Torque ripple has been a critical issue for high-performance applications using permanent magnet synchronous machines (PMSMs). An efficient approach to minimize torque ripple is to control the stator current to follow an optimized current reference, which will produce an extra torque ripple to cancel the existing one. This paper proposes a multiple reference frame (MRF) based controller for torque ripple minimization (TRM), in which the measured speed ripple is explored as the feedback control signal. The proposed MRF-based controller consists of a TRM controller whose task is to find the optimal current reference and a current controller whose task is to control the actual current to follow the optimized current reference. In TRM controller, the control of reference current magnitude and phase angle is decoupled, and proportional integral (PI) controller is able to achieve TRM control. In current controller, MRF is adopted to convert harmonic current control into dc current control; thus, PI controller is able to achieve harmonic current control with the use of MRF. Compared with existing approaches, the proposed controller is capable of TRM under both steady-state and transient conditions. The proposed controller is experimentally evaluated on a laboratory PMSM drive system.

Multiple Reference Frame Based Torque Ripple Minimization for PMSM Drive Under Both Steady-State and Transient Conditions

This paper proposes a new numerical formula and a design method to reduce the torque ripple while improving efficiency and the control performance of an interior permanent magnet synchronous motor In previous studies, the inverse cosine function (ICF) has been used for torque ripple reduction by making the air gap flux density distribution sinusoidal under a no-load condition However, in this paper, the advanced inverse cosine function (AICF) based on the ICF is proposed It determines an asymmetric rotor shape for rendering the air gap flux density distribution sinusoidal, considering a certain load condition In addition to the torque ripple reduction, lower peak values, the total harmonic distortion (THD) of the induced voltage, and a lower iron loss can be achieved by applying the AICF, compared to the other conventional methods The lower peak value and THD of the induced voltage are important because they affect the control performance of the motor The lower iron loss can also lead to a higher efficiency, particularly, in the high-speed region To verify the validity of the proposed design method, the characteristics of 8-pole, 12-slot motors that have different rotor shapes are analyzed using finite element analysis and experiments

Torque Ripple Reduction of IPMSM Applying Asymmetric Rotor Shape Under Certain Load Condition

Torque ripple has been a critical issue in permanent magnet synchronous machines (PMSMs). After PMSMs are designed, an efficient way for torque ripple minimization is to inject an optimized harmonic current into the machine to produce an additional torque ripple to cancel existing torque ripple resulted from the imperfection of machine design and manufacturing. This paper proposes a testing-based approach for optimal harmonic current design by using the speed harmonics. In particular, two testing solutions (TS), TS-A and TS-B, are proposed. In TS-A, two test signals are injected into the machine, and the optimal harmonic current is calculated from the test signals as well as the measured speed harmonics. In TS-B, two test signals are injected and adjusted to achieve the designed objective in terms of speed harmonics, and the optimal harmonic current is calculated from only the test signals. These two solutions can find the optimal harmonic current to minimize the torque ripple with minimal machine losses. Moreover, machine parameters are not required in the optimal harmonic current design, so the proposed solutions are not affected by the machine and drive nonlinearities. Compared with existing approaches, the proposed solutions have advantages in terms of computation efficiency and simple implementation. The proposed solutions are evaluated on a laboratory PMSM drive system.

Practical Testing Solutions to Optimal Stator Harmonic Current Design for PMSM Torque Ripple Minimization Using Speed Harmonics

This article proposes a modeling approach and an optimization strategy to exploit a third-harmonic current injection for the torque enhancement in multiphase isotropic permanent magnet synchronous machines with nonsinusoidal back electromotive forces. The modeling approach is based on a proper vector space decomposition and on the associated rotational transformation, aimed to properly select a set of stator current space vectors to be controlled. It is presented for a generic (i.e., asymmetrical, with an arbitrary angular shift) winding configuration. The injection strategy is related to the choice of a constant synchronous current set aimed at minimizing the average stator winding losses for a given reference torque by using the first and the third spatial harmonics of the air-gap flux density. The optimal solution has been found analytically and has been developed in detail for a selected set of asymmetrical winding configurations. Both the numerical and experimental results are in good agreement with the theoretical analysis.

/pdf/optimal-third-harmonic-current-injection-for-asymmetrical-34pasidko6.pdf

Optimal Third-Harmonic Current Injection for Asymmetrical Multiphase Permanent Magnet Synchronous Machines

This paper reveals a torque-angle approaching principle in a hybrid rotor permanent-magnet (HRPM) motor. The key is to obtain the relationship between angles of shifted surface-inserted PMs (SPMs) as well as assisted airspace barriers and the current angles of maximum PM torque as well as maximum reluctance torque. In order to find out this relationship, the PM torque and reluctance torque are separated accurately and effectively by the proposed torque separation method. In this method, the parameters in an abc reference frame are transformed to a d- - q reference frame via Park transformation, and then the model considering cross-coupling and magnetic saturation effect is used to calculate four torque components. Moreover, the shifting of SPMs has been confirmed to have both influence on the current angles of maximum PM torque and maximum reluctance torque, while the assisted airspace barriers only affect the current angle of maximum reluctance torque. Thus, the total torque can be enhanced by optimal angles of shifted SPMs and assisted airspace barriers because of higher utilization of both PM torque and reluctance torque. In order to evaluate the presented principle in the HRPM motor, a prototype is manufactured for experiments. Through theoretical analysis and experimental testing, it is verified that the proposed principle is feasible and effective.

Principle of Torque-Angle Approaching in a Hybrid Rotor Permanent-Magnet Motor

Harmonics can be injected into the permanent magnet (PM) shape to maximize the output torque in five-phase machines. The optimal harmonics of different orders for maximum torque is mathematically derived and validated by the finite element (FE) method in this paper. The output torque of the five-phase machine with sinusoidal shape can be improved by 12.5% by injecting the optimal third harmonic. Meanwhile, 3.2% further more torque improvement can be obtained with the optimal third and fifth harmonics injected. However, the output torque barely change with the seventh harmonic injection. The torque ripple of the machines with shaped PMs is much lower than the machines with conventional tile PM. The electromagnetic performance for all the machines including back electromotive force, average torque, torque ripple, etc., are compared. Finally, the five-phase machine with third and fifth harmonics injection into the rotors is prototyped to verify the analytical and FE analyses.

Optimum Injected Harmonics Into Magnet Shape in Multiphase Surface-Mounted PM Machine for Maximum Output Torque

This paper investigates the interaction of the zero sequence component into both permanent magnet (PM) shape and phase current to improve the output torque in dual three-phase surface-mounted PM (SPM) machines. The optimal zero sequence components are analytically derived and validated by finite element (FE) analyses. It is found that the optimal zero sequence components into both PM shape and current waveform are dependent on the fundamental and zero sequence harmonic winding factors. For the dual three-phase SPM machines having rotors without shaping, Sine shape, Sine shape with the zero sequence components, the electromagnetic performances including the back electromotive force (EMF) waveform, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque with the optimal zero sequence component in PM shaping and current waveform can be improved by >30% while the torque ripple remains similar to that of the one with Sine shaping. Finally, the experiments are given to verify both the analytical and FE analysis.

Z. Y. Gu

Papers

Optimum Injected Harmonics Into Magnet Shape in Multiphase Surface-Mounted PM Machine for Maximum Output Torque

Torque Improvement of Dual Three-Phase Permanent Magnet Machine Using Zero Sequence Components