Sensorless Control for Surface Mounted Permanent Magnet Synchronous Machines at Low Speed

Transcription

1 Journal of International Conference on Electrical Machine an Sytem Vol. 2, No. 4, pp. 429~435, Senorle Control for Surface Mounte Permanent Magnet Synchronou Machine at Low Spee Lu An *, Davi Franck *, an Kay Hameyer * Abtract Thi paper propoe a enorle pee control bae on a novel extenion of the torque proucing flux (active flux) oberver for the urface mounte permanent magnet ynchronou machine (SPMSM) without aitional high frequency ignal injection. From the etimate torque proucing flux, the rotor poition an pee can be calculate at low pee ue to their inepenency. Therefore, no rotor poition enor i require. Two approache of the torque proucing flux oberver are preente an compare. The reult how the tability an robutne of the expanion of the torque proucing flux oberver at low pee for the SPMSM. Keywor: Low pee, Senorle control, Surface mounte magnet, PMSM 1. Introuction Senorle control for electrical machine play an important role in inutry application, in which the number of harware component an ytem cot can be ignificantly reuce. Beie, low intallation pace requirement an le electromagnetic compatibility problem are alo avantage of the enorle control principle. There are two categorie of enorle control for the urface mounte permanent magnet ynchronou machine, which are ue in two ifferent pee range, i.e. high pee range an low pee range. In [1]-[4], the high frequency ignal injection metho i ue in orer to iagnoe the magnetic aliency, which contain the information about the rotor poition an rotor pee. It i one of the mot ue metho, which are appropriate for low pee. In [5], the rotor poition i obtaine from a preefine ramp function of the rotor pee. The rotor poition can be etermine through the integral of the rotor pee. Thi approach for low pee i witche to the one for high pee range, after the rotor ramp up with a contant q- current along thi preefine ramp from tantill to a fixe high pee range. A imilar metho i ue in [6], where a I-f feeforwar * Intitute of Electrical Machine, RWTH Aachen Univerity, Schinkeltr. 4, Aachen Germany (Lu.An@iem.rwthaachen.e, avi.franck@iem.rwth-aachen.e, Kay.Hameyer@iem. rwth-aachen.e) Receive 3 November 2013; Accepte 29 November 2013 control i realie at low pee for rotor poition an rotor pee etimation. In relation to [5], a reference frequency of tator current i preefine. The tator current i = 0 an iq=contant are operate eparately. With the ai of the reference frequency, the reference rotor poition can be etecte. In aition, the non-linearity of tator inuctance can be utilize for the rotor poition etimation [7]-[8]. Here, the elf-inuctance an mutual-inuctance are coniere. Thee are epenent on the rotor poition. The ifference between the tator voltage in free-wheeling moe operation an in converter-active-operation i etermine. The information about the rotor poition can be etecte from thi ifference. "Back EMF" metho i uually ue for the rotor poition an rotor pee etimation. Matui' oberver i an extenion of the "back EMF" oberver [9]. Two reunant parameter moel are etablihe: an electrical parameter moel an a mechanical parameter moel, which contain the information about the rotor poition an the rotor pee. An optimal experimental approach i require, in orer to provie the extene "back EMF" metho for the rotor poition an rotor pee etimation at low pee. In literature, a torque proucing flux concept [10]-[11] provie the pee etimation at low pee without the common approach of ignal injection. Such metho are uitable for interior permanent magnet ynchronou motor (IPMSM). Thi paper introuce an extenion for SPMSM, which i bae on the torque proucing flux metho an combine a iturbance feeforwar. The extenion moel i integrate into the oberver moel an i inie the

2 430 Senorle Control for Surface Mounte Permanent Magnet Synchronou Machine at Low Spee feeback circuit of the oberver. Thereby, the uncertainty of the machine parameter an the meaurement inaccuracy are coniere in orer to improve the etimation reult. The avantage of the preente approach i the low computational cot. The paper i organize a follow: Section 2: Senorle Spee Control, Section 3: Oberver moel, Section 4: Experiment, Section 5: Concluion. 2. Senorle Spee Control In thi paper, a cacae control i ue for enorle pee control. Fig. 1 how that the cacae control conit of pee control circle an current control circle, which are linke with each other. The current controller i the inner loop controller an the pee controller i the outer loop controller. The pee controller output i q * i ue a the reference variable for the i q current controller. Fig. 1. Senorle pee control cheme. Due to the linear inepenence of the tator current in q coorinate, it i poible to control the two current component i an i q eparately. The irect axi current i i et to zero in orer to control the torque prouce by quarature axi current i q. Only the q-component i reponible for the contruction of a torque control o that the current control of q-component can uperimpoe the pee control. Thereby, the PID controller i implemente in the control ytem. The tator current i q, i an the rotor pee are controlle eparately. The ifferential equation of a ieal PID controller in parallel tructure: u t K et e T e t p T t reet rate t, (1) where K p i the proportional gain, T rate i the rate time an the reet time i T reet. The PID controller can alo be ecribe a tranfer function: U E K p T. (2) rate Treet The controller parameter of the PID controller for the current an pee control are lite in Table 1. Table 1. Parameter of PID Controller Controlle variable Controller parameter Proportional gain K p,iq Rate time T rate,iq reet time T reet,iq Stator current (quarature axi) i q Stator current (irect axi) i Rotor Spee ω Proportional gain K p,i Rate time T rate,i reet time T reet,i Proportional gain K p,ω Rate time T rate,ω Reet time T reet,ω An exact rotor poition i require to control the PMSM. Therefore, a enorle control with poition oberver i eigne to provie exact rotor poition. A complete block iagram repreentation for a enorle control of PMSM uing a voltage regulate pace vector PWM voltage ource inverter i hown in Fig. 1. The oberver etimate the rotor poition an pee uing the tator current i an voltage u in the coorinate ytem, which are calculate from the meaure tator current i a,b,c an voltage u a,b,c. The etimate rotor poition i ue for the Park tranformation an the etimate pee i fe back to the pee control. 3. Oberver Moel 3.1 Oberver Moel with Flux Feeback The principle of the torque proucing flux oberver with flux feeback i hown in Fig. 2 [10]: the aim of thi metho i an accurate etimation of the torque proucing flux (active flux). With the help of the voltage moel (3) [10], the etimate tator flux can be calculate from the current i an voltage u : u R i t. (3) R i the tator reitance. i =(i, i ) T an u =(u, u ) are tator current un voltage in -coorinate, which are calculate from meaure 3 phae tator current i a,b,c un

3 Lu An, Davi Franck, an Kay Hameyer phae tator voltage u a,b,c. The current moel [10] r i i, 0 F j i, q L 0 0 i L q i i efine to etimate the magnetic flux q r i (4), which i in qcoorinate an ha to be tranforme in -coorinate: 1 r i T i. (5) The tranformation matrix from q to i ecribe a 1 co in T. (6) in co Y act = Y - L q i where L q i the q-axi tator elf inuctance an F i the tator flux. The rotor poition ˆ q el can be etimate by θ el arcco 2 2 act, act, act, n, (9) (10) with n N0. The rotor poition ˆ q el can alo be calculate by arctangent function of act, / act,. 3.2 Oberver Moel with Current Feeback The principle of the oberver with current feeback i hown in Fig. 3: imilar to the flux oberver with flux feeback, thi oberver moel conit of a current moel (11) an a voltage moel (12) [11]: i T i t 1 L F R 1 L 0 co in ; i i 0 1 L u u q T i Κ i (11) i. (12) i Fig. 2. Structure of the torque proucing flux oberver with flux feeback. A hown in Fig. 2, the ifference between the etimate an i i fe back to the voltage moel through the PI compenator gain. Thereby, the etimation of the tator flux can be correcte an improve: Y = ò ( u - R i +u comp ) t. (7) The compenation value u comp in -omain i ecribe a: u comp = ( k p + k i ) Y i ( ( ) - Y ( ) ), (8) where k p i the proportional gain an k i i integral gain, which can be experimentally acertaine. In orer to get cloer inight into the characteritic of the permanent flux in -coorinate, the active flux i efine a [10]: Y a an Y b are etimate tator flux quantitie in coorinate an ue to etermine the preent tator current. Through the proportional control factor K, the ifference between the etimate tator current î = îa, ( î b ) T an the meaure tator current i =(i, I ) T i the fee-back ignal of the voltage moel to be minimize. The active flux Y act i etermine by (9). The rotor pee can be efine with etimate rotor poition ˆ q el (10) a ˆ mech ˆ ˆ mech el ˆ mech (13) t t p or with an equation a a function, that epen on the ifference between the previou an the current value of the etimate active flux: w mech = ( q mech,n -q mech,n-1 ) T, (14) w mech = 1 T 1 é p arctan æ Y ö act,b n ç è Y - arctan æ Y öù act,b ê n-1 ç act,an ø è Y ú ëê act,an-1 øûú, (15)

4 432 Senorle Control for Surface Mounte Permanent Magnet Synchronou Machine at Low Spee where p i number of pole pair an T i the ampling time. 3.4 Extenion of Oberver Moel In orer to be able to improve the etimation reult, an extenion of the oberver i evelope. Thereby, the uncertainty of the machine parameter i coniere, e.g.: the non-linearity of the tator inuctance L+L an the change of reitance with temperature R+R. Furthermore, the meaurement accuracy coul alo affect the etimation reult. The above-mentione variable are efine a the iturbance variable of the oberver ytem. The aitional etimation error are caue by the iturbance variable. Fig. 3. Structure of the torque proucing flux oberver with current feeback. 3.3 Stability Analyi The tability of the oberver moel ha alreay been tate in [12]. The etimate error can be ecribe a with i, e C, e (16) 1 0 L C T Lq T The ynamic of the tate error can be efine by t, e K i, e KC, e. (17). (18) A Lyapunov caniate function of the oberver moel i given by 1 T V, e, e 0. (19) 2 The erivative of the Lyapunov caniate function i efine a T T V V, e, e, e KC, e. t t (20) The moel of the oberver i aymptotically table, becaue V i maller than zero with all of the poitive eigenvalue of the function KC. Fig. 4. Extenion of oberver moel. Fig. 4 ecribe the principle of the extenion. At thi, the i ˆ i, i etimate current ˆ ˆ T i electe a the input variable of the extenion. Afterwar, the etimate current î i correcte to ˆ. The extenion moel i a part of i, ext the oberver moel an i inie the feeback circuit of the oberver. Through the proportional control factor K, the ifference between the meaure tator current i an the extene etimate tator current ˆ which i correcte i, ext by the extenion i the fee-back ignal to be minimize. With the help of experiment, the correlation between the etimate current un the iturbance variable ξcan be implifie to 2 x 1 2 ( ) k x k x. (21) The parameter k 1 an k 2 can be acertaine from the meaurement. 4.1 Tet Bench 4. Experiment The parameter of the SPMSM ue in the imulation an experiment are collecte in Tab. 2. In contrat to the

5 Lu An, Davi Franck, an Kay Hameyer 433 interior permanent magnet ynchronou motor (IPMSM), the tator inuctance of the quarature axi an irect axi (L q an L ) of SPMSM ha the ame value. The above preente metho were implemente for the SPMSM. Fig. 5. Experimental tet platform. The experimental ytem etup an teting etup with harware component are efine a in Fig. 5. The above epicte enorle control metho i implemente to a SPACE platform for the permanent magnet ynchronou machine. Thereby, a three-phae aynchronou machine (ASM) i utilie a a loa machine, which i controlle by an inverter in orer to provie the eire torque. The PWM frequency of the inverter i 8 khz. The SPACE CLP1103 i ue to control the rive ytem (Fig.5). The tator current an voltage are meaure an the ampling rate i 20 khz. The information are tranmitte to the SPACE platform. A torque gauge bar i intalle on the haft between the aynchronou machine an the PM machine for the torque meaure. The etimate rotor poition i ent to the Control Dek. The return of the Control Dek i fe back to the SPACE ytem. The inverter inherit the approval an the uitable ignal, which are the input of the PM machine. etimate rotor poition, which influence each other. It i intricate to minimize the etimation error only by changing the control factor K. Fig. 7 illutrate the current etimation reult by uing compenation (Fig. 4), which oe not trongly epen on the motor parameter variation. The negative impact on the etimation are coniere, e.g. the tator reitance change ue to the motor temperature rie an influence of inuctance variation. The etimation error i conierably minimize. An incremental encoer wa ue to meaure the rotor poition which wa coniere a reference. The etimate rotor poition an the meaure rotor poition are hown in Fig. 8. By comparion, although having a tiny time elay aroun 20 m to the meaure rotor poition. The reult of the evelope enorle pee control are hown in Fig. 9. The ea-time i 10 m. Both of the approache are table at low pee. However, the controller with flux feeback reult in overhoot an i even intable at the pee of 5 rpm. When compare to flux feeback, the current feeback how improve tability an performance at low pee. 4.2 Etimation an Control Reult The etimation reult of the current by uing flux oberver with current feeback without compenation at the pee of 30 rpm i hown in Fig. 6, where the meaure current i plotte. It can be een that the hape of the etimate current i imilar to the meaure current. However, it peak value oe not accor with the peak value of the meaure current i. Thi eviation cannot be rectifie by the ajutment of the proportional control factor K (Fig. 3). The reaon for thi i that the etimate current an meaure current i are couple by the control factor K, the voltage moel an the current moel. Furthermore, the inaccurate parameter of the PMSM have negative impact on the etimate current an the Fig. 6. Etimate current without compenation. Fig. 7. Etimate current with compenation.

6 434 Senorle Control for Surface Mounte Permanent Magnet Synchronou Machine at Low Spee current etimation i minimize. Therefore, the exact active flux can be etermine. By the control uing oberver, the oberver moel with current feeback provie better reult in comparion to the oberver moel with flux feeback an how improve tability an performance at low pee. Appenix Fig. 8. Rotor poition etimation. Fig. 9. Comparion of two approache. The oberver with current feeback provie better reult in comparion to the one with flux feeback. The reaon behin i, that the flux (Fig. 2) i not irectly meaure by the flux feeback an it i calculate from the meaure tator current un voltage. Becaue of thi aitional converion, the value of flux coul actually iffer from the real value. By current feeback, the etimate current i compare to the meaure current without further tranformation (Fig. 3). Thi lea to le overlay error. 5. Concluion In thi paper two torque proucing flux (active flux) oberver moel for enorle pee control of the urface mounte permanent magnet ynchronou machine are preente an compare to each other. An extenion of the oberver i evelope in orer to improve the etimation proceure. Thereby, the uncertainty of the machine parameter i coniere un the error of the Table 2. Specification of PMSM Parameter an contraint Value Number of pole pair p 4 Maximum pee n max 4500 [rpm] Rate pee n N 2000 [rpm] Rate power P N 10.3 [kw] Rate phae to phae voltage U N 380 [V] Maximum permitte motor current I max 75 [A] Rate motor current I N 21.2 [A] Rate torque T N 49.2 [Nm] Ma moment of inertia J [kg m2] Stator reitance R 0.2 [Ω] Stator inuctance (quarature axi) L q [H] Stator inuctance (irect axi) L [H] Excitation flux ψ F [V] Time contant (quarature axi) t q = L q /R [H/ Ω] Time contant (irect axi) t = L /R [H/ Ω] Coefficient of friction μ 0 Reference [1] Jung-Ik Ha; Ie, K. Sawa, T., an Seung-Ki Sul, Senorle rotor poition etimation of an interior permanent-magnet motor from initial tate, IEEE Tranaction on Inutry Application, vol. 39, pp , May [2] Ji-Hoon Jang, Seung-Ki Sul, Jung-Ik Ha, ab Ie, K., Senorle rive of urface-mounte permanent-magnet motor by high-frequency ignal injection bae on magnetic aliency, IEEE Tranaction on Inutry Application, vol. 39, pp , July [3] Dan Xiao, Foo, G., Rahman, M.F., Senorle irect torque an flux control for matrix converter IPM ynchronou motor rive uing aaptive liing moe oberver combine with high frequency ignal injection, IEEE Tranaction on Energy Converion Congre an Expoition, ECCE, pp , September [4] Piippo, A., an Luomi, J., Senorle aaptive oberver combine with HF ignal injection for enorle control of PMSM rive, Electric Machine an Drive, pp , May [5] Zihui Wang, Kaiyuan Lu, Blaabjerg, F., A imple tartup trategy bae on current regulation for back-emf-bae enorle control of PMSM, Power Electronic, vol. 27, pp , Augut 2012.

7 Lu An, Davi Franck, an Kay Hameyer 435 [6] Fatu, M., Teoorecu, R., Bolea, I., Anreecu, G., an Blaabjerg, F., I-F tarting metho with mooth tranition to EMF bae motion-enorle vector control of PM ynchronou motor/generator, Power Electronic Specialit Conference, PESC IEEE, pp , June [7] Cheng-Kai Lin, Tian-Hua Liu, an Chi-Hun Lo, High performance enorle IPMSM rive with a wie ajutable pee range, Inutrial Electronic, IECON th Annual Conference of IEEE, pp , November [8] Lin, C.-K., Liu, T.-H., Lo, an C.-H., Senorle interior permanent magnet ynchronou motor rive ytem with a wie ajutable pee range, Electric Power Application, IET, vol. 3, pp , March [9] Caux, S., an Mauion, P., Optimal etting of PMSM oberver parameter uing 2D experimental eign, Power Electronic, Electrical Drive, Automation an Motion, SPEEDAM International Sympoium,pp 8-13, June [10] B. Ion, P. Mihaela Coruta, A. Gheorghe-Daniel, an B. Fre, Active flux DTFC-SVM enorle control of IPMSM, IEEE Tranaction on Energy Converion, vol. 24, no. 2, pp , JUNE [11] F. Gilbert Hock Beng, an M. F. Rahman, Direct torque control of an IPM-ynchronou motor rive at very low pee uing a liing-moe tator flux oberver, IEEE Tranaction on Power Electronic, vol. 25, no. 4, pp , April [12] Foo, G., Rahman, M.F., Senorle vector control of interior permanent magnet ynchronou motor rive at very low pee without ignal injection, Electric Power Application, IET, vol. 4, no. 3, pp , Lu An wa born in Liaoning, China. She receive the Dipl.-Ing. egree in electrical engineering from Gottfrie Wilhelm Leibniz Univerity Hannover, Hannover, Germany. She ha been working a a reearch aociate at the Intitute of Electrical Machine of RWTH Aachen Univerity, Germany ince October Her reearch interet inclue enorle control of permanent magnet ynchronou machine. Kay Hameyer (FIET, SMIEEE) receive hi M.Sc. egree in electrical engineering from the Univerity of Hannover an hi Ph.D. egree from the Berlin Univerity of Technology, Germany. After hi univerity tuie he worke with the Robert Boch GmbH in Stuttgart, Germany a a Deign Engineer for permanent magnet ervo motor an vehicle boar net component. Until 2004 Dr. Hameyer wa a full Profeor for Numerical Fiel Computation an Electrical Machine with the KU Leuven in Belgium. Since 2004, he i full profeor an the irector of the Intitute of Electrical Machine (IEM) at RWTH Aachen Univerity in Germany he wa vice ean of the faculty an from 2007 to 2009 he wa the ean of the faculty of Electrical Engineering an Information Technology of RWTH Aachen Univerity. Hi reearch interet are numerical fiel computation an optimiation, the eign an control of electrical machine, in particular permanent magnet excite machine, inuction machine an the eign employing the methoology of virtual reality. Since everal year Dr. Hameyer work i concerne with the evelopment of magnetic levitation for rive ytem, magnetically excite auible noie in electrical machine an the characteriation of ferro-magnetic material. Dr. Hameyer i author of more then 250 journal publication, more then 500 international conference publication an author of 4 book. Dr. Hameyer i a member of VDE, IEEE enior member, fellow of the IET. Davi Franck receive hi iploma in Electrical Engineering in 2008 a Engineer from the Faculty of Electrical Engineering an Information Technology at RWTH Aachen Univerity. Since, 2008 he ha worke a a reearcher at the Intitute of Electrical Machine (IEM) at RWTH Aachen Univerity. He i currently working towar hi octoral egree in the area of noie an vibration of electrical machine