The paper presents a method for calculating the back electromotive force and cogging torque waveforms of surface permanent-magnet motors using a model based on conformal mapping and magnetic equivalent circuits. The model takes into account the saturation of the iron core and its variation due to rotor movement. Because of the shorter execution time and achieved accuracy, it represents a good alternative to time-consuming finite-element-based models, especially in an initial stage of motor design. The proposed method has been implemented and evaluated on selected examples of 36-slot / 6-pole motors with different levels of saturation in teeth and stator yoke, and shows excellent agreement with the results obtained using finite-element method.

A Novel Method for No-Load Magnetic Field Analysis of Saturated Surface Permanent-Magnet Machines Using Conformal Mapping and Magnetic Equivalent Circuits

This paper presents feasible slot/pole number combinations of machines with two slot-pitches. They are becoming popular since they not only exhibit the low torque ripple but also the low harmonic content of the magnetomotive force. Some examples of such windings are reported in the literature, but they are limited to a specific slot/pole combination. On the contrary, a general theory is presented in this paper. The main rules for the design of such windings are illustrated and the relationship of slot (N
 s
) and pole (2p) number, and winding topologies for machines with two slot-pitches is derived. Then, the average torque, torque ripple, eddy current magnet loss, and saliency ratio of machines with slot/pole combinations N
 s
 = 2(2p ± 1) and N
 s
 = 2(2p ± 2) are investigated by the finite-element method and compared with the conventional one. The N
 s
 = 2(2p ± 1) machines have the high average torque and the low-torque ripple compared with N
 s
 = 2(2p ± 2) machines. In addition, the eddy current magnet losses for both machines are limited, and the saliency ratio of the interior permanent magnet (IPM) machine is improved compared with the conventional slot/pole number combinations. Finally, the experimental results on surface-mounted permanent magnet and IPM machines are given for validation of theoretical analyses and finite element (FE) results.

Synthesis of High Performance Fractional-Slot Permanent-Magnet Machines With Coil-Pitch of Two Slot-Pitches

The electrical machine (EM) is a key component in plug-in electric and hybrid vehicle (PEV) propulsion systems. It must be designed for high torque/power densities, wide speed range, over load capability, high efficiency at all speeds, low cost and weight, fast acceleration and deceleration, while meeting performance and reliability expectations. This paper overviews various EM technologies that are the best candidates for use in PEVs. Their basic operational characteristics, design features and relative advantages and disadvantages are discussed and compared for PEV propulsion systems. The latest and future research directions of EMs for PEVs are identified and discussed. Literature concerned with limitations and capabilities of finite element analysis and magnetic equivalent circuit analysis for EM design and analysis in PEVs is presented. Unfortunately, few papers give thorough comparisons between experimental measurements and simulation tools for EMs; even fewer compare torque. Those that report on torque show errors of 10% or more between tests and simulations. Saturation and losses appear to be the likely culprits. When nonlinear magnetic effects are taken into account, including magnetic saturation, eddy currents losses, and modeled with care, differences between simulations and tests typically are on the order of 5%.

Limitations/capabilities of electric machine technologies and modeling approaches for electric motor design and analysis in plug-in electric vehicle applications

In order to increase the torque density of the five-phase machines, the third harmonic is commonly employed. In this paper, the optimal and critical ratios for the third harmonic current injection are analytically derived and validated by finite element (FE) analyses. It is found that the optimal and critical injection ratios along with the torque improvement are dependent on the ratio of the third harmonic back electromotive force to the fundamental one. In order to improve the electromagnetic torque contributed by the third harmonic component, this paper employs unequal tooth to increase both the fundamental and third harmonic winding factors. Meanwhile, the optimal unequal tooth width combination is deduced and demonstrated by the FE method. When the third harmonic current is injected under the same amplitude constraint, the output torque can be improved. When the third harmonic current is injected under the same RMS value constraint, for the ten-slot/eight-pole equal tooth machine, the output torque can barely be increased, whilst for the unequal tooth machine, the output torque can be increased by 2.1%. Finally, the ten-slot/eight-pole machine with unequal teeth is prototyped and tested to prove the analyses.

Torque Improvement in Five-Phase Unequal Tooth SPM Machine by Injecting Third Harmonic Current

Owing to air-gap field harmonic, cogging torque, stator’s current time harmonic and the influence of flux saturation, a synchronous reluctance motor (SynRM) drive system has highly nonlinear uncertainties. Thus the linear control method for the SynRM drive system is difficult to achieved good performance under the nonlinear uncertainty action. To obtain better control performance the novel nonlinear backstepping control system using upper bound with switching function is firstly proposed for controlling the SynRM drive system to prevail the lumped uncertainty. With the proposed control system, the SynRM servo-drive system holds in robustness to uncertainties for the tracking of periodic reference trajectories. To enhance the robustness of the SynRM drive system, the novel nonlinear backstepping control system using adaptive law is proposed for estimating the required lumped uncertainty to reduce chattering phenomenon. When the inertia of the counterweight is varying, this proposed method can perform well in general situations, but cannot get a satisfactory performance. The novel nonlinear backstepping control system using reformed recurrent Hermite polynomial neural network with adaptive law and error estimated law is thus proposed to estimate the lumped uncertainty and compensate estimated error for obtaining better control performance. Furthermore, two varied learning rates of the reformed recurrent Hermite polynomial neural network is derived according to increment type Lyapunov function to speed-up parameter’s convergence. Finally, some experimental results with comparative control performances are demonstrated, and then the effectiveness of the proposed control system with better control performance is verified for the position tracking of periodic reference inputs with torque ripple consideration.

Novel Nonlinear Backstepping Control of Synchronous Reluctance Motor Drive System for Position Tracking of Periodic Reference Inputs with Torque Ripple Consideration

Purpose – The purpose of this paper is to reduce the torque ripple but not to decrease the average torque of synchronous reluctance machines by using one step or more than two axially laminated rotors with asymmetric flux-barrier. Design/methodology/approach – A 24-slot four-pole synchronous reluctance machine with overlapping windings and asymmetric flux-barrier in the rotor is, first, described and designed by finite element (FE) method for maximizing average torque. The dimensions of asymmetric flux-barrier including the pole span angle and flux-barrier angle will be optimized to minimize the torque ripple and its influence on the average torque is also investigated by FE analysis. The impact of current angle on the average torque and torque ripple are also analysed. The step laminations together with the asymmetric flux-barrier are employed for further torque ripple reduction which can consider the both rotation directions. Findings – The torque ripple of synchronous reluctance machine can be signific...

Torque ripple reduction of synchronous reluctance machines: using asymmetric flux-barrier

Purpose – The purpose of this paper is to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of synchronous reluctance machine with emphasis on output torque capability and torque ripple. Design/methodology/approach – AC synchronous reluctance machine (SynRM) or permanent magnet assisted SynRM presently receives a great deal of interest, since there is less or even no rare-earth permanent magnet in the rotor. Most of SynRM machines employ a stator that is originally designed for a standard squirrel cage induction motor for a similar output rating and application, or the SynRM machine with 24-slot, four-pole are often directly chosen for investigation in most of the available literature. Therefore, it is necessary to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of SynRM machine with emphasis on output torque capability and torque rippl...

Torque ripple reduction of synchronous reluctance machines : Optimal slot/pole and flux-barrier layer number combinations

This paper investigates the torque characteristics of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet (SPM) machine and presents its comparison with conventional 9-slot/10-pole and 12-slot/10-pole SPM machines by analytical and two-dimensional (2-D) finite element analysis (FEA). The winding factors of the 18-slot/10pole machine are firstly analyzed, and then, its back-EMF, average torque, cogging torque, and torque ripple are investigated. In addition, the influence of magnetic saturation due to stator current excitation on the average torque and torque ripple is also studied by 2-D FEA. The results show that the torque ripple can be suppressed while the average torque can be improved in the 18-slot/10-pole SPM machine compared with the 12-slot/10-pole SPM machine, while the unbalanced magnetic force in the 9-slot/10-pole SPM machine can be eliminated. Finally, the experimental results are given for validation of theoretical analyses and FE results.

Design and experimental verification of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet machine

This paper presents analytically derived optimal 3rd harmonic into phase current waveforms to improve the output torque of five phase surface-mounted PM (SPM) machines with the constraints of peak and rms values. The output torque with the 3rd harmonic current is analytically established and the optimal value of 3rd harmonic injected into the current waveform for maximum torque improvement is analytically derived and validated by finite element (FE) analyses. It is found that the optimal 3rd harmonic is dependent on the ratio of third harmonic back-EMF to the fundamental one but not 1/6 of the fundamental one as pulse width modulation in inverter. For the 10-slot/8-pole and 40-slot/8-pole five phase SPM machines having the same PM rotor, the electromagnetic performance including the back-EMF waveform, average torque, copper loss, and iron loss, are compared considering the 3rd harmonic current injection. The torque can be improved for both of the machines by injection third harmonic current under the peak current constraints, whilst only 40-slot/8-pole machine can have higher torque when 3rd harmonic current injection under the same rms value constraints.

S. Zhang

Papers

Torque ripple reduction of synchronous reluctance machines: using asymmetric flux-barrier

Torque ripple reduction of synchronous reluctance machines : Optimal slot/pole and flux-barrier layer number combinations

Design and experimental verification of an 18-slot/10-pole fractional-slot surface-mounted permanent-magnet machine

Analytical determination of 3rd order harmonic current into five phase PM machine for maximum torque