stato windings, also links each oto winding. No flux passes aound the yoke of the stato. Both otos poduce the sae toque. Fig. 9 Diffeential opeation When the vehicles ente a cuve, the inne wheel educed speed and inceases slip wheeas the oute wheel inceases speed and educed slip. Theefoe the aatue eaction fo the slowe oto exceeds that fo the faste oto. The sae total flux linkage is aintained at the stato winding and the net is that the flux linking the low speed oto is educed while that linking the high speed oto is inceased. The edistibution of the flux tends to keep the oto toques balanced. The diffeence in the fluxes passes aound the stato yoke. As the adius of the cuve followed by the vehicle is educed, this pocess Continues and flux in the stato yoke builds up to the point of satuation. Up to this point, the achine behaves like two achines in seies. Afte this point, satuation liits the flux which can pass aound the stato coe, and theefoe liits the aount by which the oto flux linkages can diffe. These oto fluxes ae then oe o less fixed, and the achine stats to take on the chaacteistics of two achines in paallel connection. This achine is designed to ake use of the agnetic satuation of electic steels. Additionally, as esults of the disc geoety, satuation will natually occu in aeas of the achine othe than the stato yoke. The oto yokes ay satuate, especially at the oute adius, and the teeth of the oto and stato will satuate, especially at the inne adius. 1) Modelling: If the achine is used fo the populsion of the wheels of an electical vehicle and is opeated along a staight path then the two cage otos otate at sae speed of the vehicle. When the two oto speeds ae equal, then thee is coplete balance between the two ai gaps of the achine and the two cage otos shae the sae aount of the powe deliveed at the achine input teinals. In this case the speed of the cage otos is only elated to the total electoagnetic toque by 214, IJIRAE- All Rights Reseved Page -6

7 Volue 1 Issue 12 (Decebe 214) T ( T dt ) Jp B.. (14) e1 L 1 1 T ( T dt) Jp B... (15) e2 L 2 2 Whee T L is the oveall load toque at the axels of the wheels. Wheneve the vehicle entes a cuved path the vehicle wheels ae foced to otate at diffeent speeds with espect to the othe, and this speed diffeential action exeted on the vehicle wheels esults in a slip constaint fo the achine cage otos. Wheneve the vehicle popelled by the achine oves along a cuved path, if Te is the aveage toque elated to the achine, the cuve tajectoy constaints the cage oto diving the inne wheel to opeate with a toque Te +ΔTl wheeas the cage oto diving oute wheel ust otate with the toque of Te-ΔTl. The diffeential toque ΔTl is ainly deteined by the tuning atio. Repesenting these equations in atix notation Te1 ( TL dt ) 1 1 Jp B Te 2 ( TL dt ) 2 2. (16) Cobining these equation with voltage equations of the axial flux induction oto atix notation V R I p L I dqs1 2 dqs1 2 dqs1 2.. (17) Whee the [R] is esistance and [L] inductance atices and ae given as R Rs Ls L L L s Rs L ( 1) L R ( 1) L ( 1) L ( ) L ( ) L R ( ) L ( ) ( ) ( ) ( 2) L ( 2) L ( 2) L R B B L 1 L R 1 L.. (18) L L s s L L J J (19) Whee B and J epesents Fictional Coefficient and Moent of Inetia and these values taken as.2 and.265 espectively. To obtain the behavioual esponse of the Twin Roto Axial flux Induction Machine as Diffeential, the cobined voltage and toque equations ust be epesented in state vaiable fo and siulate in the envionent of MAT-LAB. The siulation esults show the design of the Twin Roto Axial flux Induction Machine (TRAFIM) as a Diffeential in Electic vehicle and it coesponding speed, slip and toque vaiations. 214, IJIRAE- All Rights Reseved Page -7

8 Volue 1 Issue 12 (Decebe 214) Stato and Roto1 dq axis cuents ids iqs id1 iq1 Ids,Iqs,Id1,Iq tie in secs Fig. 1 Stato and oto1 dq axis cuents duing diffeential opeation 1 5 stato and Roto2 dq axis cuents ids iqs id2 iq2 Ids,Iqs,Id2,Iq tie in secs Fig. 11 Stato and oto2 dq axis cuents duing diffeential opeation Instantaneous otos speed in synchonous efeence fae W1 W2 33 w 1,w tie in secs Fig. 12 Speed vaiations of the oto1&oto2 duing diffeential opeation 5 Instantaneous otos toques in synchonous efeence fae 4 3 Te1 Te2 Te1,Te tie in secs Fig. 13 Toque vaiations of oto1 and oto2 duing Diffeential opeation 214, IJIRAE- All Rights Reseved Page -8

9 Volue 1 Issue 12 (Decebe 214) Instantaneous otos slips in synchonous efeence fae S1 S2 S 1,S tie in secs Fig. 14 Slip vaiations of oto1 and oto2 duing Diffeential opeation 4 x 14 3 Instantaneous otos powes in synchonous efeence fae P1 P2 2 P1,P tie in secs Fig. 15 Constant powe thoughout the opeation of an AFIM The electic vehicle of the futue is expected to be popelled by diect dive wheel otos fo oe efficient powe tain. Concening the electic vehicle application, this pape has pesented peliinay esults of a study of an oiginal axial flux achine topology which allow one to cobine the functions of both the engine and the diffeential in a single oto dive. The powe is aintained constant thoughout the opeation of a diffeential. IV. CONCLUSION A detailed liteatue suvey is conducted on Axial flux achines and thei cedentials ae highlighted. The flexibility to have high pole nube has lead the Axial flux achines to be used fo low speed opeations and diect dive applications. A single ai-gap Axial flux Induction achine is odelled in MATLAB envionent and it is extended fo a Twin oto Axial flux Induction achine case. The Axial flux achines having shote axial length ae favouable choice fo Electic vehicles. These achines povide populsion by diectly connected to wheels and incease the powe tansfe efficiency. Hence these ae also called as wheel otos. The TRAFIM is used as diffeential in Electic vehicle and peliinay esults ae pesented. The powe is assued to be constant thoughout the opeation. REFERENCES [1] Zaha NASIRI-GHEIDARI, Haid LESANI, Univesity of Tehan, A Suvey on Axial Flux Induction Motos PRZEGLĄD ELEKTROTECHNICZNY (Electical Review), ISSN 3397, R. 88 NR 2/212. [2] V. Raesh Babu, D. M.P Soni, A Novel Method of Using Twin-Roto Axial Flux Induction Machine fo Wind Enegy Convesion and the Reactive powe Copensation by TSC-TCR Intenational Jounal of Eeging Technology and Advanced Engineeing (IJETAE) ISSN , Volue 2, Issue 8, August 212. [3] V. Raesh Babu, M.P Soni, Ch. Manjeea, Modelling of Axial flux Induction achine with sinusoidal winding distibution 212 Annual IEEE India confeence (INDICON), 481 at kochi 7-9 Decebe 212. [4] W. S. Leung, J.C.C. Chan, Axial-Field Electical Machines- Design and Application, IEEE Tansactions on Powe Appaatus and Systes, Vol. PAS-99, No. 4, pp ,July/Aug 198. [5] M. Valtonen, Pefoance Chaacteistics of an Axial-Flux Solid-Roto-Coe Induction Moto, Ph.d thesis, Lappeenanta Univesity of Technology, Lappeenanta, Finland, 27. [6] Zhang C., Tseng K.J. and Nguyen T.D., Analysis and copaision of axial flux PM synchonous oto and induction oto, IEEE confeence (21), IPEC21, , IJIRAE- All Rights Reseved Page -9

10 Volue 1 Issue 12 (Decebe 214) [7] D. Platt, PhD, B.H. Sith, PhD, MlEE, Twin oto dive fo an electic vehicle IEE PROCEEDINGS-B, Vol. 14, No. 2, MARCH I993. [8]. Suita Sinha, Nial K Deb, Nikhil Mondal, Sujit k Biswas, The diffeential induction achine: Theoy and pefoance Sadhana Vol. 33, Pat 5, Octobe 28, pp Pinted in India. [9] D.M.Raaooty, A Shot Couse on Electical Machines published by ERDA, Vadodaa, 26. [1] P.C.Kause, Oleng Wasynczuk, Scott D. Sudhoff, Analysis of electic achiney and dive systes. Second edition, A John Wiley & sons, Inc publication, 24. [11] Chee Mun Ong, Dynaic siulation of electic achiney, Pentice Hall PTR, Uppe saddle ive, New Jesey, 7458, [12] Philip L. Alge, Induction achines thei behavio and uses Second edition, Godon and Beach Publishes. [13] R.Kishnan, Electic Moto Dives Modelling, Analysis and Contol Peason Education Pte.Ltd, 21. [14] D.P.S.Bia, Genealized theoy of electical achines, Fifth edition Khanna Publications. APPENDIX TABLE I PARAMETERS OF AXIAL FLUX INDUCTION MACHINE Stato Resistance 1.12 Ω Roto Resistance Ω Stato Leakage Inductance.649 H Stato Magnetizing inductance H Stato Self Inductance H Roto Leakage Inductance.649 H Roto Magnetizing Inductance H Roto Self Inductance H Stato-Roto Mutual inductance H 214, IJIRAE- All Rights Reseved Page -1