EVS28 KINTEX, Korea, May 3-6, 215 Magnetic Saturation and Iron Loss Influence on Max Torque per Ampere Current Vector Variation of Synchronous Reluctance Machine Huai-Cong Liu 1, In-Gun Kim 1, Ju lee 1 Senior Member IEEE 1 Department of Electrical Engineering, Hanyang University Seoul, 133-791, Korea, liu1988@msn.com Abstract Synchronous Reluctance Motor (SynRM) has a simple structure with high efficient and without rotor conductor loss. Therefore, it is better than induction motor for electric vehicle (EV) on aspect of efficiency. SynRM usually operates on the constant torque region using maximum torque per ampere (MTPA) control which is adopted due to rotor structure limitation. Thus, the accurate current angle is crucial for motor control. However, finite element analysis (FEA) program is not sufficient exactly to regard how the iron loss and magnetic saturation influences on the current angle. Consequently, this paper proposed a method to calculate the current angle with consideration of iron loss. Keywords: iron loss, SynRM, current vector 1 Introduction Since the adoption of vector-controlled drives, SynRM can represent a viable alternative to other types of ac motors, such as induction motor (IM) or permanent magnet synchronous motors (PMSM). Which are widely used in electric traction due to its high power density and efficiency. Most IM and PM propelling the electric vehicle (EV).However, SynRM that can compete with the robustness and low price of the IM and at the same time has higher efficiency. In the SynRM the copper losses in the rotor are eliminated which corresponds to a reduction of the losses by up to 4 %.[1] PMSM is expensive for recent high price of neodymium (Nd), dysprosium (Dy), production of rare earth materials also brought serious pollution problems. Moreover, the performance of PMSM is sensitive to temperature rise. [2] SynRM requires no PMs that has simple and rugged construction. The distinct characteristic of a SynRM is its inductance saliency. Since the flux barriers inside the rotor at the q-axis and the d-axis inductance in the synchronous reference frame is conspicuously larger than the q-axis inductance. This difference between the d-axis and q-axis inductance contributes to the additional torque which is generated, called the reluctance torque. With a constant magnitude of currents, the torque of all synchronous motor can be generated differentially according to the angle of the stator current vector. Among the various current vectors that generate a specific torque, the current vector, which has a minimum magnitude of the current vector, that is called the maximum torque per ampere (MTPA) current. MTPA controller is parameter dependent and its performance relies on the knowledge of motor parameters. [3] The electromagnetic torque of the SynRM only generates a reluctance torque which can be calculated with d-q axis inductance in the rotor reference frame and the stator d-q axis current. If d-axis and q-axis inductance is constant that MTPA controller will be very simple. But in fact d-axis and q-axis inductance varies not only with the magnetic saturation but also SynRMs are EVS28 International Electric Vehicle Symposium and Exhibition 1
known to possess magnetic non-linearity and considerable iron loss, which make it difficult to realize MTPA control and maximum efficiency control. Therefore, this paper presents a method to calculate the transient characteristics of SynRM considering both core loss and magnetic saturation, which influence on inductance and current vector changed of MTPA control. It is using an equation for a circuit model with equivalent core loss The accuracy of the proposed method was verified under various operating conditions with computer simulation and testing with a 7.5 kw SynRM drive system. As an example, experimental results demonstrate the analysis is closer to the actual motor s characteristics. [4][5] 2 Determination of motor parameters In 29 the EU commission implemented a new directive called EN 634-3:29 which divides electrical rotating motors in classes depending on power output and efficiency. The different class ranges from IE1 which is standard efficiency to IE4 which is super premium efficiency for each efficiency class the losses are reduced by 2%, but selling rate increase of 3%. In Fig1. The different classes are illustrated for a 4-pole, 6 Hz motor. The directive from 29 states among other things that from 215 the lowest efficiency class manufactured in the European Union shall be IE3. [6] core can change various parameters of the motor. The rotor rib, shape and geometry, also including the barriers geometrical arrangement which are based on the previous work where several optimization methods are exercised to enhance the motor performance (torque density, spatial harmonics and torque ripple).[7] After optimization, the design parameters are obtained, as presented in Table 1. TABLE I Design parameters for SynRM Parameters Value Unit Dia. of stator 267 mm Dia. of rotor 168 mm Depth 2 mm Core material 5PN47 Air gap.5 mm Resistance of coil.4 Ω Rated Current 12.5 Arms Poles 4 Slots 36 In general, SynRM using current control expects its output and efficiency through analysis of ideal sinusoidal current sources. Analysis of the 7.5Kwclass SynRM. d-q axis inductances are variables due to the magnetic saturation. Therefore, this phenomenon has changed MTPA current angle from 45º to 6º. [7] 2.1 Magnetic saturation analysis Inductances are highly affected by the level of saturation in the SynRM due to high amount of core in both d and q-axis flux paths. Saturation, mainly in the machine d-axis, reduces Ld and consequently torque for a certain current, see point A in Fig. 2. By increasing the current angle (Δθ) the d-axis current is reduced to point B. Fig 1. IEC 634-3 efficiency standard for a 4-pole, 6 Hz motor. A 7.5kw IE4 class SynRM for test only sustained at synchronous speed is presented throughout this paper. First, the size of the machine is conducted and its performance is investigated including the flux density, self-and mutual-inductances, electrical torque and torque ripple by the finite element method in the software. In SynRM, the flux barriers in the rotor Fig2.Saturation compensation by current angle control EVS28 International Electric Vehicle Symposium and Exhibition 2
Therefore the level of saturation and air gap flux density are reduced also Ld and torque are increased and compensated. This also means, for example, inductances in d and q-axis are not only a function of stator current but also a function of the current vector. As a result current vector for different current loadings is shown in Fig.3. The simulation result shows that magnetizing characteristic of d-q axis in SynRM becomes noline when phase current was bigger than 5A. While rated current of the machine is 12.5A, MTPA operating point of rated current angle changed from 45deg to 6deg. V d R s id idm i dc Rm e q R s i i e d q qm L d (a)d-axis equivalent circuit (b) q-axis equivalent circuit Fig.4. Magnetization as a function of applied field In which Idm,iqm : currents of equivalent iron loss circuit in d-q axis Rs : Resistance of equivalent iron loss Ra: Resistance of phase coil Ld,Lq : inductances of equivalent iron loss circuit in d-q axis V q i qc Rm L q Fig3. As function of current vector and for different stator current, for the design geometry 2.2 Modeling of core loss resistance Core loss in a SynRM motor can be modeled with a resistance Rm, in order to derive motor equations based on the d-q axes equivalent circuit analysis (ECA) in Fig.4. Rm considered as iron loss is connected parallel with speed voltage. 2 2 2 2 2 3 V {( ) ( ) } s 3 ( ) 3 e Ld i e a dm Lqidm Rm (1) 2 Wc 2 Wc 2 Wc Where: Vs is induced electromotive force of each phase, ωe is electric angular velocity of SynRM and Wc is iron loss. SynRMs with equivalent iron loss resistance, which is originated from the equivalent coreloss, would be the basis on accurate torque estimation for MTPA control. The SynRM model with the iron loss circuit is depicted as Fig.5. Current idm and iqm is different from a terminal current id,iq. That means in theory, need to use idm and iqm to calculate mechanical torque and it is given in steady state by Eq(2),(3) Vd idm R Vdm Ld i s dm Rs 1 p (2) V q i qm R V qm L m q i qm Vdm L i q dm (3) V qm Ld i qm Fig.5. Current vector diagram of SynRM New current vector would be solved by means of trigonometric function with Eq.4 idm arctan (4) iqm A process is shown in Fig.6. In order to modeling equivalent circuit, all parameter can be gated from MTPA FEM analysis. Fig. 6.Current angle calculation process Idm and iqm influence on MTPA current vector variation of 7.5Kw SynRM is shown in Fig7. EVS28 International Electric Vehicle Symposium and Exhibition 3
Fig.7 Current angle shifts due to iron loss 3 Experiment The photographs of manufactured stator and rotor are shown in Fig.8. In order to measure the inductance of d,q axis which can explain the magnetic saturation of SynRM. An experimental test platform is built, as shown is Fig.9. (a) (b) Fig.9. DC standstill test platform [ V ( t) dt R i ( t) dt] D s a d( d) (5) ia L i [ V ( t) dt R i ( t) dt] D s a q( d) (6) i a L i Inductances of d-and q-axis according to own currents is shown in Fig.11 (a), (b). The magneto-motive force acting depended on the d-axis affects. Also the q-axis magnetomotive force can create flux and vice versa, i.e the flux generation processes in the d- and q- axis are not independent of each other. But, the FEM calculated effects of the self and the mutual inductance cross saturations are not considerate in this experiment. So that FEM result was same with experiment result at rated current point. (c) Fig.8. Photographs of the prototype machine. (a) The stator. (b) The rotor lamination. (c) Winding stator with housing. 3.1 Standstill tests The DC current decay tests consist of dc current attenuation from different initial values to zero, with the rotor at a certain position with respect to the axis of stator of phase A. Using the initial value theorem, the core loss is neglected in the test. The test configuration is shown is Fig.1.[8] (a) (b) Fig. 1. Conventional D.C. current decay test. (a) d-axis. (b) q-axis EVS28 International Electric Vehicle Symposium and Exhibition 4
(a) (b) Fig.11. Inductances of d and q-axis (a) Ld-id curve (b)lq-iq curve 3.2 Load test Fig.12 shows the experimental configuration includes target motor. Load tests were carried out and the result was shown in Table 2. Fig.12. Test setup for load test The experimental value of current angle is 58, and the simulation value is 57.6, which shows that these two values are relatively similar. However, 2D simulation cannot consider the harmonic wave of current source and leakage reactance of end turn. Therefore torque of ECA is bigger than experimental data. Table 2 Comparison of ECA and experimental ECA/ Experimental data Value Unit Current angle 57.6 / 58 deg. Torque 41.8/4.37 Nm 4 Conclusion This paper illustrated the influences of core loss for the current vector with consideration of ECA. Core loss is calculated at high speed when it becomes comparable to the copper loss. In the low frequency operation range the most dominant part of loss is the copper (Joule) loss. Even if using different models from the example above, there are no big differences. But when increasing the frequency, iron loss become comparable to copper loss. High iron loss rise up its percentage in the overall power which will change the core loss branch current more. On the other side, current vector shifts to higher values for the maximum torque mainly due to saturation effects. For a certain stator current, torque is proportional to the inductance, and the inductance reduced by the saturation mainly in the d-axis. In this situation, maximum torque factor (Ld-Lq)sin(2θ) must be maximized. By increasing the current angle to 6 deg. the effect of saturation on the d-axis inductance is reduced significantly. Considering of crore losses by ECA, the real current angle is 58 deg. ECA method calculated the transient characteristics of SynRM considering both iron loss and magnetic saturation influenced on current angle of MTPA control. Experimental results demonstrate the analysis is closer to the actual motor s characteristics. References [1] ABB, IE4 synchronous reluctance motor and drive package Optimized cost of ownership for pump and fan applications (212). [2] Z. Q. Zhu and D. Howe, Electrical machines and drives for electric,hybrid, and fuel cell vehicles, Proc. IEEE, vol. 95, no. 4, pp. 746 765,Apr. 27. [3] Seung-Ki Sul Electric Machines Control Theo-ry PP32-34 [4] L. Xu, X. Xu, T. A. Lipo, and D. W. Novotny, Vector control of a synchronous reluctance motor including saturation and iron loss, IEEE Trans. Ind. Appl., vol. 27, pp. 977 985, Sep./Oct. 1991. [5] Sungmin Kim,, Young-Doo Yoon,, Seung-Ki Sul, and Kozo Ide Maximum Torque per Ampere (MTPA) Control of an IPM Machine Based on Signal Injection Considering Inductance Saturation IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 213 PP 488-497 [6] The Commission of the European Communities, Commission regulation (EC) No 64/29 (July 29). EVS28 International Electric Vehicle Symposium and Exhibition 5
[7] Nicola Bianchi, Silverio Bolognani, Diego Bon, and Michele Dai Pré, "Rotor Flux-Barrier Design for Torque Ripple Reduction in Synchronous Reluctance and PM-Assisted Synchronous Reluctance Motors. IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 3, PP 921-928.MAY/JUNE 29 [8] I. Boldea, Reluctance Synchronous Machines and Drives. Oxford,NY: Oxford University Press, 1996. Acknowledgments This work was supported by the National Research Foundation of Korea grant funded by the Korean government under Grant 213R1A2A1A115171. And Hyosung power & industrial system performance group. Authors Huai-Cong Liu received B.S degree in electrical engineering from ChunNam University. Since 212, He has been pursuing the master-doctor combind program in the Department of electrical engineering, Hanyang University. His research interests are design, analysis and control of motor/generators; power conversion systems. In-Gun Kim received B.S degree in electrical engineering from Incheon University. He received M.S degree in electrical engineering from Hanyang University. Since 213, He has been pursuing the Ph.D. degree in the Department of electrical engineering, Hanyang University. His research interests are design, analysis and control of motor/generators; power conversion systems. Ju Lee received his M.S. degreefrom Hanyang University, Seoul,South Korea, in 1988, and his Ph.D.from Kyusyu University, Japan in 1997, both in Electrical Engineering, He joined Hanyang University in September,1997 and is currently a Professor of the Division of Electrical and Biomedical Engineering. His main research interests include electric machinery and its drives, electromagnetic field analysis, new transformation systems such as hybrid electric vehicles (HEV), and high-speed electric trains and standardization. He is a member of the IEEE Industry Applications Society, Magnetics Society, and Power Electronics Society. EVS28 International Electric Vehicle Symposium and Exhibition 6