Simulink Model of Direct Torque Control of Induction Machine

Transcription

1 Ameican Jounal of Applied Science 5 (8): , 2008 ISSN Science Publication Simulink Model of Diect Toque Contol of Induction Machine H.F. Abdul Wahab and H. Sanui Faculty of Engineeing, Univeiti Kebangaan Malayia, UKM Bangi, Selango DE, Malayia Abtact: Diect toque contol (DTC) i one of the mot excellent contol tategie of toque contol in induction machine. It i conideed a an altenative to the field oiented contol (FOC) o vecto contol technique. Thee two contol tategie ae diffeent on the opeation pinciple but thei objective ae the ame. They aim to contol effectively the toque and flux. Toque contol of an induction machine baed on DTC tategy ha been developed and a compehenive tudy i peent in thi eeach. The pefomance of thi contol method ha been demontated by imulation pefomed uing a veatile imulation package, Matlab/Simulink. Seveal numeical imulation have been caied out in a teady tate and tanient opeation on a peed contol mode. Key wod: Diect toque contol, induction machine, vecto contol, Matlab/Simulink INTRODUCTION Fo many yea, induction machine have povided the mot common fom of electomechanical dive fo indutial, commecial and dometic application that can opeate at eentially contant peed. Induction machine have imple and moe ugged tuctue, highe maintainability and economy than DC moto [4]. They ae alo obut and immune to heavy loading. Baically, thee ae two type of intantaneou electomagnetic toque-contolled AC dive ued fo high pefomance application which ae: Vecto Contol (VC): baed on tato cuent contol in the field otating efeence uing PWM invete contol. Diect Toque Contol (DTC): baed on tato flux contol in the tato fixed efeence fame uing diect contol of the invete witching. Diect toque contol (DTC) ha become an altenative to the well known Vecto Contol of induction machine. It wa intoduced in Japan by Takahahi (1984) and alo in Gemany by Depenbock (1985). DTC of induction machine ha inceaingly become the bet altenative to field oientation method o vecto contol. A block diagam of a DTC ytem fo an induction machine i hown in Fig. 1, [2]. The DTC cheme i vey imple; in it baic configuation it conit of hyteei contolle, toque and flux etimato and a Fig. 1: Diect toque contol of induction machine witching table. The configuation i much imple than the vecto contol ytem due to the abence of coodinate tanfomation between tationay fame and ynchonou fame and PI egulato. It alo doe not need a pule width modulato and a poition encode, which intoduce delay and equie mechanical tanduce epectively. DTC baed dive ae contolled in the manne of a cloed loop ytem without uing the cuent egulation loop [4]. DTC cheme ue a tationay d-q efeence fame (fixed to the tato) having it d-axi aligned with the tato q- axi. Toque and flux ae contolled by the tato voltage pace vecto defined in thi efeence fame. The baic concept of DTC i to contol diectly both the tato flux linkage (o oto flux linkage, o magnetizing flux linkage) and electomagnetic toque of machine imultaneouly by the election of optimum Coeponding Autho: H. F. Abdul Wahab, Faculty of Engineeing, Univeiti Kebangaan Malayia, UKM Bangi, Selango DE, Malayia 1083

2 invete witching mode. The ue of a witching table fo voltage vecto election povide fat toque epone, low invete witching fequency and low hamonic loe without the complex field oientation by eticting the flux and toque eo within epective flux and toque hyteei band with the optimum election being made. The DTC contolle conit of two hyteei compaato (flux and toque) to elect the witching voltage vecto in ode to maintain flux and toque between uppe and lowe limit. The main objective of thi pape i to develop the imulink model of diect toque contol of induction machine baed on the mathematical modelling. DTC DEVELOPMENT The develop toque contol of invete fed induction machine i caied out by hyteei contol of magnitude tato flux and toque that elect one of the ix non-zeo and two zeo invete voltage vecto hown in Fig. 2. The election i made in ode to maintain toque and flux eo inide the hyteei band in which the eo ae indicated by T e and Ψ epectively. Noting that Te = Teef Te (1) ψ = ψ ef ψ (2) The ix diffeent diection of V noted a V i ( i = 1 6), conideing Sa, S b and S c a the combination of witche tatu of the invete ae given by the expeion: q j2 j4 2Vdc π π V 3 3 = Sa + e Sb + e Sc 3 (3) Stato Flux Contol: By electing the appopiate invete output voltagev, the tato flux ψ otate at i the deied fequency ω inide a pecified band. If the tato ohmic dop ae neglected, the tato voltage impee diectly the tato flux in accodance with the equation a follow: o dψ V = (4) dt dψ = V dt (5) Theefoe the vaiation of the tato flux pace vecto due to the application of the tato voltage vecto V duing a time inteval of t can be appoximated a: ψ = V t (6) Toque Contol: The electomagnetic toque given by equation (7) i a inuoidal function ofγ, the angle between ψ and ψ a hown in Fig. 3. Since the oto flux change lowly, the apid vaiation of tato flux pace vecto will poduce a vaiation in the developed toque becaue of the vaiation of the angle γ between the two vecto: q 3 T = P i jψ 2 (7) V 3( 010 ) V 2 ( 110 ) V ( 011) 4 0 V1( 100 ) V ( 001) 5 V ( 000 ) V ( 111) 7 V ( 101) 6 Fig. 2: Invete output voltage vecto and voltage invete d ψ + ψ γ γ ω ψ ψ ψ Fig. 3: Stato flux and oto flux pace vecto d 1084

3 ( ) 3 P L T m e = ψ 2 + ψ jψ 2 2 LL L m (8) q-axi Theefoe to obtain a good dynamic pefomance, an appopiate invete voltage vecto V i ha to be elected to obtain tonge otation peed of ω. The actual value of tato flux can be expeed a: whee V and and cuent epectively. ( ) ψ = V i R dt (9) i indicate the meaued tato voltage The electomagnetic toque i calculated by mean of equation (10): ( d d ) 3 Te = P ψ iq ψ qi (10) 2 Switching Table: On the bai of the toque and flux hyteei tatu and of the tato flux witching ecto, which i denoted by α, DTC algoithm elect the invete voltage vecto to apply to the induction machine fom the Table 1. The output of the witching table ae the etting fo the witching device of the invete. Figue 4 how the elation of invete voltage vecto and the tato flux witching ecto. 1 q tan ψ α = ψ = ψ d (11) Active witching vecto: V 1(100); V 2 (110); V 3 (010); V 4 (011); V 5 (001); V 6 (101) Zeo witching vecto: V 0 (000); V 7 (111) Table 1: Switching table of invete voltage vecto dψ dt e α(1) α(2) α(3) α(4) α(5) α(6) ecto ecto ecto ecto ecto ecto V2 V3 V4 V5 V6 V1 0 V7 V0 V7 V 0 V7 V0-1 V6 V1 V2 V3 V4 V5 0 1 V3 V4 V5 V6 V1 V2 0 V0 V7 V0 V7 V0 V7-1 V5 V6 V1 V2 V3 V V 4 V 3 α(4) α(5) V 5 α(3) α(6) α(2) Whee: -30 o < α(1) < 30 o 30 o < α(2) < 90 o 90 o < α(3) < 150 o 150 o < α(4) < 210 o 210 o < α(5) < 270 o 270 o < α(6) < 330 o V 6 V 2 α(1) Fig. 4: Invete voltage vecto and tato flux witching ecto SIMULATION RESULTS AND DISCUSSIONS To tudy the pefomance of the developed DTC model, a cloed loop toque contol of the dive i imulated uing Matlab/Simulink imulation package. The block diagam of the imulink model i hown in Fig. 5. Stat-up with No Load: Toque contol dynamic pefomance of developed DTC model i evaluated by applying a tep input of amplitude 30 Nm afte 0.4 m to toque efeence while the tato flux efeence i maintained at 1 Wb. The width of the hyteei band i adjuted to ±0.01 Wb fo the flux compaato and ±0.01 Nm fo the toque compaato. Maximum tep ize of 0.1 m i ued in thi imulation. The obtained epone ae hown in Fig. 6. The equation of toque fo no load unning with ingle inetia and negligible fiction i hown below: V 1 d Te = J (12) dt Fom Fig. 6(a), the etimated electomagnetic toque emain at zeo at peiod befoe 0.4 m, o the oto doe not otate. At t=0.4 m, a tep of 30 Nm i

4 Fig. 5: Developed model of diect toque contol of induction machine applied to the toque efeence and the electomagnetic toque immediately inceae to each the demand toque. Thi caue the oto to acceleate at a ate dictated by the oto inetia. Fom the toque epone, the acceleation i given by: d Te 30 2 = = = 600 ad/ dt J 0.05 diffe only by 2.8%. Thu, the mall diffeence in pecentage can veify the accuacy of the developed model. In thi no load ituation, the oto peed would eventually acceleate to ynchonou peed of ad/. Thee i 5.9% diffeence with the calculated of ynchonou peed, 2 f ω = = ad/. The epone i hown in P Fig. 7. The oto peed epone in Fig. 6(b) behave Figue 6(c) how the tato flux magnitude linealy duing tat-up. Thi i validating the equation epone ha ien to it final value of 1.0 Wb that i of the peed fo no load unning with ingle inetia and equal to the tato flux efeence. The tato flux negligible fiction a below: magnitude i alo contained within it hyteei band of ±0.01 Wb a hown in Fig. 6(d). The locu of the Te = dt (13) tato fluxe i peented in Figue 6(e). Since the tato J flux magnitude i contantly maintained in the Fom the oto peed epone plot, the hyteei band, the locu daw the figue of a cicle. coeponding acceleation of the oto peed can be In DTC cheme, a diect contol of the tato calculated a below: cuent i not peent and thi may detemine ove cuent when a tep vaiation of toque and flux ae d applied to the input command. Figue 6(f) and 6(g) = = = ad/ dt t how the tato cuent epone. Due to the uncontolled cuent duing tat-up, the machine Both of the above acceleation calculation baed exceed the ated cuent with tato cuent amplitude, on the etimated toque and the peed epone ae i > 80 A a hown in Fig. 6(g). It can be noted that 1086

5 (a)etimated toque (b) Roto peed (c) Stato flux magnitude (d) Stato flux magnitude contained in hyteei band (e) Locu of the tato flux (f) D-axi and q-axi tato cuent Fig. 6: a-g: DTC behaviou duing tat-up with no load (G) Stato cuent 1087

6 Fig. 7: Steady tate epone of oto peed with no load (a) Etimated toque even a mall vaiation of tato flux command a in Fig. 6(c), caue a lage vaiation of the tato cuent. A contol method to limit the cuent amplitude can be applied. [3] ha popoed to pe-flux the machine pio to apply the toque demand to limit the tating cuent tanient in DTC in ode to pevent the damage of the witch powe of invete. Dynamic Behaviou: The tanient pefomance of the developed DTC model ha been teted by applying a tep load toque command fom +20 to -20 Nm on the mechanical dynamic. The flux efeence i maintained at 1.0 Wb. Figue 8 how the eult obtained. A een in Fig. 8(a) and 8(b), the etimated electomagnetic toque how a good epone and the cuent wavefom i almot inuoidal immediately afte the tep command. Thi demontate that the developed DTC achieved high dynamic pefomance in epone to change in demand toque. Howeve, thee ae ome pefomance degadation with toque ovehoot in the toque tanient owing to the hyteei contolle ued. Figue 8c how the tato flux magnitude, emphaizing the decoupled action of toque and flux contol. It i obeved that the vaiation of moto toque doe not influence fluxe. Thu, DTC ytem can aue independent flux and toque contol. Effect of Flux Hyteei Band: The flux hyteei band mainly affect the tato cuent ditotion [1],[5]. Thu, fo a fixed toque hyteei band, the ditotion inceae with the flux hyteei band. Some imulation eult ae hown fo diffeent value of the flux hyteei band amplitude. Fig. 9 how the obevable fact fom the developed model. If mall flux hyteei band amplitude of ±0.01 Wb i applied, the tato flux vecto locu appoache a cicle and the 1088 (b) D-axi tato cuent (c) Stato flux magnitude Fig. 8: Dynamic behaviou of DTC duing a load toque tep command fom +20 Nm to -20 Nm phae tato cuent wavefom i inuoidal. A the amplitude of the flux hyteei band inceae to ±0.1 Wb, the tato flux locu appoache to a hexagon hape and the tato cuent ditotion ha alo inceaed. Effect of Toque Hyteei Band: The election of the width of the hyteei band ha impotant effect

7 (a) Flux hyteei band at ±0.01 Wb (b) Flux hyteei band at ±0.1 Wb Fig. 9: The effect of flux hyteei band on the DTC pefomance (a) Hyteei Band = ±0.01 Nm witching fequency and thu the witching loe [1],[5]. If the band i too mall, a toque ovehoot may caue and it mut be elected appopiately. It affect the the toque eo to exceed the hyteei band. Thi will eult in a evee voltage vecto to be elected to educe the toque. A evee voltage vecto will educe the toque apidly and hence may in tun caue a toque undehoot. Theefoe, the toque ipple can become high if the toque hyteei band i et too mall. Figue 10 how the effect of the toque hyteei band. CONCLUSIONS (b) Hyteei band = ±10 Nm Fig.10: The effect of toque hyteei band on the DTC pefomance 1089 The wok caied out in thi pape i aimed and focued to develop a diect toque contol imulink model. The DTC achitectue allow the independent and decoupled contol of toque and tato flux. The implementation of the DTC model ha been deeply decibed and jutified it ealization. In ode to how the effectivene of the model, a numeical imulation ha been pefomed on a 7.5 kw induction machine fed by an IGBT PWM invete. The feaibility and the validity of the developed DTC model, baed on witching table technique, have been poved by imulation eult obtained in the toque contol mode.

8 ACKNOWLEDGEMENTS The autho would like to thank Pofeo J.W.Finch and M.Damion Giaoui fo hi guidance and valuable time. APPENDIX The tet machine i a thee phae and 50 Hz induction machine having the following paamete a hown in Table 2: Table 2: Paamete of the teted induction machine Powe ating, P ated 7500 W Rated voltage, V ated 400 V Rated cuent, I ated 16 A Pole pai, P 2 Stato eitance, R Stato inductance, L H Roto eitance, R Roto inductance, L H Magnetizing inductance, L m H Inetia, J 0.05 kg m 2 REFERENCES 1. Caadei, D., G. Gandi, G. Sea and A. Tani, Effect of flux and toque hyteei band amplitude in diect toque contol of Induction Machine. Poc. IECON 94, Bologna, Italy, Caadei, D., F. Pofumo, G. Sea and A. Tani, FOC and DTC: two viable cheme fo induction moto toque contol. IEEE Tan. Powe Electonic, 17(5): Chapui, Y.A. and D. Roye, Diect toque contol and cuent limitation method in tat up of an induction machine. IEE Conf. Powe Electonic and Vaiable Speed Dive, Takahahi, I. and Y. Ohmoi, High Pefomace diect toque contol of induction moto. IEEE Tan. Ind. Appl. 25 (2): Va, P., Vecto Contol of a.c. machine.oxfod Univeity Pe. 1090