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永磁同步电动机直接转矩控制方法的比较研究


第 25 卷 第 16 期 2005 年 8 月 文章编号:0258-8013(2005)16-0141-06

中 国 电 机 工 程 学 报 Proceedings of the CSEE 中图分类号:TM351 文献标识码:A

Vol.25 No.16 Aug. 2005 2005 Chin.Soc.for Elec.Eng. 学科

分类号:47040

永磁同步电动机直接转矩控制方法的比较研究
史涔溦 1,邱建琪 1,金孟加 1,Friedrich W. Fuchs2
(1.浙江大学电气工程学院,浙江省 杭州市 310027; 2.Faculty of Engineering, Christian-Albrechts-University of Kiel, 24143 Kiel, Germany)

STUDY ON THE PERFORMANCE OF DIFFERENT DIRECT TORQUE CONTROL METHODS FOR PERMANENT MAGNET SYNCHRONOUS MACHINES
SHI Cen-wei1, QIU Jian-qi1, JIN Meng-jia1, Friedrich W. Fuchs2 (1. College of Electrical Engineering, Hangzhou 310027, Zhejiang University, China; 2. Faculty of Engineering, Christian-Albrechts-University of Kiel, 24143 Kiel, Germany)
ABSTRACT: A modified direct torque control strategy based on error flux linkage vector compensation (EFVC-DTC) for permanent magnet synchronous machines (PMSM) is presented. The theoretical background of EFVC-DTC is introduced and an algorithm to estimate the flux linkage error is proposed. The steady state and dynamic performances of EFVC-DTC have been compared with those of the conventional direct torque control (DTC). The simulation and experimental results confirm that both flux linkage and torque ripples are significantly reduced in EFVC-DTC with a fixed switching frequency while the dynamic torque response is almost as good as the basic DTC. KEY WORDS: Permanent magnet synchronous machine (PMSM); Direct torque control (DTC); Error flux linkage vector compensation; Space vector pulse-width-modulation (SVM) 摘要: 提出一种用于永磁同步电动机的基于磁链误差矢量补 偿的直接转矩控制(EFVC-DTC)策略,给出了磁链误差矢 量的估计算法, 并将该控制策略下的稳态和动态运行性能与 常规 DTC 进行比较. 仿真及实验结果表明 EFVC-DTC 可以 使电力开关器件工作在基本固定的频率上, 磁链和转矩脉动 显著减小,比常规 DTC 具有更优越的稳态性能, 而动态转矩 响应几乎与常规 DTC 相同. 关键词:永磁同步电机;直接转矩控制;磁链误差补偿;空 间矢量调制

1

INTRODUCTION

In recent years, with the development of PM material, ac drives using permanent magnet

synchronous machines (PMSM) have been applied in many fields where high performance and rapid torque response are required. Consequently many interests are focused on the study of the control strategies of PMSM[1-5]. It is well known that the most popular two control strategies are field oriented control (FOC) and the direct torque control (DTC), which have been invented in 1970's and 1980's respectively. Although both of them were firstly used with induction machines, they can also be well applied on PMSMs[6]. Former studies have shown that DTC has many advantages over FOC in the aspects of faster dynamic response, lower parameter dependence, simpler configuration due to the elimination of coordinate transformation and position sensors. But basic DTC strategies still have some drawbacks such as high sampling frequency, torque ripple and current distortion because of the variable switching frequency[7-8]. Many researchers have devoted to the improvement of the steady state performance of the basic DTC, especially for induction machine (IM) since the first industrial product has been produced in 1996 by ABB company[9-12]. In Reference[13], the technology of space vector pulse-width-modulation (SVM) used in IM DTC system with low torque and flux ripples was reported. Nowadays some of the approaches have been introduced into the DTC improvement for PMSM, which multiple voltage vectors are used and fixed switching frequency

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142

中 国 电 机 工 程 学 报

第 25 卷

operation are allowed so as to improve the torque ripple and current distortion, but generally they require more complicated modified control systems [14-15]. In this paper, the principle of EFVC-DTC is introduced and an algorithm to estimate the flux linkage error is proposed. The voltage vectors in EFVC-DTC are selected according to the flux linkage error, and by applying SVM strategy, the by applying SVM strategy, the EFVC-DTC system has a constant switching frequency so that the flux and torque ripple will be greatly reduced. These results can be achieved without increasing the complexity of the power circuit. The simulation and implementation studies are carried out with a 1.2kW prototype surface-mounted PMSM. The simulation and experimental results confirm that both flux linkage and torque ripples are significantly reduced in EFVC-DTC while the dynamic torque response is almost as good as the basic DTC.

where p is the number of pole pairs. isd, isq are d,q components of stator current, ψ sd, ψsq are d,q components of stator flux linkage. Substituting the flux linkages into the torque equation (1) yields 3 p 3 p Tem = ψ f ψ sq = ψ sψ f sin δ (2) 2 Ls 2 Ls where δ represents the load angle, shown in Fig.1. ψ sq sin δ = (3) ψs This torque equation is solvable in the stator flux xy-reference frame.

3 PRINCIPLES OF DIFFERENT DIRECT TORQUE CONTROL METHODS FOR PMSM
3.1 Basic direct torque control system It can be seen from equation (2) that if the modulus of the stator flux linkage ψ s is controlled constant, the torque can be controlled by changing the load angle δ or the angular velocity of ψ s relative to ψ f. The stator flux linkage vector can be expressed as ψ s = ( us Rs is )dt Neglecting the stator resistance Rs, ψ s can be directly expressed as the integral of the stator voltage vector. The control of δ under basic DTC is usually accomplished by changing the power switches according to the appropriate space voltage vectors, which are selected from a predefined optimal switching table. The selection of the voltage vectors is based on the synthesizing of the stator flux linkage position signal and the two hysteresis comparator output signals, which are generated by the errors between the reference and estimated value of the torque and flux linkage amplitude, respectively.The selected voltage vectors in each of the six sectors are shown in Fig.2 [3]. 3.2 Direct torque control system based on error flux linkage compensation Because the basic DTC system consists of two Bang-Bang controllers, this will unavoidably result in variable switching frequency and undesirable torque

2 MATHEMATIC MODEL OF SURFACE MOUNTED PMSM IN DIFFERENT REFERENCE FRAME
A simplified representation of a surface-mounted PMSM with the vector diagram in different coordinate system is shown in Fig.1.
y is q β



(4)

ψs δ θr ψf α d

x

图 1 隐极 PMSM 不同坐标系下的矢量图 Fig.1 Vector diagram in different reference frame of non-salient PMSM

For PMSMs with surface-mounted magnets, the rotor can be considered non-salient so that the armature inductance was one value Ld=Lq=Ls. With the rotor flux linkage ψ f lying on the d-axis, stator flux linkage and electromagnetic torque equations in the rotor dq-reference frame are given by ψ sd = Ls isd + ψ f (1) ψ sq = Ls isq T = 3/ 2 p(ψ i ψ i ) sd sq sq sd em

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第 16 期
(101) (011)

史涔溦等: 永磁同步电动机直接转矩控制方法的比较研究
(001) (100) (100) (011) (010) (001) (101) θ4 (010) (110) θ3 θ2 θ1 (010) (110) (001) (101) (110)

143

ψ s ,k +1 = ψ s, k +1 ψ s ,k +1 = ( ψ s,k +1 ψ s ,k +1 )
cosθ k ψ s,k +1 ωk Ts sin θ k +

j( ψ s,k +1 ψ s ,k +1 )sin θ k +
j ψ s,k +1 ω k Ts cosθ k

(9)

θ5 θ6 (101) (001) (100) (011) (100) (011) (010) (110)

The voltage space vectors are then determined by the following equation v s ,k +1Ts = ψ s ,k +1 + Rs Ts is ,k +1 (10) The selection rule of voltage vectors is shown in Fig.4, for example, if v s (= V e jθ s ) is between the
s

Fig.2

图 2 PMSM 常规 DTC 的开关表 Switching table for the basic DTC of PMSM

ripple. Fig.3 shows the EFVC-DTC system structure based on the concept of space vector pulse- widthmodulation (SVM). It employs a PI torque controller together with a reference algorithm block to get the stator flux linkage reference vector. Besides, a SVM block is introduced to generate the proper voltage vector, which is applied to the inverter to compensate the flux linkage vector error between the reference and the estimated values.The reference flux vector ψ s and the estimated flux vector ψ s can be expressed

adjoining basic vectors V1 and V2 over a time period of Ts, V1 and V2 will be selected to apply for intervals T1 and T2 respectively, and the null vectors V0 will be applied for the duration of T0.
V3(010) V2(110) Tsvs

T2V2 V4(011)

θs V1(100)

T1V1

V5(001)

V6(101)

in the stator flux system as follows ψ s = ψ s ∠θ = ψ s cos θ + j ψ s sinθ ψ s = ψ s ∠θ = ψ s cos θ + j ψ s sinθ
ψs* T* T RsTs i + ω* reference + algorithm ψ *
s

(5) (6)
PMSM N S

Fig.4

图 4 电压空间矢量调制 Voltage space vector modulation

SVM ψs Vα, Vβ iα, iβ

Inverter

The space vector vs can be expressed as 1 v s = [T1V1 + T2V2 + T0V0 ] Ts

(11)

∠ψ s

By solving for T1 ,T2 and T0 from equation (12), the desired space vector can be synthesized. 3 V2 = v s Ts sin θ s T2 2 1 T1 V1 = vs Ts cosθ s 2 T2 V2 Ts = T1 + T2 + T0

× 3/2

Vdc iabc θr

flux and torque estimator

(12)

图3

基于磁链误差矢量补偿的 PMSM DTC 系统结构 Fig.3 DTC system structure for PMSM based on error flux linkage vector compensation

where θ has to grow with the time as ψ s is rotating θ = θ + θ = θ + ω dt where ω* is the angular velocity of ψ s . Taking into consideration of the time discrete operation of the SVM, for the k+1 period θ k+1 = θ k + ω k Ts (8) where Ts represents the sample interval. So the flux linkage error vector comes to



(7)

where θs is the phase angle of vs. However, the maximum amplitude of vs should be limited to the circle shown in Fig.4 to prevent distortion in the resulting currents. By using more voltage vectors within a sampling interval, better steady state performance is expected in EFVC-DTC.

4 SIMULATION AND EXPERIMENTAL RESULTS
The PMSM parameters used in this paper are shown in Tab.1.

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144 表 1 永磁同步电动机参数 Tab.1 PMSM parameters
Parameters Rated output power/kW Rated line voltage/V Voltage constant/(V/rmin1) Number of pole pairs Maximum speed/(r/min) Stator resistance/ Stator inductance/mH Inertia/(kgm2)

中 国 电 机 工 程 学 报
20 10 Value I/A 1.2 220 156/2000 4 2000 0.095 3.1 0.00664 0

第 25 卷

10 20 2.08 2.09 t/s 2.10

(a)常规 DTC 下电流仿真波形(Ts=50s)

I/A

The simulation results of the steady state flux linkage and torque of the basic and EFVC-DTC at 2000 r/min with 6Nm load are compared in Fig.5, which shows that the ripples in both the flux linkage and the torque are greatly reduced in EFVC-DTC, even though the sampling frequency of the EFVC-DTC (10 kHz, shown in Fig.5(b)) is only one half of that of the basic DTC (20 kHz, shown in Fig.5(a)). The main reason is that the switching frequency of basic DTC is not constant, and the dominant switching frequency of it usually will be much lower than that of the EFVC-DTC at the same sampling frequency.
F/Wb 0.18 0.16 0.14 0.12 2.08 10 6 2 2.08 2.09 t/s (a)常规 DTC(Ts=50s) 2.10

5A/格

2.5ms/格

t/ms

(b)常规 DTC 下电流实测波形(Ts=50s) 20 10 I/A 0

10 20 2.08 2.09 t/s 2.10

(c)EFVC-DTC 下电流仿真波形(Ts=100s)

I/A

2.09 t/s

2.10

T/(Nm)

5A /格

2.5ms/格

t/ms

(d)EFVC-DTC 下电流实测波形(Ts=100s)

图6

F/Wb

0.18 0.16 0.14 0.12 2.08 10 6 2 2.08 2.09 t/s (b)EFVC-DTC(Ts=100s) 2.10

2000r/min, 6Nm 负载下的稳态电流仿真及实测波形 Fig.6 Simulation and experimental results of the steady state current at 2000 r/min with 6Nm load

r/min with 6 Nm load under the basic DTC and the EFVC-DTC, respectively. It can be seen obviously
2.09 t/s 2.10

T/(Nm)

that the current waveform of the basic DTC has significant distortion while that of the EFVC-DTC is much smoother and sinusoidal. The experimental current waveforms agree very well with the modeling results, which confirm that the steady state performance is greatly improved under EFVC-DTC. Although relatively better results will be expected by choosing higher mean switching frequency in basic DTC, the extremely high sampling frequency will lead to a high hardware requirement, which is not practical

图5

2000r/min, 6Nm 负载下的稳态磁链及转矩 Fig.5 Steady state flux and torque at 2000 r/min with 6Nm load

Fig.6 shows the simulation results as well as the experimental results of the steady state current at 2000

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史涔溦等: 永磁同步电动机直接转矩控制方法的比较研究

145

for implementation. The simulation and experimental results of the dynamic performances of two DTC methods are compared in Fig.7, with the reference torque is given as a step from–6 Nm to 6 Nm. Fig.7 shows that the torque under basic DTC will undulate within a band of the reference, while that under EFVC-DTC will settle down with the reference value after a short period of time. The simulation torque responses for the basic DTC and the EFVC-DTC in terms of the times for which the estimated electromagnetic torque to reach the reference value are about 0.3ms and
10 6 T/(Nm) 2 2 6 0.059 0.060 0.061 0.062 t/s (a)常规 DTC 下仿真动态转矩响应(Ts=50s) 10 0.058 Tref Test

0.5ms, respectively, while the corresponding measured response time are 0.4ms and 0.6ms, which nearly coincide with the simulation results. This confirms that the torque responses of the two systems are quite close except for a slight delay under EFVC-DTC due to the introduce of SVM unit.

5

CONCLUSION

T/(Nm) 4.3Nm/格

In this paper, an improved DTC method based on error flux linkage vector compensation for PMSM is proposed and comparative studies with the basic DTC are carried out on both the steady state and dynamic performance. The modeling and experimental results confirm that EFVC-DTC allows constant switching frequency which is usually higher than the dominant switching frequency of the basic DTC when the same power devices are used. Consequently, compared with that of basic DTC, the steady state performance of EFVC-DTC system has been greatly improved with less distortion in stator current as well as lower ripple in flux linkage and torque, whilst the chief advantages of the basic DTC such as high dynamic response and simple configuration of the power circuit are still retained.

0.5ms/格
10

REFERENCES
t/ms
[1] [2] Peter Vas.Vector control of ac machines[M].Oxford:Clarendon Press,1990. Mohan N.Advanced electric drives:analysis,control and modeling using simulink[M]. MNPERE, Minneapolis, Minnesota, USA, 2001. 万文斌,徐衍亮,唐任远.永磁同步电动机的高性能电流控制器 [J].中国电机工程学报,2000,20(12):24-27. Wan Wenbin, Yanliang, Xu Tang Renyuan. High performance current controller for permanent magnet synchronous motor[J].Proceedings of the CSEE,2000,20(12):24-27. [4] 王江,王家军,许镇林.基于逆变器死区特性的永磁同步电动机 系统的自适应变结构控制[J].中国电机工程学报,2001,21(8): 37-41. Wang Jiang,Wang Jiajun,Xu Zhenlin.Adaptive variable structure control of PMSM system based on inverter dead-time[J].Proceedings of the CSEE,2001,21(8):37-41. [5] 周扬忠,胡育文,田蕉.永磁同步电机控制系统中变比例系数转 矩调节器设计研究[J].中国电机工程学报,2004,24(9):204-208. Zhou Yangzhong, Yuwen, Hu Tian Jiao. Research of torque controller with variable proportion in permanent magnet synchronous motor drive[J].Proceedings of the CSEE,2004,24(9):204-208. [6] Takahashi I,Noguchi T.A new quick-response and high-efficiency control strategy of induction motor[J].IEEE Transactions on Industry Applications,1986,22(5):820-827.

(b)常规 DTC 实测动态转矩响应(Ts=50s)

6 T/(Nm) 2 2 6 0.020 0.021 0.022 t/s (c)EFVC-DTC 仿真动态转矩响应(Ts=100s) 10 0.018 0.019 Tref Test [3]

T/(Nm) 4.3Nm/格

1ms/格

t/ms

(d)EFVC-DTC 实测动态转矩响应(Ts=100s)

图 7 仿真及实测动态转矩响应 Fig.7 Simulation and experimental results of dynamic torque response

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146
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中 国 电 机 工 程 学 报
Zhong L, Rahman M F. Analysis of direct torque control in Permanent magnet synchronous motor drives[J].IEEE Transactions on Power Electronics,1997,12(3):528-535. CSEE,2004,24(7):210-214.

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[13] Lascu C,Boldea I,Blaabjerg F.A modified direct torque control for induction motor sensorless drive[J].IEEE Transactions on Industry Applications,2000,36(1):122-130. [14] Swierczynski D, Kazmierkowski M P, Blaabjerg. F. DSP based direct torque control of permanent magnet synchronous motor (PMSM) using space vector modulation (DTC-SVM)[C].Proceedings of the 2002 IEEE International Symposium,2002. [15] Tang Lixin,Zhong Limin,Rahman M F et al.A novel direct torque control for interior permanent-magnet synchronous machine drive with low ripple in torque and flux-a speed-sensorless approach [J].IEEE Transactions on Industry Applications,2003,39(6): 1748-1756. 收稿日期:2005-02-21. 作者简介: 史涔溦(1970-) ,女,博士,副教授,主要从事微特电机及其控 制技术方面的研究; 邱建琪(1974-) ,男,博士,讲师,主要从事微特电机及其控制 技术方面的研究; 金孟加(1980-) ,男,博士研究生,主要从事微特电机及其控制 技术方面的研究; F.W.Fuchs(1948-) ,男,博士,教授,主要从事电力电子及电气 传动技术方面的研究.

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