U d = Rid + pψ d − (ωe1 + ωe2 )ψ q (3) TABLE I. PARAMETERS OF SIMULATION MODEL U q = Riq + pψ q + (ωe1 + ωe2 )ψ d (4) Parameters VC and SVPWM R/Ω 2.875 Te = 1.5n p ψ d iq − ψ q id ( ) (5)Where ψd, ψq , U , Uq, id , id , Ld , Lq , R are the d, q axis flux Ld、Lq/H [8.5e-3, 8.5e-3] dlinkages, voltages, currents, effective inductances, resistance Ψr/Wb 0.175of the outer rotor respectively, ψ f is the flux linkage due to [0.8e-3,the inner rotor magnets, p is the differential operator, n p is the J1、J2/(kg.m2) 1.2 e-3]number of pole pairs, Te is the electromagnetic F1、F2/(N.m.s) [0.002,0.003]torque, ωe1 , ωe2 are the electrical angular velocity of the inner np 4and outer rotor respectively. Referring to the equation of mechanical motion of V. SIMULATION ANALYSISconventional PMSM, the mechanical motional equations of Configure the parameters such as starting time, simulationDRPMSM are time step, method, required error limit and so on. Then set ⎧ d 1 both model to start at 0s, end at 1.5s, and select Ode45 ⎪ dt ω1 = J (Te − F1ω1 − Tm1 ) variable step-size method. The given rotation speed is 450 ⎪ 1 (6) ⎨ rad/min during0~0.4s then 750 rad/min during 0.4s~1.5s, and d ⎪ ω = 1 (T − F2ω 2 − Tm 2 ) suddenly add a load of 1 N im at 0.5s. The given magnet flux ⎪ dt 2 J 2 e ⎩ linkage is 0.175Wb. On this basis, simulate and analyze theWhere J1 , J 2 , Tm1 , Tm 2 , F1 , F2 , ω1 and ω2 are the moment output characteristics of DRPMSM, and compare the rotationof inertia, load torque, damping coefficient and mechanical speed, torque and current response under VC and SVPWMangular speed of the inner and outer rotor respectively. mode, which are shown in Fig.4-Fig.5. w1, w2 in Fig.4 (a) and Fig.5 (a) shows the mechanical angular velocity of III. SIMULATION MODAL magnetic pole rotor and armature rotor relative to the motor Referring to PMSM motor model, combined with frame, respectively.DRPMSM mathematical model, we can establish a simulation 50model for the motor based on MATLAB, as shown in Fig 2, 45which consists of coordinate transformation module, electric 40 w2 w1 35module and mechanical module. peed(rad/s) 30 abc 25 dq0 vd ,vq id1 1 uabc 20 sin_cos S we iq1 dq0 abc _to_dq 0 abc 15 iq ,id s in_cos iabc 1 Transformation 10 0 dq 0_to_abc Transformation 5 sin 0 2 Tm 1 the 0 0.5 Time/s 1 1.5 cos Tm 1 iq we 2 (a) id w1,w2 15 w12 3 Tm 2 wm,the ,Te 3 Tm 2 wm the Te 10 mec Figure 2. Simulation model of DRPMSM 5 Te(N ) .m Fig.3 shows its mechanical submodel, which is based on(6). 0 -5 IV. SIMULATION Design Vector Control system and Space Vector PWM -10 0 0.5 Time/s 1 1.5Control system to verify the accuracy of the motor model， (b)where the parameters of the motor are shown in Tab.1. 15 1 Tm 1 1/J1 1/s 1/s p 1 10 F1 the C rren ) p 2 t(A 5 1 we u 2 1.5*p*(Flux * u(1)+(Ld -Lq )*u(1)*u(2)) 0 iq Mux 3 3 w1,w2 1 id -5 4 F2 -10 wm ,the ,Te 0 0.5 1 1.5 1/J2 1/s 1/s p Time/s (c) 4 Tm 2 Figure 3. Model of mechanical part Figure 4. Rotation speed (a), Torque (b) and Current (c) response under VC control 4205
50 45 current response, it can be concluded that DRPMSM has good 40 w1 performance the same as conventional PMSM in different control systems. w2 35 speed(rad/s) 30 VI. CHARACTERISTIC ANALYSIS OF DUAL-ROTOR 25 20 15 PERMANENT-MAGNET SYNCHRONOUS MOTOR 10 5 The simulation above is just to verify whether the model 0 0 0.5 1 1.5 is correct, rather than study the characteristics of DRPMSM, Time/s (a) which will be analyzed below. 10 Due to the electromagnetic torques are equal in size, from the mechanical motional equations of DRPMSM and (6), may 5 obtain d d Te(N.m) J1 ω1 − J 2 ω2 = ( F2ω2 + Tm2 ) − ( F1ω1 + Tm1 ) (7) dt dt 0 Assumed the rotating speed is steady, then F2ω2 + Tm 2 = F1ω1 + Tm1 (8) Since F1 and F2 are constant, when stably running, the -5 0 0.5 1 1.5 Time/s (b) relationship between load and rotating speed of the two rotors 10 is Tm1 − Tm 2 = F2ω2 − F1ω1 (9) 5 Then the relationship between speed of inner and outer rotors is Current(A) (T − T ) + F1ω1 0 ω2 = m1 m 2 (10) F2 -5 0 0.5 1 1.5 Analyzing and comparing the above formulas, we can see Time/s that the steady operation qualification and transient analysis (c) of inner and outer rotors of DRPMPSM is much different Figure 5. Rotation speed (a) , Torque (b) and Current (c) response under SVPWM control from conventional PMSM. For PMSM, there is only one Fig.4-5 show that the dual-rotor permanent-magnet mechanical motion equation, so the analysis of steady-statesynchronous motor can run steadily both in VC and SVPWM and transient operation is quite simple, relatively; but forstrategies, which proves that the simulation model is correct. DRPMSM, there are two equations of mechanical motion, Fig.4 (a) and Fig.5(a) show that the motor has a rapid with more parameters and identical electromagnetic torque.speed response both under VC and SVPWM control. With The rotating speed relationship of inner and outer rotor isanalyzing the smoothness of the curve, we can see the speed shown as (6)-(10), so the analysis of steady-state and transientresponse under VC is more stable and less pulsatile, while the operation is more complicated.overshoot under SVPWM control is smaller. Formula (10) shows that the rotating speed of inner and Fig.4 (b) and Fig.5 (b) show that the motor has rapid outer rotor may not be equal as the load torques and dampingtorque response both under VC and SVPWM control, both coefficient of two rotors are not the same. Assumed using thetorque is 0 when no-load running. However, torque response same parameters in Tab.1, we can observe the speed of innerunder SVPWM is more stable, less pulsatile, and its overshoot and outer rotor by merely changing the load, as shown inis smaller than VC. Especially at the starting and speeding Fig.4(a)-Fig.5(a), Fig.6 and Fig.7 (where the load ismoment, the impact of the motor torque under SVPWMcontrol is much smaller. Tm1=1 N im , Tm2=1 N im ; Tm1=1 N im , Tm2=1.1 N im ; Fig.4 (c) and Fig.5 (c) show that the current waveforms Tm1=1 N im , Tm2=1.2 N im , respectively). 70under both controls are fairly ideal when steady-state running. 60 w1 w2However, the impact of phase current is smaller under 50 pe( d ) s e d ra /sSVPWM control than VC at the starting and speeding 40moment. 30 When adding load suddenly, both current wave will be 20distorted, but soon stabilized again. 10 From the above simulation waveforms analysis it can be 0 0 0.5 1 1.5 2 2.5 3 Time/sobtained, the dual-rotor permanent magnet synchronous motor Figure 6. Rotating speed (Tm1=1 N im , Tm2=1.1 N im )model can be stable operating under VC and SVPWM control,which demonstrates that the model is correct. By comparingthe different control systems in motor speed, torque and 4206Authorized licensed use limited to: Amirkabir University of Technology. Downloaded on November 27,2010 at 09:28:16 UTC from IEEE Xplore. Restrictions apply.
90 80 w1 MATLAB/Simulink can easily conform to the mathematical 70 w2 model of conventional permanent magnet synchronous motor, it can also execute effective simulation on the motor’s p e (a / ) S e dr ds 60 dynamic and static performance. Through applying to vector 50 40 30 control and space vector PWM control, the model is verified 20 to be correct. 2) Vector control system decouples the motor torque 10 0 -10 0 0.5 1 1.5 2 2.5 3 and flux linkage to separate the control of motor flux and Time/s torque control by means of vector transformation, so that the Figure 7. Rotating speed (Tm1=1 N im , Tm2=1.2 N im ) motor has benefits as in direct current governor system. Space As the speed curve shown in Fig.4 and Fig.5, during vector PWM control system gives up the idea of decoupling0~0.5s, motor is running with no load, so the relationship of vector control. It directly uses the resulted voltage spacebetween the speed of two rotors is only related to damping vector PWM waveforms to control the inverter by orientingcoefficient, from (9) we obtain ω1 = 3 ; during 0.5s~1.5s, the the stator flux linkage, which makes the motor torque to ω2 2 respond quickly. These two kinds of control strategies can beload torques of inner and outer are equal, so their relationship applied to different application situation.of speed is only related to damping coefficient as well, which 3) Using MATLAB/Simulink toolbox to simulate andis also ω1 = 3 . analyze novel motor model or its control strategy, can greatly ω2 2 improve the developing efficiency, shorten the system In Fig.6, the situation is the same as above during 0~0.5s. developing time, and reduce developing costs.After 0.5s, the speed response of inner rotor is as slow as 4) By deducing the equation of mechanical motion forouter rotor, then achieve steady operation after 2.5s. The DRPMSM, we can obtain the relationship between speed ofrelationship between speed of two rotors can be obtained by two rotors when running in steady and transient state, which 2ω − 100 leads a further understanding of DRPMSM characteristics and(10), which is ω2 = 1 , when they are running in running state and paves way for its application and control of 3 wind power generation.steady state. The result of simulation indicates that when thespeed of inner and outer rotor differs too much, the REFERENCESmechanical shock will increase, which will do harm to the  Fengge Zhang, Nikolaus Neuberger, Eugen Nolle, Peter Gruenberger,motor and shorten its service life when running in this state and Fengxiang Wang, “A new type of induction machine with inner andfor long time. outer double rotors,” IEEE International Conference on Power In Fig.7, the situation is the same as above during 0~0.5s. Electronics and Motion Control, 2004(1), pp.286-289.After 0.5s, the speeds response of inner rotor is as slow as  Ronghai Qu and Thomas.A.Lipo, “Dual-rotor, radial-flux, toroidallyouter rotor, then achieves steady operation after 2.5s. The wound, permanent magnet machines,” IEEE Transactions on industryresult of simulation indicates that after 1.2s the two rotors applications, 2003(39), pp.1665-1673.rotate in the same direction. When running in steady state,  Federico Caricchi, Fabio Crescimbini and Ezio Santini, “Basic principle and design criteria of axial-flux permanent-magnet machines havingtheir relationship of speed can be obtained by (10), which is counterrotating rotors,” IEEE Transactions on Industry Applications, 2ω − 200 1995(30), pp.1062-1068.ω2 = 1 . 3  Hongling Zhao and Shuangqing Guo, “Wind power generator with double rotors rotating reversely,” Renewable Energy, 2005(3):36-38. In the analysis of simulation waveforms above, we canobtain: the response on rotating speed of inner and outer rotor  Yutao Luo, Peng Kuang and Yanwei Liu, “Drive characteristis of dontrarotating double rotors using on electric vehicles,” Journal ofis rapid, and the relationship between the speeds of two rotors South China University of Technology(Natural Science Edition),is only relative to damping coefficient. If the loads are 2008(36), pp.7-12.unequal, both rotors get slow response on speed, when  Shiqing Zhang, Jianqi Qiu, Junjie Chu and Ruiguang Lin, “Modelingrunning in steady state their speed is relative to load torque and simulation of dual-rotor BLDC motor,” Proceedings of the CSEE,and damping coefficient, and it’s likely to appear three kinds 2004(24), pp.176-181.of running states. As for a designed motor, damping  Yunxiang Xie and Zhuqiang Lu, “Simulation and modeling of directcoefficient is constant, so the torque of inner and outer rotor torque control of permanent-magnet synchronous motor based on MATLAB/Simulink,” Journal of South China University ofdetermines the speed of inner and outer rotor and running Technology(Natural Science Edition), 2004(1), pp.19-23.state of DRPMSM..  Xiuhe Wang, Permanent Magnet Motor, Beijing: China Electric Power Press, 2007. VII. CONCLUSIONS  Renyuan Tang, Modern Permanent Magnet Motor, Beijing: China 1) The simulation model we built for novel dual-rotor Machine Press, 1997.permanent-magnet synchronous motor based on 4207Authorized licensed use limited to: Amirkabir University of Technology. Downloaded on November 27,2010 at 09:28:16 UTC from IEEE Xplore. Restrictions apply.