Department of Electrical Engineering Southern Taiwan University Robot and Servo Drive Lab. 2015/5/19 Reduction of Torque Ripple Due to Demagnetization in PMSM Using Current Compensation Professor: 王明賢 Student: 方偉晋 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 20, NO. 3, JUNE 2010 Xi Xiao, Member, IEEE, and Changming Chen 1068~1071

Department of Electrical Engineering Southern Taiwan University Abstract Torque pulsations exist in permanent magnet synchronous motors (PMSMs) due to the nonsinusoidal flux density distribution around the air-gap. The torque pulsations vary periodically with rotor position and are reflected by speed ripple, which influence the PMSM drive performance. 2015/5/19 Robot and Servo Drive Lab. 2

Department of Electrical Engineering Southern Taiwan University Abstract To estimate flux magnitude, an extended Kalman filter is built by using the state variables, such as stator current and PM flux. With this extended Kalman filter method we can accurately track flux linkage. A current compensation method is proposed to reduce the negative influence caused by demagnetization. The compensated currents are derived from the estimated flux linkage. 2015/5/19 Robot and Servo Drive Lab. 3

Department of Electrical Engineering Southern Taiwan University Outline Introduction FLUX LINKAGE ESTIMATION METHOD ANALYSIS OF THE FLUX LINKAGE THE CURRENT COMPENSATION METHOD SIMULATIONS AND EXPERIMENTS CONCLUSION 2015/5/19 Robot and Servo Drive Lab. 4

Department of Electrical Engineering Southern Taiwan University 2015/5/19 Robot and Servo Drive Lab. 5 Introduction Permanent magnet synchronous motors (PMSMs) are increasingly being used in a variety of applications. Unlike electricity excitation synchronous machine, PMSM does not have excitation winding. This advantage eliminates the rotor copper losses due to the wear of the brushes. PMSM have some merit, such as high power density, high efficiency and high reliance and good dynamic performance.

Department of Electrical Engineering Southern Taiwan University 2015/5/19 Robot and Servo Drive Lab. 6 Introduction In many applications, such as the conveyor belt speed control, torque pulsations are highly undesirable and must be eliminated. Presence of these torque pulsations results in instantaneous torque that pulsates periodically with rotor position changing.

Department of Electrical Engineering Southern Taiwan University Introduction Broadly speaking, PMSMs’ implementation in industrial servo applications can be divided into two groups: one focuses on the improvement of the motor design and the other emphasizing the active control of the stator current compensation. 2015/5/19 Robot and Servo Drive Lab. 7

Department of Electrical Engineering Southern Taiwan University Introduction But the principal source of torque pulsation in PMSM is the harmonics presenting in the air-gap flux. Thereafter, the information on the rotor flux linkage is very important. The rotor flux linkage can vary in a wide range given specific operating conditions such as temperature rise or saturation. 2015/5/19 Robot and Servo Drive Lab. 8

Department of Electrical Engineering Southern Taiwan University Introduction We propose a method to measure the non-perfect sinusoidal flux density distribution in a PMSM. An extended Kalman filter (EKF) is used to observe the rotor flux. By choosing a new set of variables as the state variables, a four-order Kalman filter is constructed. 2015/5/19 Robot and Servo Drive Lab. 9

Department of Electrical Engineering Southern Taiwan University Introduction In this paper, a feedback current compensation controller is applied for reducing the torque ripple in high performance PMSM drives, in which the feedback compensation currents are derived by using the estimated flux linkage. 2015/5/19 Robot and Servo Drive Lab. 10

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD Motor Equations 2015/5/19 Robot and Servo Drive Lab. 11

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD 2015/5/19 Robot and Servo Drive Lab. 12

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD In order to observe the rotor flux linkage, the rotor flux linkage is chosen as a state variable. Because the rotor flux linkage can not change sharply, the derivative of the rotor flux linkage is zero. 2015/5/19 Robot and Servo Drive Lab. 13

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD Combine (2) with (3), the PMSM voltage equations and the flux linkage equations can be expressed in the rotor reference frames as the following equations. 2015/5/19 Robot and Servo Drive Lab. 14

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD The Modeling of the EKF 2015/5/19 Robot and Servo Drive Lab. 15

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD 2015/5/19 Robot and Servo Drive Lab. 16

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD The second step (innovation) corrects the predicted state estimation and its covariance matrix through a feedback correction scheme that takes the utility of the actual measured quantities. This is realized by the following recursive relations: 2015/5/19 Robot and Servo Drive Lab. 17

Department of Electrical Engineering Southern Taiwan University FLUX LINKAGE ESTIMATION METHOD where the filter gain matrix K and the transformation matrix H are defined by 2015/5/19 Robot and Servo Drive Lab. 18

Department of Electrical Engineering Southern Taiwan University ANALYSIS OF THE FLUX LINKAGE One of the essential sources of the torque pulsations in the PMSMs is harmonics present in the air-gap flux. In the PMSMs, practically used in industry, it is difficult to achieve a perfect sinusoidal flux density distribution around the air gap periphery. 2015/5/19 Robot and Servo Drive Lab. 19

Department of Electrical Engineering Southern Taiwan University ANALYSIS OF THE FLUX LINKAGE This “non-perfect” flux linkage connecting the permanent magnet and the stator currents contains the harmonics of the order of 5, 7, 11,…., in the a-b-c frame(triple harmonics are absent in Y-connected stator windings). 2015/5/19 Robot and Servo Drive Lab. 20

Department of Electrical Engineering Southern Taiwan University ANALYSIS OF THE FLUX LINKAGE 2015/5/19 Robot and Servo Drive Lab. 21

Department of Electrical Engineering Southern Taiwan University ANALYSIS OF THE FLUX LINKAGE 2015/5/19 Robot and Servo Drive Lab. 22

Department of Electrical Engineering Southern Taiwan University THE CURRENT COMPENSATION METHOD 2015/5/19 Robot and Servo Drive Lab. 23

Department of Electrical Engineering Southern Taiwan University THE CURRENT COMPENSATION METHOD 2015/5/19 Robot and Servo Drive Lab. 24

Department of Electrical Engineering Southern Taiwan University THE CURRENT COMPENSATION METHOD 2015/5/19 Robot and Servo Drive Lab. 25

Department of Electrical Engineering Southern Taiwan University THE CURRENT COMPENSATION METHOD 2015/5/19 Robot and Servo Drive Lab. 26

Department of Electrical Engineering Southern Taiwan University SIMULATIONS AND EXPERIMENTS 2015/5/19 Robot and Servo Drive Lab. 27

Department of Electrical Engineering Southern Taiwan University SIMULATIONS AND EXPERIMENTS 2015/5/19 Robot and Servo Drive Lab. 28

Department of Electrical Engineering Southern Taiwan University SIMULATIONS AND EXPERIMENTS 2015/5/19 Robot and Servo Drive Lab. 29

Department of Electrical Engineering Southern Taiwan University SIMULATIONS AND EXPERIMENTS 2015/5/19 Robot and Servo Drive Lab. 30

Department of Electrical Engineering Southern Taiwan University SIMULATIONS AND EXPERIMENTS 2015/5/19 Robot and Servo Drive Lab. 31

Department of Electrical Engineering Southern Taiwan University CONCLUSION Torque pulsations exist in PMSM due to nonsinusoidal flux density distribution around the air-gap. To deal with the problem, an instantaneous current compensation method was considered. The proposed method has been applied to reduce the torque ripple of synchronous reluctance with permanent magnet motor. 2015/5/19 Robot and Servo Drive Lab. 32

Department of Electrical Engineering Southern Taiwan University CONCLUSION A smooth torque production is seen in the simulation experimental result because of the current compensation. The proposed current compensation controller is shown to reduce the sixth and twelfth flux linkage harmonic significantly. Both the simulation and the experimental result confirmed the accuracy of the estimation algorithm. 2015/5/19 Robot and Servo Drive Lab. 33