An adaptive high speed PMSM control for electric vehicle application

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1 An adaptve hgh peed PMSM control for electrc vehcle applcaton Flah Aymen Natonal School of Engneerng of Gabe Sbta aaâd Natonal School of Engneerng of Gabe Abtract: Th paper deal wth a new hgh peed drect torque control method appled on the permanent magnet ynchronou motor. Th hgh peed control algorthm characterzed by t effcency and t adaptaton to the motor parameter varaton. Baed on the feld weakenng prncple and on the model reference adaptve ytem (MRAS), th algorthm buld. Where, the MRAS ued for onlne etmated the motor parameter varaton and the feld weakenng for onlne generatng the reference flux magntude. The novel hgh peed control method, how the ytem good performance and t effcency, epecally n the loe power mnmzaton. Keyword: PMSM, Adaptve hgh peed, power loe, DTC. 1. INTRODUCTION Envronmental and economc conderaton are the major reaon for the development of electrc vehcle and added to the eane mantenance and the mplcty archtecture, thee lat are more and more n ue. Thee vehcle performance are baed on the motor type ued. Effectvely, numerou electrcal motor are propoed for th applcaton. Several work are tuded and compared thee lat n order to defne the bet and effcent one that can be ued n th applcaton. In [1], Zhu wa etablhed a comparatve tudy between, the Bruhle DC motor, nducton motor, wtchng reluctance motor and the permanent magnet ynchronou motor. However, the Permanent Magnet Synchronou Motor (PMSM) drve are the mot compettor to the other. Due to t uperor advantage uch a hgh effcency, low nerta, hgh torque to current rato, hgh power factor, maller ze, lower weght and almot no need for mantenance, make t more preferable face to the other motor. In the electrcal vehcle applcaton, the vehcle can be operated at a varable peed runnng. Where, the motor peed control extremely mportant. Effectvely, many control trategy have been developed for mprovng the performance of the PMSM drve. The vector control (VC) technque, propoed by Hae and Blachke, ued n many applcaton ntereted to control the nducton motor a preented by Harnefor n [] and Holtz n [3]. However, t dependence of a three PI controller, preent the method dffculte. Where, the degn of the peed and current regulator depend on exact mathematcal model wth accurate parameter. The DTC technque appeared after the VC trategy, t advantage a le machne parameter dependence, mpler mplementaton, qucker dynamc torque repone and t good robutne, make t more advantageou to ue th control trategy. Many work are propoed baed on th lat by orenz n [4], Boldea n [5] and acu [6]. Thee author wa dcued the DTC weakne a fluctuaton problem. Therefore, many DTC tratege are propoed and numerou modfcaton are preented to mprove the global performance, epecally by acu n [6] and [7], where the torque pulaton are mnmzed. After compared thee DTC method, acu demontrated the mplcty of the clacal DTC baed on the wtchng table. Started from th theory, other work are carred out to mprove the performance of th lat. Effectvely, the tator flux locu dvded nto twelve ector ntead of x, whch all x actve tate wll be ued n each ector a preented n [8]. Th lat propoed DTC trategy, proved t effcency n the nducton motor peed and torque control and t performance n the loe power mnmzaton a preented n [6]. Baed on thee advantageou, th trategy ued to control the PMSM. Th control method ue the tator flux and electromagnet torque a reference nput, for generatng the dered tator voltage. Generally, the econd nput gnal can be obtaned by the peed controller. However, the frt one mut be calculated. A our applcaton wll be runnng n the hgh peed mode, a tator flux magnetzaton neceary. Therefore a feld weakenng bloc eental for generatng the requred tator flux. Th phenomenon preented by many author a Sneyer n [9], John n [1] and [11], by orenz n [1], by Harnefor n [13] and other pecalt a Holtz and Sul n [14] and [15] repectvely. The man dea of th approach contng to, demagnetze the d_ax armature reacton current d. Many feld weakenng method are preented n the lterature a Mormoto approach decrbed n her paper [16], [17] whch he ntroduced the voltage and current converter lmt n the analytcal expreon of the feld weakenng. Other theore are baed on the tator current error and the actual peed lke cted n 1

2 [18], [19]. However, the preented problem of all thee approache are appeared n the PMSM parameter varaton due to temperature varaton, vbraton or dut. Some author lke Schferl and po [] are tuded the nfluence of thee parameter varaton on the feld-weakenng performance, epecally n a tator nductance varaton term. The latet work preented n [1], take nto account the motor retance effect. But, thee approache are crtczed for not condered all the motor parameter. Therefore we propoe n th work a new adaptve feld weakenng approach appled on the DTC trategy and take account any PMSM parameter varaton, a permanent magnet, tator retance and nductance. The adaptaton mechanm guaranteed by an onlne PMSM parameter etmaton baed on a model reference adaptve ytem (MRAS).The effectvene of the propoed algorthm hown n the feld weakenng workng regon. Where, wth the new algorthm, th lat can be moved proportonally to the PMSM parameter varaton. In other hand, the reult proved the mportance of the propoed adaptve hgh peed algorthm n the copper loe mnmzaton face to the non adaptve one. Th paper organzed a followng: n ecton II a decrpton of the PMSM control trategy gven. The ecton III, decrbe the propoed adaptve hgh peed algorthm. Where a mulaton reult demontrate the effectvene of the propoed algorthm n the feld weakenng zone movement. Secton IV degned for the dcuon of the mulaton reult, where the mportance of the adaptve feld weakenng algorthm proved n the copper loe mnmzaton n hgh peed range.. PMSM Control Strategy The PMSM control devce can be operated wth many control tratege. One can ue feld orented vector control or drect torque control tratege. However, the necety of a rapdly torque control make the econd method more advantageou. The practcal mplementaton of the propoed control trategy (DTC) mple of ue. To help the theoretcal tudy we ntroduce a mathematcal model of the propoed devce to be controlled. So, tarted form the nonlnear dfferental equaton [], [3]. The voltage expreon can be preented n the ytem of equaton (1). dd vd Rd d qq dt (1) dq vq Rq q d d m dt The tator flux expreon n the rotatng (d, q) frame are gven n (). d d d m q q () q The electromechancal torque can be expreed n (3), f the PMSM alent. However, for the non alent cae, d = q = then the expreon depend only on magnet flux and quadrature tator current. 3 P Te d q qd (3) The PMSM-DTC drve carred out by hytere control of tator flux and torque that drectly elect one of the x non-zero and two zero dcrete voltage vector for the nverter [4]. The electon of the voltage vector made to retrct the motor tator flux and torque error wthn the hytere band and obtan the fatet torque repone [5]. The electon of the voltage vector n conventonal DTC baed on the output error produced by the torque and the flux hytere controller (τf and τt ) and provded a nput to a wtchng table [6]. The tator flux expreon derved from (4), ung only the meaured tator voltage and current [8]. v R dt (4) Th equaton the foundaton for mplementng the flux etmator. It may be mplemented drectly, or approxmated by varou method to avod ntegrator drft [6]. The ampltude and angular poton of the tator flux vector mut be known o that the DTC can choe between an approprate et of vector dependng on the flux poton and ampltude. 1 (5) tan In clacal DTC, there are two tate per ector that preent a torque ambguty. In fact, they are not ued. It can be een n the frt ector that the vector V1 and V4, are not ued n the clacal DTC becaue they can ncreae or decreae the torque at the ame ector dependng on f the poton n t frt 3 degree or n t econd one. It eem a good dea that f the tator flux locu dvded nto twelve ector ntead of jut x, all x actve tate wll be ued per ector. Conequently, t aren the dea of the twelve ector DTC. Th novel tator flux locu llutrated n Fg.1. Fg. 1. The 1 ector DTC trategy

3 It ha to be ntroduced the dea of mall torque ncreae ntead of torque ncreae, manly due to the fact that the tangental voltage vector component very mall. Conequently t torque varaton wll be mall a well. 3. Adaptve Hgh Speed Control Algorthm For operatng at hgh peed regon, a pecfc control algorthm, baed on flux weakenng technque, appled [9]. Effectvely, t prncple mlar to the DC machne, where the flux a eparately controlled entty. So, a flux mnmzaton mportant for attaned a hgh peed regon. In the DC motor th acton mple. However, n the PMSM, the flux manly produced by the rotor magnet (λ m ). Refer to the mathematcal flux expreon, at the rated peed the drect tator current d equal to zero, but f the dered peed above the baed one, the dea refer to mnmze the drect tator current d, where t value reduced to the negatve value d<. When performng th control, the current and voltage are kept below a maxmum value. The maxmum of current and voltage are uually et by the nverter [17] and the lmt ytem of equaton, take nto account the maxmum voltage and maxmum current a expreed n (6) [16]. The value I max and V max are repectvely the maxmum nverter phae-current and phae-voltage ampltude. Id Iq Imax Vd Vq V (6) max Therefore, the prncple of feld weakenng can be decrbed by two crcle n the tator current reference, a llutrated n Fg. [3]. Two type of crcle are then preented. The frt for the current lmtaton condton. However, the crcle center zero and the radu the maxmum current. The econd type decrbe the crcle voltage lmt. The radu proportonal to the peed nvere. Effectvely, when the peed ncreae, the voltage crcle radu decreae. The voltage crcle center depend on the PMSM parameter. In the electrcal vehcle applcaton, many caue can modfy the motor parameter. One can depct the temperature that affect the tator retance and epecally the permanent magnet value. Where, ther value can ncreae or decreae above the rated one, repectvely. The mathematcal expreon related the temperature factor, the tator retance and the magnet flux value can be expreed repectvely by equaton (7) and (8). lbob R T ( T ) S bob ( T) 1 c ( T (7) T) B ( H, T ) B ( T) H a a Br B 1 ( ) a r B a r T T a a r r a Th varaton can modfy the flux wakenng zone. The et of fgure Fg. 3 to Fg. 5 demontrate thee effect. Some author, neglect the tator retance varaton on the feld weakenng algorthm, when the peed varaton above the rated one a preented n [16]. However, th varaton can nfluence on the feld weakenng zone. In Fg. 3, takng nto account the two fled weakenng algorthm. The normal one propoed by Mormoto where he neglect the tator retance parameter and the propoed one whch conder t. Zone B preent the Mormoto feld weakenng zone. Zone A the feld zone wth the preent feld weakenng algorthm. And Zone C, preent the feld weakenng zone when a tator retance varaton appled. The ame tet are appled on the feld weakenng zone, f a tator nductance or permanent magnet flux varaton appled, repectvely n Fg. 4 and Fg. 5. Zone B preent the feld weakenng zone f thee varaton are ntroduced for the propoed feld weakenng algorthm. The correpondng PMSM parameter varaton are llutrated n Fg. 9, 1 and 11. (8) Decreang peed 1 q max Current lmt max Increang peed 3 C o d / m d Feld weakenng zone Voltage lmt Fg. 3. Feld weakenng Zone for tator retance varaton Fg.. Feld weakenng trategy dagram 3

4 developed n order to dentfy the PMSM parameter, baed on the POPOV tablty theory [8]. The propoed etmator need only the onlne meaurement of current, voltage, and rotor peed to effectvely etmate the tator retance and nductance and the rotor flux lnkage multaneouly. By choong d and q component of the tator current a varable tate, the PMSM tate equaton take the followng form: Fg. 4. Feld weakenng Zone for tator nductance varaton Fg. 5. Feld weakenng Zone for permanent magnet flux varaton So the dea refer to llutratng an adaptve fled weakenng (AFW) whch adjuted f any varaton of tator retance, nductance or permanent magnet flux, occur. Started from the tow maxmum lmt condton on the nverter, maxmum voltage and maxmum current, and tacked account that the quadrature tator current obtaned from the peed controller [3]. The reference drect tator current can be then obtaned from (9). V max R q d R qm q d m (9) The lmt condton on the tator current f the quadrature component equal to zero become: d m 4Vmax R d 4 R m d lm q R d d And the drect tator current reference : max max q q m V R I R m (1) (11) In (11), all the PMSM parameter are tacked account. So PMSM parameter etmaton needed. The model reference adaptve ytem (MRAS) etmator d d c vd q q c v q e (1) f For a urface PMSM, non alency effect d = q =. d, q, u d, u q are the d and q component of the tator current and voltage. c 1/ / And ef m I f. R / The adjutable parameter tate equaton gven by: ˆ ˆ d d c vd ˆ ˆ q v q q c I f (13) k ˆ 1 d d k ˆ q q G the correcton gan matrx to be choen o a to acheve pre-pecfed error charactertc, where k 1, k are two lmted potve real. The problem of the ytem tablty can be reolved by the applcaton of the POPOV tablty theore, where two neceary condton mut be atfed [], [9] : The tranfer functon matrx of the lnear forward block mut be real and trctly potve, and accordng to [] the gan matrx G preented n (13), aure th condton. The nonlnear feedback block meet POPOV ntegral nequaton preented by: t1 T w edt, where γ a potve contant for any t. So the expreon of the adaptve parameter can be wrtten a [8]: R k r R () k pr d ed qeq (14) 1 kl 1 k pl uded uqeq () (15) m kf m kpf eq () (16) Then the adjutable drect reference tator current gven a: 4

5 d max ˆ ˆ ˆ ˆ max q q m V R I R ˆ m ˆ (17) Fnally, the propoed feld weakenng algorthm can be formed, and the Fg.6 llutrate the propoed algorthm. After obtaned the quadrature reference tator current from the peed controller, the drect adaptve reference one can be obtaned under the maxmum voltage and maxmum current condton. After compared the dered peed value and the reference one, wth the wtchng bloc, we can generate the drect reference tator current. The drect tator current error wll be tacked a an nput for the PI controller for generatng the drect reference tator flux. Then, wth the quadrature reference flux the reference tator flux obtaned and appled on the global control algorthm. - + PI Eq(3) q q q T e v q v d q d Eq(13) ˆ - + Eq(14) Eq(15) Eq(16) R m q MCMV d Comparatve Swtcher rated 1 - d + - d q PI q d 4. Smulaton Reult To verfy the effectvene of the propoed hgh peed control algorthm n the DTC twelve ector trategy for controllng the PMSM. A dgtal mulaton baed on Matlab/Smulnk oftware package ha been carred out. The PMSM charactertc are gven n table.1. After accordng the dfferent component n the Matlab/Smulnk envronment, the effectvene of the propoed hgh peed algorthm n the copper loe mnmzaton wll be approved. The global control cheme llutrated n Fg. 7 The prncple of th applcaton tend to mulate the electrc vehcle comportment. The motor tarted wth a maxmal load torque. T l =1.5N.m, f the gven peed under the rated peed (5) and decreae to T l = 1.N.m f the gven peed ncreang up the rated peed motor. A a robutne tet of the global control cheme, an abrupt load torque varaton appled n the rated, at t=.4ec, and over the rated peed, at t=.8ec. The obtaned reult how the effectvene of the propoed control cheme. In Fg.8 (a) to Fg.8 (e), we demontrate the behavor PMSM reult a peed, electromagnet torque, tator current and magnet flux. The obtaned reult are llutrated under a varable gven peed. A a ramp form, the gven peed tarted from rpm to rpm then from rpm to 35rpm. The fled weakenng reult can be llutrated n the Fg.8. (d) and Fg. 8. (e). Fg. 6. The adaptve hgh peed control algorthm T e Te + - T e AFW + - vd vq d q T Battery Inverter PMSM Speed Encoder Fg. 7. Block dagram of the propoed DTC Hgh peed PMSM overall control ytem Where, the negatve evoluton of the drect tator current and the flux mnmzaton reult at the hgh peed regon verfy the feld weakenng prncple. Fg. 8. (a) Speed reult 5

effectven of the propoed hgh peed control algorthm proved, where the loe power value mnmzed n the cae of tator nductance and permamemnt magnet flux varaton, epaclay n the hgh peed mode. Fg. 8.

6 effectven of the propoed hgh peed control algorthm proved, where the loe power value mnmzed n the cae of tator nductance and permamemnt magnet flux varaton, epaclay n the hgh peed mode. Fg. 8. (b) Electromagnetc Torque reult Fg. 8. (c) Quadrature Stator current reult Fg. 9. Power oe for tator retance varaton Fg. 8. (d) Drect Stator current reult Fg. 8.(e) Feld weakenng trajectory n the α-β flux frame Fg. 1. Power oe for tator nductance varaton After verfed the overal hgh peed control cheme performance under a wde peed range. The propoed algorthm wll be tetted. Where, PMSM parameter varaton are appled n order to how the adaptve hgh peed control algorthm performance n term of adaptaton and totally copper loe. Fg. 9, 1 and 11, how the etmated tator retance, nductance and permanent magnet flux varaton and the correpondng copper loe n the normal feld weakeng (NFW) algorthm and n the propoed one (AFW). The 6

7 REFERENCES Fg. 11. Power oe for permanent magnet flux varaton 5. CONCUSION In th paper a novel adaptve hgh peed control algorthm carred out. Baed on the MRAS etmator and the maxmum lmtaton of current and voltage, the planned algorthm buld. The mportance of the propoed algorthm demontrated for the mnmzaton of the copper loe. A comparatve tudy between the adaptve feld weakenng algorthm and the normal one verfy the mportance of the AFW. A mulaton reult demontrate the effectvene and the robutne of the global control cheme wth the gve algorthm. Power 4W Rated Current Irated A Maxmum Current Imax 5A Rated Speed ωrated 5rpm Rated Torque Tleated 1.5N.M Stator Inductance.15 H Stator retance R 5.Ω Permanent flux λm.4wb Inerta factor J 85e 6kg.m Table 1. PMSM parameter and rated characteretc APPENDIX v d, v q Drect and quadrature tator voltage λ d, λ q Drect and quadrature tator flux d, q Drect and quadrature tator current d, q Drect and quadrature tator nductance ω Mechancal peed λ m Magnet flux R Stator retance T l oad torque P Pole number J Rotor nerta coeffcent AFW Adaptve Feld Weakenng NFW Normal Feld Weakenng MCMV Maxmum Current Maxmum Voltage K p, K PI-MRAS parameter α c Copper Coeffcent T, T Temperature coeffcent S bob and bob Col Secton and Col ength ΔB r Remanent nducton varaton H a Magnetque Feld B a Magnetque nducton n Temperature T a B ra, Remanent nducton Permeablty coeffcent μ ra 1. Z. Q. Zhu, D. Howe, Electrcal machne and drve for electrc vehcle, hybrd and fuel cell vehcle, Proceedng of IEEE Tran. Vol. 95, n. 4, 7, pp O. Wallmark,. Harnefor, O. Carlon, Senorle control of PMSM drve for hybrd electrc vehcle, IEEE 35th Annual Power Electronc Specalt Conference, Vol.4, 4, pp J. Holtz, T. Thmm, Identfcaton of the machne parameter n a vector controlled nducton motor drve, Conference Record of the 1989 IEEE Indutry Applcaton Socety Annual Meetng, 1989, pp T. R. Obermann, Z. D. Hurt, R. D. orenz, Deadbeat-drect torque & flux control motor drve over a wde peed, torque and flux operatng pace ung a ngle control law, IEEE Energy Converon Congre and Expoton, 1, pp I. Boldea, C. I. Ptc, C. acu, G-D. Andreecu,. Tutelea, F. Blaabjerg, P. Sandholdt, DTFC- SVM moton-enorle control of a PM-ated reluctance ynchronou machne a tarter-alternator for hybrd electrc vehcle, IEEE Tranacton on Power Electronc, Vol. 1, n. 3, 6, pp C. acu, I. Boldea, F. Blaabjerg, A modfed drect torque control for nducton motor enorle drve, IEEE Tranacton on Indutry Applcaton, Vol.36, n.1,, pp C. acu, I. Boldea, F. Blaabjerg, Drect torque control of enorle nducton motor drve: a ldng-mode approach, IEEE Tranacton on Indutry Applcaton, Vol. 4, n., 4, pp G. S. Buja, M. P. Kazmerkowk, Drect torque control of PWM nverter fed AC motor a urvey, IEEE Tran. Ind. Electron, Vol. 5 n. 4, 4, pp B. Sneyer, D.W. Novotny, T.A. po, Feldweakenng n bured permanent magnet AC motor drve, IEEE Tranacton on Indutral Applcaton, Vol. 1, 1985, pp S. R. Macmnn, T. M. Jahn, Control technque for mproved hgh-peed performance of nteror PM ynchronou motor drve, IEEE Tranacton on Indutry Applcaton, Vol.7, n. 5, 1991, pp A. M. E-Refae, T. M. Jahn, Optmal flux weakenng n urface PM machne ung fractonallot concentrated wndng IEEE Tranacton on Indutry Applcaton, Vol.41, n.3, 5, pp F. Brz, A. Dez, M. W. Degner, R.D. orenz, Current and flux regulaton n feld-weakenng operaton [of nducton motor],the Thrty-Thrd IAS Annual Meetng IEEE Indutry Applcaton Conference, Vol.1, 1998, pp

8 13.. Harnefor, K. Petlanen,. Gertmar, Optmumeekng feld weakenng control of nducton motor drve Eghth Internatonal Conference on Power Electronc and Varable Speed Drve,, pp M. Wla, H. Abu-Rub, H. J. Holtz, Speed enorle nonlnear control of nducton motor n the feld weakenng regon, 13th Power Electronc and Moton Control Conference, 8, pp Km, S.-H.; Sul, S.-K.; Park, M.-H, Maxmum torque control of an nducton machne n the feld weakenng regon, Conference Record of the 1993 IEEE Indutry Applcaton Socety Annual Meetng, 1993, pp S. Mormoto, Y. Takeda, T. Hraa Expanon of operatng lmt for permanent magnet motor by current vector control conderng nverter capacty, IEEE Tranacton. Indutry Applcaton, Vol. 6, n. 5, September/October, 199, pp S. Mormoto, Y. Takeda, T. Hraa,Flux Weakenng Control Method for Surface Permanent Magnet Synchronou Motor, IPEC. Tokyo 9, 199, pp Y. Sozer, D. A.Torrey, Adaptve Flux Weakenng Control of Permanent Magnet Synchronou Motor, IEEE Conf pp Z.Q. Zhu, Y. S. Chen, D. Howe, Onlne Optmal Flux Weakenng Control of Permanent Magnet Bruhlen AC Drve, IEEE Tranacton Indutry Applcaton, Vol. 36, n. 6,, pp R.F. Schferl, T.A. po, Power capablty of alent pole permanent magnet ynchronou motor n varable peed drve applcaton, IEEE Tranacton on Indutral Applcaton, Vol. 6, 199, pp M. Turn, E. Chrcozz, R. Petrella, Feedforward Flux- Weakenng Control of Surface- Mounted Permanent-Magnet Synchronou Motor Accountng for Retve Voltage Drop, IEEE Tranacton. Indutral. Electronc, Vol. 57, n. 1, Jan. 1, pp A. Quntao,. Sun, On lne parameter dentfcaton for vector controlled PMSM drve ung adaptve algorthm, IEEE Vehcle power and propulon conference (VPPC), X. Junfeng, X. Jangpng, A new method for permanent magnet ynchronou machne wth oberver, IEEE power electronc pecalt Conference, T. J. Vyncke, R. K. Boel, J. AMelkebeek, Drect Torque Control of Permanent Magnet Synchronou Motor, 3RD IEEE Benelux Young Reearcher Sympoum n Electrcal Power Engneerng, n. 8, 6, pp J. Habb, S. Vaez-Zadeh, Effcency Optmzng Drect Torque Control of Permanent Magnet Synchronou Machne, Proc. IEEE Power Electronc Specalt Conference (PESC), 5, pp M. Meaoud, H. Kraem, M. Ben Hamed,. Sbta, M. N. Abdelkrm, A Robut Senorle Drect Torque Control of Inducton Motor Baed on MRAS and Extended Kalman Flter, eonardo Journal of Scence (JS), Academc Drect, Vol. 7, 8, pp K. E. Qundere, E. F. Ruppert, M. E Olvera, Drect torque control of permanent magnet ynchronou motor drve wth a three level nverter, 37th IEEE Power Electronc Specalt Conference, 6, pp A. Flah,. Sbta, M. Ben hamed, Onlne MRAS-PSO PMSM parameter etmaton, IREMOS, Vol. 4. n. 3, 11, pp Kan, Q. Zhang, J. Shen, S. Paul, Comparon of two novel MRAS tratege for dentfyng parameter n permanent magnet ynchronou motor, Internatonal Journal of Automaton and Computng, Vol. 3, 1, pp A. Flah, H. Kraem and.sbta Robut hgh peed control algorthm for PMSM enorle drve, IEEE 9th Internatonal Mult-Conference on Sytem, Sgnal & Devce, SSD 1, pp

Additional File 1 - Detailed explanation of the expression level CPD

Additional File 1 - Detailed explanation of the expression level CPD Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor