Journal o Modeling and Optimization 8: (16) Permanent Magnet Synchronou Motor Direct Torque Control Conidering the Eect o Salient Pole Wenjie Chen, Yi Zhang, Haieng Wei 1. School o Electrical and Inormation, Jiangu Univerity o Science and Technology, Jiangu Zhenjiang 1, China E-mail:wh1@16.com Abtract: Salient eect without conidering the impact tudy or the direct torque control o permanent magnet exiting problem, it etablihed a permanent magnet mathematical model involving motor aliency, decribing the working principle o direct torque control ytem, building control ytem imulation model, and ue o motor torque, power angle imulation waveorm analyi reveal the inluence o the mechanim o aliency by reluctance torque o permanent magnet direct torque control. Keyword: Salient eect; permanent magnet ; direct torque control; reluctance torque; motor power angle. 1. Introduction Permanent magnet ha high eiciency, high power denity, mall torque ripple, tarting torque and dynamic repone at, wide peed range and advantage ha become reearch hot point in the ield o power tranmiion, and ha been widely ued in electric traction and electric vehicle electric drive ield [1-. Due to the imple control method and torque repone at, eay to realize the digital good dynamic perormance advantage, permanent magnet direct torque control caued many cholar to conduct the reearch, and achieved certain outcome [. Torque and tator lux linkage double hyterei loop tructure i adopted in the direct torque control, and the peed o the motor torque i realized by electing the appropriate voltage vector control tator lux linkage amplitude and rotation peed by the look-up table method. A new direct torque control method or permanent magnet baed on back tepping control i propoed in thi paper [; A direct torque control method o permanent magnet baed on duty cycle modulation i propoed in the paper [; A direct torque control trategy baed on motor torque angle i propoed in thi paper [5; A novel [6 adaptive quadrature eedback compenation tator lux oberver or permanent magnet direct torque control i propoed; In order to improve the dynamic and tatic perormance and to improve the robutne o the peed control, a ractional order intelligent integral control trategy i propoed in thi paper [7; A peed etimation method baed on the rotor lux o the direct torque control algorithm i propoed in thi paper[8. Through the analyi o the literature it how that the permanent magnet direct torque control i baed on the exiting multi alient pole permanent magnet a the reearch object, ignoring the inluence o the aliency o direct torque control. However, even the implicit pole type permanent magnet i diicult to completely eliminate the alient pole eect due to the limitation o the motor aembly proce. In view o the above problem. Firtly, thi paper tudie the permanent magnet alient pole eect o phyical caue, analyi o the alient pole eect o permanent magnetic torque and angle and lux eect, permanent magnet reluctance torque and angle o mathematical expreion i derived and MATLAB were built to mimic really i obtained by conidering the eect o alient pole permanent magnet direct torque control parameter o repone curve, and reveal the eect o alient pole eect on motor control.. Salient Pole Eect o Permanent Magnet Synchronou Motor Permanent magnet alient pole eect ha two caue: one i due to the aymmetric tructure o the motor and another i due to the rotor or tator iron magnetic aturation. Among them, 1
8: (16) Journal o Modeling and Optimization aymmetry o motor tructure, epecially the rotor magnetic circuit aymmetry and i a major caue o all the permanent magnet alient pole eect. Permanent magnet Permanent magnet Permanent magnet (a) Surace mount type (b)interpolant (c)built-in type Fig.1 rotor tructure o permanent magnet Fig.1 i the rotor tructure o permanent magnet. Permanent magnet according to permanent intallation poition o the magnet on the rotor can be divided into three dierent type, including urace mounted, plug type and embedded type, the interpolation type permanent magnet ynchronou motor rotor due to the preence o larger permeability rotor erromagnetic material between adjacent permanent magnetic material, leading to the rotor magnetic circuit aymmetry alient pole rate i higher; Similarly, in the permanent magnet o permanent magnetic material located inide the rotor due to the erromagnetic material o the rotor, the magnetic circuit aymmetry, alient pole rate higher; The rotor o urace mounted permanent magnet i in the electromagnetic perormance o the rotor tructure, the alient pole eect i not obviou. The rotor o urace mounted permanent magnet ynchronou motor i in the electromagnetic perormance o the rotor tructure, the alient pole eect i not obviou. The vector diagram o permanent magnet i hown in Figure.. D-q or rotor ynchronou rotating coordinate ytem; u i are tator voltage vector and current vector; i the tator lux vector; r i the rotor lux vector; The included angle between the tator lux and rotor lux i δ, that i, the power angle. According to the theory o motor analyi, while ignoring the permanent magnet direct axi inductance LD and the change o axi LQ inductance, and conider the eect o alient pole magnetic circuit, permanent magnet in d-q rotating coordinate expreion o electromagnetic torque o the tator lux linkage equation and d-q rotating coordinate ytem are a ollow: d = id Ld + (1) q = iqlq T = P [ diq qid () In the ormula, L d, L q i the cro, direct axi inductance, P i the pole logarithm. The expreion o the current in the d-q coordinate ytem can be obtained by the above ormula (1): d id = Ld () q iq = L And the ormula () i derived to obtain the expreion o the ollowing: T = P [ diq qid = P [( Li d d + ) iq ( Li q q ) id () = P [ iq + ( Ld Lq ) idiq The expreion (1) and () the expreion given by (), the torque o the motor torque expreion can be alient eect: P P 1 1 T = in δ + ( )in δ (5) L L L d q d P In expreion (5), the deinition o Tem = inδ i the main electromagnetic torque. T L em i the d magnetic ield o the tator and rotor o permanent magnet magnetic ield through the air gap caued by the interaction o electromagnetic torque, i due to the reluctance torque motor caued by unbalanced magnetic q
Journal o Modeling and Optimization 8: (16) ield DQ axi, the reluctance torque caued by motor alient eect. β u q i α δ θ Fig. deinition o d-q coordinate ytem in permanent magnet. Direct Torque Control o Permanent Magnet Synchronou Motor Permanent magnet tator lux i produced by the tator winding el-inductance o armature reaction lux and rotor permanent magnet in the tator winding excitation o rotor induction lux through the vector ynthei, including induction rotor lux i by permanent magnet parameter deciion; ub armature reaction lux produced by the tator current. Direct torque control o permanent magnet i according to the amplitude o tator lux and electromagnetic torque bia, baed on the tator lux linkage vector where the poition choen directly uitable voltage pace vector, to achieve the control o motor torque and tator lux linkage. The tator lux linkage ormula or permanent magnet : jθ = L i + e (6) Under the condition that the tator reitance i neglected, the tator lux vector increment i: = ( t) ( t1) u t (7) I the tator lux amplitude i approximately contant, the torque increment expreion can be got: P T = [ Lq co δ ( Lq Ld)co δ δ (8) LL d q The intantaneou value o work angle can be expreed a: δ = arctan( q / d) (9) The expreion i only related to d and q, which can not only repreent the power angle o the implicit pole motor, but alo the power angle o the alient pole motor. The tator lux angle can be expreed a: δ + θ = arctan( β / α) (1) Permanent magnet direct torque control block diagram hown in Fig.. Direct torque control contain two cloed-loop control o lux el - control and torque el - control. Flux el-control part include the three-phae voltage and current detection, three-phae tatic to two-phae tationary coordinate tranormation, lux etimator, lux hyterei comparator and the witching table. The torque control part include the torque etimator, torque hyterei comparator and the witching table.. Direct torque control imulation conidering alient pole eect In the MATLAB6.5/SIMULINK environment, baed on the principle o direct torque control, a imulation model o permanent magnet with alient pole eect i et up, and the imulation model i hown in Fig.. Simulation model o the main module include: coordinate tranormation module, torque hyterei and lux hyterei ring module, lux partitioning o the choice and implementation module, witching table module, the tator lux calculation module, a permanent magnet module and the motor electromagnetic torque and reluctance torque calculation module etc. Among them, the inverter witching table i hown in Table 1. d α
8: (16) Journal o Modeling and Optimization Inverter PMSM S ABC Switching table /Converion Flux hyterei comparator Flux etimator Judging ector Torque hyterei comparator T Torque etimator Fig. the block diagram o direct torque control o permanent magnet Flux_re Speed_re V_a_b_c v_ala_beta Flux Convert_to PI Speed_T PI V_a_b_c Section Section Sector Selector Flux_real S_lux Flux_re Flux_Relay Torque_re S_Torque torque Torque_real Load_torque lux Pule Torque_Relay Switching Table Ua TL Ub Ia Ib n pule Te theta PMSM Motor Ua Ub phi_a_b Ia Ib Flux_et Flux1 phi_a_b theta Tem+Tez Tem Tez Te1 Te1 Tem Tez Repeating Sequence Out In Te n theta Out In Fig. Simulation model o permanent magnet with alient pole eect Table 1 Inverter witch table Dicrete ytem T=1e-5 φ τ θ1 θ θ θ θ5 θ6 1 1 u u u u 1 u u u u u u u u u u u u u u u u u u u u
Journal o Modeling and Optimization 8: (16) Table Parameter o permanent magnet Parameter Value Parameter Value Rated voltage /V 11 Magnetic chain given value /W.7 b Quadrature axi inductance 16.9 Rated current /A 5 /mh 1.11 Rated requency /HZ 5 Direct axi inductance /mh Rated rotor peed /r/min 15 Stator reitance /Ω.6 Conidering eect o alient pole permanent magnet imulation parameter uch a Table how, in the actual imulation, PI peed regulation device proportion coeicient and integral coeicient wa 1 and 1, torque limiting 5N. M, width o torque hyterei.1n.m and lux hyterei loop width.1wb. 5. Simulation reult and analyi Fig.5-1 i a permanent magnet at a load o N.m peed rom zero peed to a given peed 1r/min repone waveorm. From the imulation reult viible, direct torque control, permanent magnet can moothly rom zero peed to rie to 1r/min; tarting time lated about.. In the tart tage, total motor torque to accelerate to 5N. M o maximum torque, although gradually decline, to 1r/min and table operation in the N.m; electromagnetic torque in 6N. M o maximum torque acceleration and 1r/min to table operation in.5n.m; reluctance torque maximum torque -1.5N.m weaken o electromagnetic torque, 1r/min to table operation in -.5N.m. Baed on the tarting tage total torque o motor, the electromagnetic torque and the reluctance torque o the comparative analyi, it can be ound that the permanent magnet alient pole eect caued by the reluctance torque oet the electromagnetic torque, reduce the motor torque, delaying the proce o motor tarting. From Fig.9 it can be een direct torque control in permanent magnet tator lux linkage locu can till control a tandard circular, the table amplitude to a given value.7wb, the illutrate alient pole eect i conidered not to the permanent magnet tator lux control eect. Fig.1 or motor tarting proce o power angle curve, a hown in the igure, the motor power angle in the motor tarting phae change i larger, the change trend and total torque o motor, electromagnetic torque and reluctance torque variation trend conitent, motor tarting moment, angle to nearly DEG peak, motor peed ater a mooth power angle tability in the vicinity o 15 degree. n (r/min) 1 1 8 6 Rotate peed n -.5.1.15..5..5..5.5 Fig.5 Speed o permanent magnet ynchronou motor n Te/ N.m 6 5 1 The total torque motor Te -1.5.1.15..5..5..5.5 Fig.6 Total torque o permanent magnet Te 5
8: (16) Journal o Modeling and Optimization Tez/ N.m Tem/ N.m 7 6 5 1-1 Electromagnetic Tem Tem -.5.1.15..5..5..5.5 Fig.7 Electromagnetic torque o permanent magnet Reluctance torque Tez.. -. -. -.6 -.8-1 -1..5.1.15..5..5..5.5 Fig.8 Reluctance torque o permanent magnet Tez Y Axi.5 X Y Plot -.5 -.5.5 X Axi Fig.9 Stator lux track o permanent magnet δ/ 5 5 15 1 5 Angle valueδ.5.1.15..5..5..5.5 Fig.1 The power angle o permanent magnet δ 6. Concluion In thi paper, in order to take into account the alient pole eect o the permanent magnet a reearch object to tudy the eect o alient pole eect mechanim o direct torque control o permanent magnet, through the theoretical analyi and the imulation reearch obtained concluion are a ollow: permanent magnet i running, the alient pole eect will produce contrary to the direction o the electromagnetic torque o the reluctance torque, and it ize and electromagnetic torque amplitude variation trend. The reluctance torque oet a portion o the electromagnetic torque, weakening the permanent magnet ' torque output capacity, how to control due to the eect o alient pole motor reluctance torque will be the next tep needed or key reearch problem. 7. Acknowledgment Thi work wa inancially upported by National Natural Science Foundation o China (615161). 8. Reerence [1 Liu Ying-pei, Li Ran. A enor-le operation optimization method [J. The Chinee Electrical Engineering Journal o permanent magnet direct torque control, 1, (): 568-577. [ Li Zheng, Hu Guang-da, Cui Jia-rui et al. Integral liding mode variable tructure control or permanent magnet peed regulating ytem [J. Proceeding o the Chinee ociety o electrical 6
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