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简介:本文档为《A Decoupling Control Strategy of IPM Machine Accounting forpdf》,可适用于电子通讯领域,主题内容包含ADecouplingControlStrategyofIPMMachineAccountingforCompensationofCrosssatu符等。

A Decoupling Control Strategy of IPM Machine Accounting for Compensation of Cross-saturation Based on SVPWM Technique WANG Aimeng1, SHI Wenjuan2 School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei 071003, P. R. China 1. E-mail: aimeng668@yahoo.com 2. E-mail:ishiwenjuan@126.com Abstract: In this paper, the evaluation of magnetic saturation effects in an interior permanent magnet synchronous motor (IPMSM) over the entire operation range including constant torque region and in flux-weakening range is presented. The decoupling control model for IPMPM with magnetic saturation compensation based on SVPWM method is established. Upon the comparison the model with saturation compensation and ones without saturation compensation, the simulation results show that performance of the decoupling control system with saturation compensation is more stable and more accurate than that of without compensation in constant power region especially operating at a higher speed. And the decoupling control system with saturation compensation improves effectively the system following-up performance, robustness and the control accuracy. Keywords: Decoupling Control, Compensation of Magnetic Saturation, SVPWM, IPMSM 1 INTRODUCTION Interior permanent magnet (IPM) machine is mostly used in electric traction application because it can exhibit a high torque density and has a wide constant power region [1-3]. Since the effective air gap in the IPM motor is small, and the effects of magnetic saturation and cross-saturation are dominant, which influence its control performances [4]. Mostly previous work reported in the literature has focused on cross saturation model and saturation impacts on IPM machine drives [5-8]. Paper [9] reports a method of fully decoupling the problematic cross-coupling with estimated parameters from on-line self-tuning to improve the performance of the current regulator. In this paper, the purpose is to present an improved current control method for IPM machine accounting for magnetic saturation and cross coupling based on decoupling control method by using SVPWM technology. Since the inductances are function of d- and q-axes currents that vary with operating conditions due to magnetic saturation, the compensated value of inductance is used in the control algorithm. Several models of IPM machine drives are set up by using different parameters including liner and non liner magnetic cross-saturation inductance parameters in the machine in flux-weakening control. Through the comparison of different models verify the excellent performance of the control system with decoupling control and compensation of magnetic saturation. 2 THE MATHEMATIC MODEL AND CONTROL STRATEGIES OF IPMSM 2.1TheMathematic Model of IPMSM The machine model in the rotor reference frame is represented by ( ) ( ) ( ) d d d q q q q q d d f u R pL i L i u R pL i L i ω ω ψ = + = + + + (1) 3 ( ) 2e n f q d q d q T p i L L i iψ = + (2) Where id, iq are the d- and q-axes components of armature current , ud, uq are the d- and q-axes components of terminal voltage, Ψf are the permanent magnet flux linkage, Ld, Lq are the d- and q-axes stator inductances, pn is the number of pole pairs and p=d/dt. 2.2 Control Strategies of IPMSM In the constant torque region, the reluctance torque [the second term in (2)] developed by saliency is exploited through the maximum torque per ampere control strategy. The relationship between Id and Iq for the maximum torque per ampere control as followed: 2 2 2 2 2 2( ) 4( ) f f d q q d q d q a d i i L L L L i I i ψ ψ = + = (3) Due to current constraint, when Ia=Iam, the maximum torque is produced. The maximum torque per ampere control strategy is superior to the Id=0 control method, and converts smoothly flux-weakening control. In the constant power region, the current and voltage are limited by the inverter capacity, and the current and the voltage constraint are followed: 2 2 2 2 a d q am a d q am I I i I V u u V = + = + (4) In the flux-weakening constant power region, for the current vector is on the voltage limit ellipse in all operating region, the current vector track can be derived from Va=Vam: 2 2 2 1 ( )f amd q q d d Vi L i L L ψ ω = + (5) When Va=Vam, the current vector is controlled according for (5) in the steady state. Proceedings of the 29th Chinese Control Conference July 29-31, 2010, Beijing, China 1672 3 THE EFFECT AND COMPENSATION OF MAGNETIC SATURATION For IPM machine, due to the larger effective air-gap length on the d-axis, the variation of magnetizing reactance Ld depending on Id current is minimal. Since saturation in the d- axis results in a reduced d-axis inductance, the torque capability of the saturated motor in the constant torque range may be slightly increased due to the increase of the saliency ratio Lq/Ld. But the field-weakening performance is reduced due to a reduction of the d-axis inductance. The effective air-gap length on the q-axis is small and the magnetic saturation is dominant. The q-axis inductance varies depending on the q-axis current and as a result, the control performance is affected by magnetic saturation. The variation of the measured q- and d-axes inductance values versus the q- and d-axes current of IPM motor used for our experimental results are shown in Fig.1. In the low speed range, the obvious variation of Lq is caused by the larger Iq current due to the big torque. In the high speed range, the torque is small, i.e the Iq is relatively small, so the variation of Lq is minimal. Therefore the effects of magnetic saturation exist mainly in the low speed range. The q- and d-axes inductance values are respectively 0.47Hm and 0.2Hm in rated operation. The cross-coupling is presented mainly as the effect of a q-axis current on the back-emf or magnet flux, the back-emf reducing slightly with an increase of q-axis current due to the magnetic saturation on the d-axis. The torque and the terminal voltage reduce when the control system operate with maximum torque per amp control, as shown in fig.2. 0 10 20 30 40 50 60 70 80 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 Iq(A) Lq (H m ) (a) -80 -70 -60 -50 -40 -30 -20 -10 0 0.1 0.15 0.2 0.25 0.3 0.35 Id(A) Ld (H m ) (b) Fig.1 Variation of q- and d-axes inductance versus q- and d-axes current (a) q-axis inductance (b) d-axis inductance In flux-weakening range, the demagnetizing current Id is increase while Iq must be reduced, as a result Lq increase as shown in figure 1[10]. If the Lq is assumed to be a constant parameter, i.e the magnetic saturation is ignored, so the control performance become worse and the control system may be unstable. The figure.1 shows the relationship between Lq and Iq, Ld and Id, this information can be used to build a lookup table to compensate the effects of magnetic saturation. The compensation of magnetic saturation extend the speed range in flux-weakening region as shown in the fig.3 0 10 20 30 40 50 60 70 0 5 10 15 20 25 Is(A) Te (N . m ) with consideration of saturation without consideration of saturation (a) 0 10 20 30 40 50 60 70 107 108 109 110 111 112 113 114 115 Is(A) Te rm in a lv o lta ge (V ) with consideration of saturation without consideration of saturation (b) Fig. 2 Comparison of torque and terminal voltage vs .Is current with consideration and without ones at the condition of MTPA region. (a) Torque(b) Terminal voltage 0 1000 2000 3000 4000 5000 6000 7000 0 5 10 15 20 25 30 35 40 45 we(rpm) Te (N . m ) without compensation of saturation with compensation of saturation Fig.3 Torque versus speed with and without compensation of saturation 4 THE DECOUPLING ALGORITHM WITH COMPENSATION OFMAGNETIC SATURATION In the IPMSM vector control system, Id,Iq and Ud,Uq exist cross-coupling which is ignored to simplify the control strategy. But in the high-performance control system, this simplification will affect the integration of control performance. The d-and q-axes currents cannot be controlled independently by Ud and Uq, due to cross-coupling effects between d- and q-axes back-emf. In low-speed region, the influence of cross-coupling is small on the control system. However, the effect increases as the speed increases, especially in high-speed flux-weakening region, the current responses is affected by cross-coupling effect. The terminal voltage exceeds the limited value in this region, the same time, the current controller is saturated and the actual current cannot follow the commanded current. So the feedforward decoupling method is used to compensate the terminal 1673 voltage. Decoupling model is established through theoretical analysis. ( ) dec d e q q qec q e f d d u u L i u u L i ω ω ψ = = + + (6) In some cases, the decoupling control does not work perfectly when the motor current is increased. In order to find the causes of these problems, various parameters due to magnetic saturation are examined. The decoupling block with compensation of magnetic saturation is added to the speed control system. It eliminates interactions between d- and q- axes current control. The decoupling block is shown in fig 4. di qi qi di eω + + eω qi di Fig.4 Decoupling control model with parameters compensation 5 CONTROL SYSTEM OF IPMMOTORWITHPROPOSED STRATEGY AND SIMULATION RESULTS Fig.5 describes the variable-speed IPMSM Drive system on which the decoupling scheme is investigated. The parameters of IPM motor are listed in the Table1. ,d q ,α βq i di eT decu qecu uα uβ dqi eθ eθ eω di Fig.5 Control block diagram of the proposed decoupling control for IPMSM with compensation of magnetic saturation. Tab. 1 A 7.5kW IPM motor parameters Parameter Value Number of pole pairs Armature resistance Magnet flux-linkage D-axis inductance Q-axis inductance Maximum torque Output power Maximum speed 4 0.025Ω 0.062Wb 0.2mH 0.47mH 24Nm 7.5kW 6500rpm The decoupling control is equal to the compensation of terminal voltage and this effect is apparent, especially in high-speed range. The effects of proposed voltage command compensation in the flux-weakening range are shown in figure.6. Due to the current regulator saturation, the d- and q- axes currents controlled by conventional current regulator cannot follow the current commands. The responses time of current and the speed is reduced by the proposed voltage command compensation. The motor start quickly to the commanded speed by higher start torque, and the followed performance is ideal, no overshoot. When added the 5 Nm load at 0.15s, the speed reduce slightly and is recovered immediately. Then the control system step up from 4000rmp to 5000rpm at 0.2s and it with decoupling control reaches the commanded speed faster than ones without decoupling control. The d-and q-axes currents are unstable and recover faster than without decoupling control. The q-axes inductance varies depending on q-axis current, according to different operation mode (start motor, no-load operation, loaded operation, add speed with load), as shown in figure.7. The start torque is improved and the motor reaches quickly the commanded speed, i.e the dynamic performance is optimal. 6 CONCLUSIONS The simulation results indicate that the decoupling control method can effectively improve the system following-up performance, robustness and control accuracy. The decoupling control eliminates unstable transient responses due to saturation of current controller caused by the terminal voltage exceeding the limited voltage in high-speed flux- weakening range. The compensation of magnetic saturation extends the speed range in flux-weakening region. Therefore, it should find a wide application in the design of high- performance drive system for interior permanent magnet motor taking account for magnetic saturation. The system will be realized and the algorithm will be verified by DSP control system in the future work, and the decoupling control can eliminate cross-coupling effects, especially in high-speed flux-weakening region. 0.05 0.1 0.15 0.2 0.25 0.3 -10 0 10 20 30 40 50 t(s) Te (N . m ) w ithout decoupling compensation w ith decoupling compensation (a) 0 0.05 0.1 0.15 0.2 0.25 0.3 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 t(s) w e (rp m ) with decoupling compensation without decoupling compensation (b) 1674 0 0.05 0.1 0.15 0.2 0.25 0.3 -20 0 20 40 60 80 100 120 t(s) Iq (A ) without decoupling compensation with decoupling compensation (c) 0 0.05 0.1 0.15 0.2 0.25 0.3 -100 -50 0 t(s) Id (A ) without decoupling compensation with decoupling compensation (d) Fig.6 Step responses of speed and torque with and without decoupling compensation in flux-weakening range (w* 40005000rpm,Te05Nm) (a) Torque, (b) Speed, (c) Q-axis current , (d) D-axis current 0 0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 6 7 8 x 10-4 t(s) Ld ,L q(m H) Lq Ld Fig.7 Variation of Lq and Ld in different operation modes ACKNOWLEDGEMENTS The acknowledgement is for funding of study abroad scientific research foundation of North China Electric Power University. REFERENCES [1] B. Sneyers, D.W. Novotny, T.A Lipo, “Field-Weakening in Buried Permanent Magnet AC Motors Drives”, IEEE Trans. on Ind. Appl., 1985,21: 398-407. [2] T.M. Jahns, G.B. Kliman, T.W. Neumann, “Interior Permanent- Magnet Synchronous Motors for Adjustable-Speed Drives”, IEEE Trans. on Ind. Appl., 1986, 22: 738-747. [3] J-W Park, K-H Koo, J-M Kim, “Improvement of Control Characteristics of Interior Permanent Magnet Synchronous Motor for Electric Vehicle”, Rec. of Ind. Appl. Soc. Ann. Mtg, Rome, 2000: 1888-1895. [4] Shigeo Morimoto, Masayuki Sanada,and Yoji Takeda,“Effects and Compensation of Magnetic Saturation in Flux-Weakening Controlled Permanent Magnet Synchronous Motor Drives”, IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, 1994, 30(6): 1632-1637. [5] G. H. Kang, J. P. Hong, G. T. Kim, and J. W. Park,“Improved parameter modeling of interior permanent magnetsynchronous motor based on finite element analysis,” IEEETrans. Ma@., 2000, 36(4): 1867-1870. [6] Edward C. Lovelace, Thomas M. Jahns, Fellow, IEEE, and Jeffrey H. Lang “Impact of Saturation and Inverter Cost on Interior PM Synchronous Machine Drive Optimization”, IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, 2000, 36,(3): 723- 729. [7] Emil Levi, Member, IEEE, and Viktor A. Levi “Impact of Dynamic Cross-Saturation on Accuracy of Saturated Synchronous Machine Models” IEEE TRANSACTIONS ON ENERGY CONVERSION, 2000, 15(2): 224- 230. [8] Bojan Stumberger, Gorazd Stumberger, Drago Dolinar, Anton Hamler, and Mladen Trlep, “Evaluation of Saturation and Cross- Magnetization Effects in Interior Permanent-Magnet Synchronous Motor” , IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, 2003, 39(5): 1264-1271. [9] Hyunbae Kim and R.D. Lorenz, “Improved Current Regulators for IPM Machine Drives Using On-Line Parameter Estimation” IEEE Trans. Ind. Appl., 2000, 1:86-91. [10] Aimeng Wang and T.M.Jahns, “Accuracy Investigation of Closed-Form Prediction for the Operating Envelope Performance Characteristics of Interior PM Synchronous Machines” Proceeding of International Conference on Electrical Machines and System,2007:675-679. 1675

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