AN INDIRECT ROTOR-FLUX-ORIENTED CONTROL OF A TWO-PHASE INDUCTION MOTOR DRIVE

Transcription

1 Numbe2 Jounal of Engineeing AN INDIRECT ROTOR-FLUX-ORIENTED CONTROL OF A TWO-PHASE INDUCTION MOTOR DRIVE ABSTRACT Tuki K. Hassan Dept. of Elect. College of Engineeing Univesity of Al-Mustansiayh A vecto contol is poposed fo a two phase induction moto dive. The moto is diven by H-bidge cuent-egulated pulsewidth modulated voltage souce invete. The vecto contol is based upon oto field oientation concepts that have been adopted fo this type of machine. Simulation esults ae povided to illustate the system opeation and the MATLAB/SIMULINK has been used fo simulation. الخالصة يتناول هذا انبذث يقتزح باستخذاو سيطزة ان ىجه في يسىق ان ذزك انذثي ثنائي انطىر ديث يستخذو يبذل نىع قنطزة H وان سيطز عهيه بطزيقت تض ين عزض اننبضت نىع تنظيى انتيار. سيطزة ان ىجه تستنذ عهى يبادئ اعتبار فيض انذوار ك ذىر وانتي تى استخذايها نهذا اننىع ين ان كائن.تى ايجاد نتائج ان ذاكاة باستخذاو MATLAB/SIMULINK نتىضيخ ع م ان نظىيت. KEY WORDS Two phase induction moto, indiect oto-flux-oiented contol. INTRODUCTION Contol systems utilize the factional-hosepowe size electomagnetic components as motos and sensos to measue speed and position of contolled elements. A two phase induction moto is used as a contol moto, and is suitable fo contol systems up to a few hunded watts. The two phase induction moto has two-phase windings located in stato slots,which ae displaced fom each othe by 90 electical degees. One winding is always supplied and is called the excitation(o main) winding. The contol signal is applied to the othe winding (called contol o auxiliay winding), such that with no contol signal the moto must be at standstill. In ode to develop a toque the two windings voltages must be shifted in timephase. The moto opeates fom a single-phase supply and utilize a phase-splitting Available iasj.net 2659

2 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive capacito to develop a otating field in the ai gap. Howeve, due to an elliptical otating field, a pulsating toque that causes highe noise than a thee-phase induction moto. In ecent yeas vaious schemes have been poposed fo invete-diven two phase induction moto. In efeences (1, 2) squae voltage wavefoms with quadate phase shift ae supplied to the two-phase windings of a two phase induction moto diven by an invete. Though this dive is simple and cheap, the contol ange of speed is limited and the hamonic content of the output is high. In efeences (3, 4) phasediffeence angle contol of a two-phase induction moto is used which can extend the speed contol ange without a substantial incease in cost of the dive. Howeve, unde phase diffeence angle contol, the toque pulsation still exists. In efeence ( 5) space-vecto pulse width-modulation (SVPWM) invete is poposed fo constantpowe opeation of a two phase induction moto. Though with this scheme a smooth toque is obtained,the dive can not suitable fo constant toque with vaiable speed applications which ae needed highly in industy. Also the dynamic esponse of the speed is vey slow and the system has no ability to eject the distubances in the load toque, system paametes and the dc powe supply, since the system is an open loop system. This pape intoduces a vaiable speed dive fo a two phase induction moto.a cuent-egulated pulsewidth modulated two phase voltage-souce invete is designed as a balanced two phase supply fo the moto. A vecto contol method and the oto field oientation concepts have been adopted fo this type of machine to obtain closed loop speed contol dive system like a sepaately excited dc moto dive. Simulation esults ae pesented to demonstate the main chaacteistics of the poposed dive system, and the MATLAB/SIMULNK has been used to pefom the simulation studies. MACHINE MODEL The simplified epesentation fo the 2-phase machine is shown in Fig.1.When a stato winding is distibuted fo the pupose of poducing a sinusoidal MMF wave in space, it is convenient to conside the winding as an equivalent single coil and expess the mutual coupling between it and an equivalent oto coil as a sinusoidal function of the angula displacement between thei magnetic axes. bs-axis b-axis a-axis Stato Roto b a bs θ as-axis as Fig.1 A 2-phase Symmetical Machine. Available iasj.net 2660

3 Numbe2 Jounal of Engineeing If the induction machine has eithe a squiel-cage oto o a coil-wound oto with the same numbe of phases as the stato, the oto can be consideed as having equivalent coils (shown in Fig.1). The stato windings ae identical,i.e.,both windings have an identical numbe of effective tuns N s, identical esistance s,identical leakage inductance L ls,and self inductance L s. Similaly oto windings ae identical which have the same effective tuns N,esistance,leakage inductance L l, and self inductance L. The voltage equations fo the stato phases ae witten v as p i (1) as s as v bs p i (2) bs s bs In the case of the oto phases v a p i (3) a a v b p i (4) b b Fo induction moto with squiel cage oto v a =0,v b =0,theefoe equation 3 and equation 4 can be witten 0 p i (5) a a 0 p i (6) b b Whee λ is the total flux-linkages of a paticula winding, and p is the opeato d/dt. Figue 2 shows the angula elation of the stato and oto axes of a 2-phase machine with the thid set which is an othogonal set (d-q axis). It is clea that as-bs set is fixed in the stato. The a-b set is fixed in the oto and hence otates at an electical angula velocity of ω Available iasj.net 2661

4 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive q-axis b-axis bs-axis d-axis β a-axis θ as-axis Fig.2 Axes of 2 pole 2 phase symmetical machine The equations of tansfomations which can be coelated to the angula elation of the axes in Fig.2, ae Stato Roto f f ds qs f cos f sin (7) as bs f cos f sin (8) bs as Whee f f d q f cos f sin (9) a b f cos f sin (10) b a (11) In these equations the vaiable f can epesent eithe voltage, cuent, o fluxlinkage.if the tansfomation equations ae used to tansfom the voltages, cuents, and flux-linkages of both the stato and the oto to the abitay efeence fame (d-q axis),with the oto vaiables ae efeed to the stato windings and with the selfinductances sepaated into leakage inductance component and a magnetizing inductance component, the following equations ae obtained (6 ),( 7) : v ds p i (12) ds qs s ds v qs p i (13) qs ds s qs Available iasj.net 2662

5 Numbe2 Jounal of Engineeing 0 p ( ) i (14) d q d 0 p ( ) i (15) q d q Whee L i ds qs ls ds L i ls qs M ( i M ( i ds qs i i d q ) ) (16) (17) L i M (18) d q l l d q ( id ids) L i M (19) ( iq iqs) p (20) p (21) Fo the 2-phase machine, L ls L L (22) s ms L L L l ms (23) M L ms (24) N s Lms Ls (25) N L s is the mutual inductance between stato and oto. N s and N ae the effective tuns of a stato and oto phase winding espectively. The pimes ae used to denote oto quantities efeed to the stato windings. It is clea that the voltage equations (12) to (15) of the symmetical induction machine may be expessed in any efeence fame by setting the speed of the abitay efeence fame, ω, equal to the speed of the desied efeence speed. Fo example, the voltage equations expessed in the stationay efeence fame may be obtained by setting ω to zeo. Fo a efeence fame fixed in the oto ω is set equal to the electical angula velocity of the oto, ω. The voltage equations in the synchonously otating efeence fame ae obtained by setting ω equal to the electical angula velocity of the fundamental fequency component of the applied stato voltages ω e. Available iasj.net 2663

6 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive An expession fo the instantaneous electomagnetic toque can be obtained by applying the pinciple of vitual displacement ( 7 ).This expession is P Te ( )( q id d iq ) (26) 2 Whee P is the numbe of poles. In ode to obtain the dynamic chaacteistics, it is necessay to elate toque and speed, and the elation can be expessed as 2 2 Te ( ) Jp ( ) B Tl (27) P P Whee T l is load toque, J is the moment of inetia, and B is the fiction constant. INDIRECT ROTOR-FLUX ORIENTATION The indiect oto-flux oiented contolle is deived fom the dynamic equations of the machine in the synchonously otating efeence fame, i.e., ω=ω e. The oto voltage equations of the two phase induction moto in synchonously otating efeence fame ae given by Whee 0 i p (28) d sl q d 0 i p (29) q sl d q sl (30) e L i M (31) d q l l d q ( id ids) L i M (32) ( iq iqs) Whee ω sl is the slip fequency in ad/sec. The fluxes and cuents in the above equations ae epesented in the synchonously otating efeence fame. In the vecto contol stategies, the ac motos ae contolled like sepaately excited dc motos which have independent channels fo the flux and toque contol. In ode to link the d-axis of the efeence fame to the oto flux vecto, the q component of this flux has to be equal to zeo ( 8 ) q 0 (33) (34) d Available iasj.net 2664

7 Numbe2 Jounal of Engineeing Substituting (33),(34) in (28),(29),(31) and (32) causes the new oto flux and voltage equations i p 0 (35) d i q 0 (36) sl Whee L i Mi (37) d ds L i Mi 0 (38) q qs L L M l (39) The oto cuents in tems of the stato cuents ae deived fom equations (37) and (38) as i d Mi L ds ( 40) Miqs i q (41) L The oto flux in tem of the stato cuent i ds can be obtained by substituting equation (40) in equation (35) as Mids 1 s (42) Whee s is the laplace tansfom (s=p) and τ is the oto time constant which is L (43) Substituting (33),(34) and (41) in (26) cause the new electomagnetic toque equation to be T e P M ( ) iqs (44) 2 L Available iasj.net 2665

8 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive Equation (44) indicates that the developed toque depends on the oto flux and quadatue-axis component of the stato cuent (i qs ). The toque vaiation is popotional to the vaiation of I qs when the oto flux is contolled as a constant and the behavio of the two phase induction moto becomes like a sepaately excited dc moto. Equations (36) and (41) ae used to deive a fomula fo slip fequency ω sl in tems of i qs and λ / as Miqs sl (45) Fo the indiect oto-flux oientation, the oto flux position equied fo coodinates tansfomation is geneated fom the oto speed ω and the slip fequency ω sl as ( dt (46) e sl ) IMPLEMENTATION OF INDIRECT ROTOR- FLUX-ORIENTED CONTROL SCHEME The block diagam that is shown in figue (3) epesents the indiect oto fluxoiented contol scheme fo two phase induction moto dive. The dc supply voltage is conveted to balanced two phases supply though H-bidge invete ( 2 ), ( 4 ) which is consisted of fou insulated gate bipola tansistos (IGBT). Fig. 4 shows the H-bidge invete and the way of connecting the two phase windings. This is a cheape method because it uses only fou semiconducto switches. Fig. 4 also shows that two capacitos ae connected in seies in the dc link to fom a midpoint that is connected to neutal point N. In pactice, two lage esistos ae also needed in paallel with the capacitos to balance the voltage of the capacitos. The output of the invete is applied to the stato windings of the moto. Moto atings and its paametes ae given in Appendix. The oto speed ω m is sensed and compaed with the efeence speed ω * m and the eo is conveted to the efeence * toque T e using popotional-integal contolle (P-I contolle). The efeence quadatue-axis stato cuent i * qs (toque cuent ) and the slip fequency ω sl ae calculated in tems of the efeence toque and the oto flux using equation (44) and equation (45) espectively. Fo the indiect oto-flux-oiented contol, the oto flux position (angle) is calculated using equation (46). The stato cuents i as and i bs ae measued and conveted to the diect-axis component i ds and quadatue-axis component i qs of the stato cuent using the equations (7) and (8) of tansfomation fom stationay efeence fame to the synchonously otating efeence fame (Pak tansfomation). The oto flux efeed to stato (λ ) is calculated in tem of diect-axis component of stato cuent (i ds ) using equation (42).The dive has oto-flux contol loop. The oto flux command (λ ) is constant and the dive opeates in the constanttoque egion. The P-I contolle is used fo the oto flux loop and the output of the contolle epesents the efeence diect-axis component of stato cuent ( i * ds ). Available iasj.net 2666

9 Numbe2 Jounal of Engineeing The cuents i * ds and i * qs ae efeence command cuents fo the cuentegulated pulse width modulation (CRPWM) block that will foce moto stato cuents to follow these efeence cuents.thee ae two P-I contolles in the CRPWM block which convet the cuent eos between the efeences and feedback into efeence magnet and toque voltages.these voltages ae tansfomed to stationay efeence fame using invese pak tansfomation and then conveted to moto teminal voltages by using sinusoidal pulsewidth modulation ( 9 ). λ Roto Flux Calculato V dc H-Bidge Invete Invete i as i bs 2-Phase Induction Moto CRPWM _ P-I Contolle + i ds * λ * Ref. Roto Flux + i qs * _ Toque Cuent and Slip Calculato + ω sl + + ω P/2 P-I Speed Contolle + T e * _ i ds i qs dq ab ω e θ e dt _ ω m Speed Senso Refeence Speed Fig.3 Block diagam of the indiect oto- flux-oiented contol of a two phase induction moto dive ω m * Q 1 Q 3 R Q 4 Q 2 C C V dc R v bs N v as Fig.4 H-bidge invete with phases connection Available iasj.net 2667

10 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive RESULTS Digital simulations wee caied out to simulate the contol esponses of the indiect oto-flux-oiented contol scheme using MATLAB/SIMULINK. The simulations set up such that the dive system is tested with low and high values of a step efeence speed command,also the system is tested with load and with no load fo each efeence speed command. Fig.5 and Fig.6 show the simulated values of the oto speed and the two- phase stato cuents of the moto espectively. A step efeence speed command of 30 ad/sec value is applied with no load toque.the oto speed tacks the efeence speed at steady state with small oveshoot ( appoximately 1 ad/sec ). The stato cuents ae balanced and each is limited to a maximum value of 12 A at stating in ode to potect the semiconducto switching devices of the invete fom high cuent. The outputs of the speed contolle and flux contolle ae povided with limites to pevent stato cuents fom exceeding pemissible value. The stato cuents dop to a low no load of (2A) value when the speed eaches the steady state. Fig.7 and Fig.8 epesent the oto speed and stato cuents espectively fo the same step efeence speed command (30 ad/sec) with applied load of 4 Nm.The oto speed esponse is simila with the case of no load (Fig.5).The stato cuents ae aised to a value of 4.5 A (maximum value) popotional to the applied load. Fig.5 Roto speed fo efeence value of 30 ad/sec With no load Fig.6 Two phase stato cuents fo efeence value of 30 ad/sec With no load Available iasj.net 2668

11 Numbe2 Jounal of Engineeing Fig.7 Roto speed fo efeence value of 30 ad/sec With load value of 4 Nm Fig.8 Two phase stato cuents fo efeence value of 30 ad/sec with load value of 4 Nm The dive system is tested at speed nea the ated speed by applying a step efeence speed command value of 130 ad/sec. Fig.9 shows the oto speed which tacks the efeence speed at steady state. Fig.10 shows the two phase stato cuents with small no load value at steady state. Fig.11 and Fig.12 epesent the oto speed and stato cuents fo the case of 4 Nm applied load and efeence speed of 130 ad/sec. Fig.9 Roto speed fo efeence value of 130 ad/sec With no load Fig.10 Two phase stato cuents fo efeence value of 130 ad/sec with no load Available iasj.net 2669

12 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive Fig.11 Roto speed fo efeence value of 130 ad/sec With load value of 4 Nm Fig.12 Two phase stato cuents fo efeence value of 130 with load value of 4 Nm To investigate the obustness of the poposed dive system, we analyzed the speed esponse and the stato cuents of the moto to step change in load toque. Fig.13 and Fig.14 show the oto speed and the stato cuents when the moto is stated by applying a step efeence speed of 30 ad/sec with no load toque. Afte 0.35 sec, a step load toque of 4 Nm value is applied.avey small dip in speed (appoximately 0.5 ad/sec) occus and the speed etuns to its oiginal value afte 0.15 sec.the stato cuents inceases to a value of 4.5 A (maximum value ) at the instant of applying the load. Fig.15 and Fig.16 epesent the oto speed and stato cuents fo the case of stating the moto with applied load of 4 Nm and efeence speed value of 30 ad/sec. Afte 0.35 sec a load is emoved,a small ise in speed occus which decay to zeo afte 0.15 sec.the stato cuents is educed to its no load value at the instant of emoving the load. Figs ae simila to Figs but with 130 ad/sec efeence value in ode to veify the obustness at high speed. Available iasj.net 2670

13 Numbe2 Jounal of Engineeing Fig.13 Roto speed fo efeence value of 30 ad/sec with no load.afte 0.35sec load toque of 4 Nm value is applied Fig.14 Stato cuents fo efeence value of 30 ad/sec with no load.afte 0.35sec load toque of 4 Nm value is applied Fig.15 Roto speed fo efeence value Fig.16 Stato cuents fo of 30 ad/sec with 4 Nm load. Afte efeence of 30 ad/sec with 0.35 sec the load toque is emoved 4 Nm load. Afte 0.35 sec the load is emoved Available iasj.net 2671

14 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive. Fig.17 Roto speed fo efeence value of 130 ad/sec with no load.afte 0.35 sec the load toque of 4 Nm value is applied Fig.18 Stato cuents fo efeence value of 130 ad/sec with no load. Afte 0.35 sec the load toque of 4 Nm value is applied Fig.19 Roto speed fo efeence Fig.20 Stato cuents fo value of 130 ad/sec with efeence value of 130 ad/sec 4 Nm load.afte 0.5 sec with 4 Nm load.afte 0.5 sec the load toque is emoved the load toque is emoved Available iasj.net 2672

15 Numbe2 Jounal of Engineeing Figs show the oto speed,stato cuents and oto flux espectively.the moto is stated with 30 ad/sec efeence speed and no load toque. Afte 0.3 sec the efeence speed is inceased to 130 ad/sec. The oto speed tacks the efeence speed at steady state fo each step. The oto flux tacks the efeence of 0.5 Wb value and independent upon the speed command. Fig.21 Roto speed fo efeence value Fig.22 Stato cuents fo of 30 ad/sec with no load. Afte 0.3 sec efeence value of 30 ad/sec the efeence is inceased to 130 ad/sec with no load. Afte 0.3 sec the efeence is inceased to 130 ad/sec Fig.23 Roto flux fo efeence flux value of 0.5 Wb Available iasj.net 2673

16 T.K.Hassan An Indiect Roto-Flux-Oiented Contol of A two-phase Induction Moto dive CONCLUSIONS This pape has discussed the indiect oto-flux-oiented contol scheme fo two phase induction moto. The modeling appoach poposed made it possible to adapt some high pefomance contol fo use with a two phase moto dive system. Simulation tests wee consideed satisfactoy and have confimed the claimed featues. In spite of being moe complex than othe stategies, like the standad V/Hz, the use of indiect oto-flux- oiented contol may not esult in additional cost in tems of data pocessing. This is due to the innovations of micoelectonics that incease the capability of pocessing infomation and educing cost and powe consumption of the integated cicuits. Based on simulation esults, the following conclusions ae made: 1. The oto speed can be vaied fom zeo up to ated value. 2. Balanced sinusoidal cuents ae obtained due to sinusoidal pulse width modulation. 3. The dive system is obust against the vaiation of the load toque. Small dip in speed occus when a step of load toque is applied,this dip decays to zeo afte shot time (appoximately 150 msec.).. Small ise in speed occus when the load is emoved.this ise decays to zeo afte shot time (appoximately 150 msec.). The poposed dive system can be expeimentally built with digital signal pocessing boad fo fast calculations of contol algoithms in eal time. Also the H- bidge invete with IGBT tansistos can be built to convet the dc voltage in to two phase balanced supply using sinusoidal PWM. APPENDIX The specifications of two phase moto that is used fo simulation ae: 1hp, 2Φ, 110 V, fou poles and the paametes of the moto ae: M mH, 10. mh L l s mh L l , 2.4 s J 0.02 kg.m 2, B kg.m 2 /sec Available iasj.net 2674

17 Numbe2 Jounal of Engineeing REFERENCES 1. L. M. C. Mhango and R. Peyman, Analysis and simulation of a high-speed twophase AC dive fo aeospace applications, Poc. IEE-Elect. Powe Applicat., vol. 144, no. 2, pp Ma I. R. Smith, D. Ceighton, and L. M. C. Mhango, Analysis and pefomance of a novel two- phase dive fo fan and wate-pumping applications, IEEE Tans. Ind. Electon., vol. 36, pp , Nov D. Jang and G. Cha, Phase-diffeence contol of 2-phase invete-fed induction moto, in Conf. Rec. IEEE-IAS Annu. Meeting, 1989, pp Do- Hyun and J. S. Won, Voltage, fequency and phase-diffeence angle contol of PWM invetes-fed two-phase induction motos, IEEE Tans. Powe Electonics, vol. 9 pp , July M. A. Jabba, Ashwin M. Khambadkone, and Zhang Yanfeng, Space-vecto modulation in a two-phase induction moto dive fo constant-powe opeation, IEEE Tans. Industial Electonics, Vol. 51, No. 5, pp , Octobe P. C. Kause, O. Wasynczuk, and S. D. Studhoff, Analysis of Electic machiney, Piscataway, NJ: IEEE Pess, P. C. Kause, and C. H. Thomas, Simulation of symmetical induction machiney, IEEE Tans. Powe Appaatus and Systems, Vol. PAS-84, No. 11, pp , Novembe Rik W. De Doncke, Fancesco Pofumo, Michele Pastoelli, and Paolo Feais, Compaison of univesal field oiented (UFO) contolles in diffeent efeence fames, IEEE Tans. Powe Electonics, Vol. 10, No. 2, pp , Mach J. Holtz, Pulsewidth modulation fo electic powe convesion, Poc. IEEE, Vol. 82, No. 8, pp , Aug Available iasj.net 2675