Sensorless Permanent Magnet Synchronous Motors (PMSM) For Torque Ripple Reduction

Transcription

1 Jythi Mangaveni Chitta and Srinivaa Ra Maturu Senrle Permanent Magnet Synchrnu Mtr (PMSM Fr Trque Ripple Reductin Jythi Mangaveni Chitta and Srinivaa Ra Maturu Abtract- Permanent Magnet Synchrnu Mtr (PMSM are widely ued in high-perfrmance drive, ranging frm erv t tractin applicatin. The paper preent a dicrete pace vectr pule-width mdulatin applied t DTC f PMSM, which i a cmprmie between perfrmance and lw cmplexity becaue the ue f lk-up table. DSM i able t prduce mre vltage vectr than are available with the claical DTC, by uing different lk-up table depending n them value f the emf vltage induced in the tatr winding, DSM i able t prduce mre vltage vectr than are available with the claical DTC, by uing different lk-up table depending n the value f the emf vltage induced in the tatr winding, PWM and PI current regulatr that Field Oriented Cntrl (FOC need, Reductin f the ripple trque culd be btained by calculatin f the tatr flux vectr variatin required t exactly cmpenate the flux and trque errr Althugh thi technique can clearly reduce the trque and flux ripple, mre than ix vectr directin are neceary t achieve a decupled cntrl f flux and trque f the Machine. Thi paper al preent the cntrl f an PMSM thrugh enrle vectr cntrl uing pi cntrller Perfrmance f the prped trategy i verified by imulatin uing MATLAB. Index rm PMSM, I. INTRODUCTION Permanent Magnet Synchrnu Mtr (PMSM are widely ued in high-perfrmance drive, ranging frm erv t tractin applicatin. Thi extenive ue i partly due t the imprtant increae in energy denity, mainly becaue f the develpment f high cercive permanent magnet material at lwer ct, like Nedymium Irn Brn (NdFeB. Other advantage recgnized in PMSM are high efficiency and reliance, and gd dynamic perfrmance with high trque/inertia rati. Tgether with a uitable cntrl, the PMSM ha the ptential f replacing the inductin mtr in a number f indutrial, cmmercial and dmetic applicatin f variable peed drive. Direct Trque Cntrl (DTC wa intrduced in 984 by Takahahi et al. [] a a new apprach fr trque and flux cntrl f the Inductin Machine (IM. The right electin f the vectr vltage allw a decupled cntrl f flux and trque, withut the d- q crdinate tranfrmatin, PWM and PI current regulatr that Field Oriented Cntrl (FOC need. DTC ffer advantage uch a lwer parameter dependency and cmplexity cmpared with the FOC, which make the ytem mre rbut and eaier t Implement. Althugh, me drawback have been al tated in the literature. Amng them are: Jythi Mangaveni Chitta i a M.ch Student and Srinivaa Ra Maturu i wrking a Aciate Prfer, bth are with Department f Electrical and Electrnic Engineering, Dadi Intitute f Engineering and chnlgy, Anakapalle, iakhapatnam, Andhra Pradeh, India - Difficult t cntrl flux and trque at lw peed, - Current and trque ditrtin during the change f the ectr in α- β plane,- ariable witching frequency and al a high ampling frequency needed fr digital implementatin f hyterei cntrller. Hwever, the majr DTC ytem drawback i it relatively high trque ripple. A lw trque ripple i deirable becaue the trque ripple generate nie and vibratin, caue errr in enrle mtr drive, and aciated current ripple are in turn repnible fr the EMI. Baically, the high current and trque ripple in DTC are due t the preence f hyterei cmparatr tgether the limited number f available vltage vectr. Since the intrductin f the DTC, reearch ha been dne t lve thee prblem, and pecially the trque ripple [2]. Reductin f the ripple trque culd be btained by calculatin f the tatr flux vectr variatin required t exactly cmpenate the flux and trque errr. Mrever, the cntrl ytem huld be able t generate any vltage vectr, which implie the ue f Space ectr Pule Mdulatin (SPM [3], and cmplicate the cntrl cheme. An apprximatin t thi ideal behavir can be achieved by uing a higher number f vltage vectr than the ued in claical DCT. On thi way, in [4] the number f available vectr i increaed by uing a three-level inverter. Anther alternative t increae the number f available vectr i an n-line mdulatin between active and null vectr, in rder t btain a theretically infinite number f applicable vectr in every ix patial directin riginated by the pwer inverter [5]. Althugh thi technique can clearly reduce the trque and flux ripple, mre than ix vectr directin are neceary t achieve a decupled cntrl f flux and trque f the machine. Fr example, in [6] the imple witching table i replaced by everal witching table, btaining a cmbinatin f three vltage vectr int the ame ampling perid, which i called dicrete pace vectr mdulatin (DSM in the paper. In the late 99, DTC fr the PMSM have been preented [7], with the ame advantage a fr IM. Hwever, new prblem appear regarding applicatin f zer vectr. In an IM, the tatr flux linkage i uniquely determined by the tatr vltage. Therefre, zer vltage vectr can be applied t help t reduce flux and trque ripple. On the cntrary, the tatr flux linkage in a PMSM will change even when the zer vltage vectr are applied, becaue the magnet mve with the rtr. Then, indefinite cntrl n the flux i btained if zer vltage vectr are ued, andcnequently they huld nt be ued in DTC fr the PMSM. Thi i epecially true at a lw peed, when the zer vltage vectr applicatin n the PMSM hld the trque Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

2 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 2 rather than decreae it. A well a imprving dynamic, deletin f zer vectr al caue mre magnificent trque and flux ripple in teady tate, and cmplicate the cntrl f the mtr mthly in the lw peed range. Therefre, the way f minimizing trque ripple becme the main reearch ubject in a DTC f PMSM. Sme paper n the DTC in PMSM have appeared in recent year, preenting imilar technique t reduce the trque ripple than the ued in IM, mainly by mean f a cntant inverter witching frequency by uing SPM [8]. Hwever, the applicatin f SM ignal generatr make the cntrl tructure f the mdified DTC ytem mre cmplicated and wren the dynamic repne f the drive by intrducing undeirable delay. An apprximatin t SPM in a DTC f PMSM i preented in [9], but nly active vectr are ued, and variable witching frequency i btained. In thi paper the DSM technique i ued t lve the trque ripple prblem in a PMSM cntrlled by a DTC. DSM divide each ample perid in three equal time interval. The ytem i therefre able t generate a higher number f vltage pace vectr and the witching frequency i cntant. Tgether with a 5- level trque hyterei cmparatr and a mre precie witch table that al depend n the level f the back-emf, the trque ripple i decreaed. II. CONTROL SCHEMES FOR PMSM MOTORS PMSM cntrl technique can be divided int calar and vectr cntrl. Scalar cntrl i baed n relatinhip valid in teady-tate.. cntrlled. Scalar cntrl i ued e.g. where everal mtr are driven in parallel by the ame inverter. B. lt/hertz cntrl lt/hertz cntrl i amng the implet cntrl cheme fr mtr cntrl. The cntrl i an pen-lp cheme and de nt ue any feedback lp. The idea i t keep tatr flux cntant at rated value that the mtr develp rated trque/ampere rati ver it entire peed range. The vltage equatin fr a permanent magnet mtr were derived in chapter. In qdcrdinate thee equatin are where vq and vd are tatr vltage, r tatr reitance, i tatr current, ω angular velcity and λ i the flux linkage. In tatinarity the derivative term diappear, furthermre, if peed i high the emf vltage, ωλ, i relatively high and the reitive vltage drp may be ignred. In thi cae, if tatr flux i t be kept cntant, the vltage applied huld be directly prprtinal t the rtr angular frequency. At lwer peed an extra bt vltage i applied t cmpenate fr the reitive drp. The principle i valid nly fr tatinarity when the derivative term vanih. C. ectr Cntrl The prblem with calar cntrl i that mtr flux and trque in general are cupled. Thi inherent cupling affect the repne and make the ytem prne t intability if it i nt cnidered. In vectr cntrl, nt nly the magnitude f the tatr and rtr flux i cnidered but al their mutual angle. III. TRANSFORMATION TO qd-frame Figure 2., Sme cmmn cntrl technique ued fr PMSM. Cntrl methd in the dahed bx belng t the DTC family Amplitude and frequency f the cntrlled variable are cnidered. In vectr cntrl amplitude and pitin f a cntrlled pace vectr i cnidered. Thee relatinhip are valid even during tranient which i eential fr precietrque and peed cntrl A. Scalar Cntrl Scalar cntrl i baed n relatinhip valid in teady tate. Only magnitude and frequency f vltage, current, etc. are A. Reference Frame The required tranfrmatin in vltage, current, r flux linkage i derived in a generalized way. The reference frame are chen t be arbitrary and particular cae, uch a tatinary, rtr and ynchrnu reference frame are imple intance f the general cae. R.H. Park, in the 92, prped a new thery f electrical machine analyi t repreent the machine in d q mdel. He tranfrmed the tatr variable t a ynchrnuly rtating reference frame fixed in the rtr, which i called Park tranfrmatin. He hwed that all the time varying inductance that ccur due t an electric circuit in relative mtin and electric circuit with varying magnetic reluctance culd be eliminated. In 93, H.C Stanley hwed that time varying Inductance in the vltage equatin f an inductin machine due t electric circuit in relative mtin can be eliminated by tranfrming the rtr variable t a tatinary reference frame fixed n the tatr. Later, G. Krn prped a tranfrmatin f bth Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

3 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 3 tatr and rtr variable t a ynchrnuly rtating reference that mve with the rtating magnetic field. B. Axe Tranfrmatin We knw that per phae equivalent circuit f the inductin mtr i nly valid in teady tate cnditin. Neverthele, it den t hld gd while dealing with the tranient repne f the mtr. In tranient repne cnditin the vltage and current in three phae are nt in balance cnditin. It i t much difficult t tudy the machine perfrmance by analyzing the three phae. In rder t reduce thi cmplexity the tranfrmatin f axe frm 3 Φ t 2 Φ i neceary. Anther rean fr tranfrmatin i t analyze any machine f n number f phae. Thu, an equivalent mdel i adpted univerally, that i d q mdel. q d Here v i zer-equence cmpnent, cnvenient t et = that q axi i aligned with a-axi. Therefre ignring zer-equence cmpnent, it can be implified a- 2 va vb vc va vb vc Equatin 3.3 & 3.4 cnitively called a Clark Tranfrmatin. Figure 3. (b hw the ynchrnuly rtating d e -q e axe, which rtate at ynchrnu peed w e with repect t the d - q axe and the angle =. The tw-phae d -q winding are tranfrmed int the hypthetical winding munted n the d e -q e axe. The vltage n the d -q axe can be tranfrmed (r relved int the d e -q e frame a fllw: Fig 3.(a. 3- t 2- Tranfrmatin Cnider a ymmetrical three-phae inductin machine with tatinary a-b-c axi at 2/3 angle apart. Our gal i t tranfrm the three-phae tatinary reference frame (a -bc variable int tw-phae tatinary reference frame (d - q variable. Aume that d - q are riented at angle a hwn in fig: 3.(a. The vltage v d andv q can be relved int - b-c cmpnent and can be repreented in matrix frm a, a b c c c( 2 c( 2 in in( 2 in( 2 The crrepnding invere relatin i C C ( 2 C ( 2 2 Sin Sin( 2 Sin( q d a b c q d Fig 3.(b tatinary frame d -q t dynchrnuly rtating frame d e -q e tranfrmatin = c in = in + c Cntitutively eq 2.5 and 2.6 are knwn a Tranfrmatin. Park Fr cnvenience, the upercript e ha been drpped frm nw n frm the ynchrnuly rtating frame parameter. Again, relving the rtaing frame parameter int a tatinary frame, the relatin are = c + in = in + c..3.8 CONSTITUTIELY EQ 3.7 AND 3.8 ARE KNOWN AS INERSE PARK TRANSFORMATION I.CONTROL STRATEGY FOR DTC The blck diagram f direct trque and flux cntrl i hwn in Figure 6 explain the cntrl trategy. The peed cntrl lp and the flux prgram a a functin f peed are hwn Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

4 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 4 a uual and will nt be dicued. The cmmand tatr flux Ψ * * and trque T e magnitude are cmpared with the repective etimated value and the errr are prceed thrugh hyterei-band cntrller, a hwn. The flux lp cntrller ha tw level f digital utput accrding t the fllwing relatin H fr E HB (4. H fr E HB (4.2 H fr E HB (4.3 H (4.5 fr HB E HB The feedback flux and trque are calculated frm the machine terminal vltage and current. The ignal cmputatin blck al calculate the ectr number S(k in which the flux vectr Ψ lie. Fig.4.2 Direct Trque and Flux Cntrl Blck Diagram TABLE I SWITCHING TABLE OF INERTER OLTAGE ECTORS Fig.4. Flux Sectr The vltage vectr receive the input ignal H Ψ H and S(k generate the apprpriate cntrl vltage vectr (witching tate fr the inverter by lkup table, which i hwn in Table- (the vectr ign i deleted. The inverter vltage vectr (ix active and tw zer tate and a typical Ψ are hwn in Figure 5. Neglecting the tatr reitance f the machine. d ( dt (4.6 (r. t (4.7 The flux in machine i initially etablihed t at zer frequency (dc alng the trajectry OA hwn in Figure 5. With the rated flux, the cmmand trque i applied and the Ψ * vectr tart rtating. TABLE 2 FLUX AND TORQUE ARIATIONS DUE TO APPLIED. OLTAGE ECTOR. MODEL REFERNCE ADAPTIE SYSTEM (MRAS Figure 5 hw the imulink blck diagram Mdel Referencing Adaptive Sytem (MRAS. Which i cnit Tw blck ne i called Reference Mdel and ther i Adaptive Mdel. The vltage mdel tatr-ide equatin, are defined a a Reference Mdel and the imulink blck diagram f Reference Mdel i hwn in Fig. The Adaptive Mdel receive the machine tatr vltage and current ignal and calculate the rtr flux vectr ignal, a indicated by equatin, which i hwn in Fig 2. By uing uitable adaptive mechanim the peed r, can be etimated and taken a feedback. Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

5 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 5 Fig 2: Simulink blck diagram fr Mdel Referencing Adaptive Sytem with pi I. MATLAB BASED MODELING AND PERFORMANCE Fig 6. Blck diagram f SM-DTC Fig 6.4 Steady repne at % rated peed fr claical DTC, DTC Fig 6.2 Blck diagram f the prped DTC Fig 6.3 Blck diagram f the prped DTC.with MRAS Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

6 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 6 Fig 6.5Steady-tate repne at % rated peed fr claical DTC, DTC Fig 6.9 Prped mdel with MRAS II. CONCLUSIONS Fig 6.6 Start-up repne frm tandtill t rated peed fr DTC The paper preent a dicrete pace vectr pule-width mdulatin applied t DTC f PMSM and Senrle cntrl.the benefit f ectr cntrl withut uing any haft encder which i a cmprmie between perfrmance and lw cmplexity becaue the ue f lk-up table. The mathematical mdel f the drive ytem ha been develped and reult have been imulated. Simulatin reult f ectr Cntrl and Senrle Cntrl f DTC- PMSM uing MRAS technique uing Pi cntrller were carried ut by uing Matlab/Simulink and frm the analyi f the imulatin reult, the tranient and teady tate perfrmance f the drive have been preented and analyzed. Frm the imulatin reult, it can be berved that, in teady tate there are ripple in trque wave and al the tarting current i high. III. REFERENCES Fig 6.7 Speed reveral frm 5 t 5 r/min Fig 6.8 Repne t external diturbance [] I. Takahahi and T. Naguchi, A new quick - repne and high efficiency cntrl trategy f an inductin mtr, IEEE Tran. Ind. Appl., vl IA-22, pp , Sep [2] G. S. Buja, and M. P. Kazmierkwki, Direct Trque Cntrl f PWM Inverter-Fed AC Mtr A Survey, IEEE Tran. n Ind. Electrnic,.vl.5, n. 4, pp , Augut 22. [3] C. Lacu, I. Bldea, and F. Blaabjerg, A Mdified Direct Trque Cntrl fr Inductin Mtr Senrle Drive, IEEE Tran. On Ind. Applicatin, l. 36, N., pp. 22-3, January/February 2. [4] K-B Lee, J-H Sng, I. Chy, and J-Y Y, Trque Ripple Reductin in DTC f Inductin Mtr Driven by Three-Level Inverter With Lw Switching Frequency, IEEE Tranactin n Pwer Electrnic, vl. 7, n. 2, March 22 [5] A. Aria,. L. Rmeral, E. Aldaba, M.G. Jayne, Imprving direct trque cntrl by mean f fuzzy lgic, IEE Electrnic Letter,. 37, Iue, pp. 69-7, January 2. [6] D. Caadei, G. Serra, A. Tani, Implementatin f a direct trque cntrl algrithm fr inductin mtr baed n dicrete pace vectr mdulatin. IEEE Tranactin n Pwer Electrnic, vl. 5, n. 4, July, 2. [7] L. Zhng, M. F. Rahman, W. Y. Hu, and K. W. Lim, Analyi f Direct Trque Cntrl in Permanent Magnet Synchrnu Mtr Drive. [8] D. Swierczynki, and M.P. Kazmierkwki, Direct trque cntrl f permanent magnet ynchrnu mtr (PMSM uing pace vectr mdulatin (DTC -SM-imulatin and experimental reult, Prceeding f the 28th Annual Cnf. Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.

7 Jythi Mangaveni Chitta and Srinivaa Ra Maturu 7 f the IEEE Indutrial Electrnic Sciety, IECON 2, Sevilla, Spain, 5-8 Nvember, 22, l., pp IX. AUTHORS Jythi Mangaveni Ch i currently ding her Pt Graduate cure in Pwer and Indutrial Drive in Electrical and Electrnic Engineering Department, Dadi Intitute f Engineering and chnlgy, Anakapalle, iakhapatnam, India, Bachelr degree in Electrical and Electrnic Engineering frm Jawaharlal Nehru chnlgical Univerity- Kakinada, Andhra Pradeh, India, in 2. Mail id: Jythi.chitta@gmail.cm Srinivaa Ra M received hi Mater degree frm Jawaharlal Nehru chnlgical Univerity-Kakinada, India, and Bachelr degree frm Jawaharlal chnlgical Univerity- Hyderabad, India. He wrked a an Aitant Engineer(E fr Damdar alley Crpratin. He i Currently wrking a an Aciate Prfer f Electrical and Electrnic Engineering Department at Dadi Intitute f Engineering and chnlgy, Anakapalle, iakhapatnam, India. He preented everal chnical paper in variu Natinal and Internatinal Jurnal in thi area. And He i prviding technical aitance t evaral lar mdule manufacturing rganizatin. Internatinal Jurnal f Emerging Trend in Electrical and Electrnic (IJETEE ISSN: l. 8, Iue., Oct-23.