Harmonic Winding Factors Research Articles

Multiple Multiphase Combined Star–Polygon Winding Analysis

In order to improve the efficiency and to reduce the field amplitudes of spatial harmonics influencing noise and vibration of electrical machines, three- and five-phase combined star-polygon windings have been suggested in the literature. Besides, the efficiency of an electrical machine is dependent on the fundamental winding factor and the noise/vibration level is related to the winding factors of some higher/lower harmonics. However, there is no systematic method to calculate the winding factor of each spatial harmonic for a multiple topology. This paper deals with proposing different topologies of multiple series multiphase combined star-polygon windings and accordingly with the calculation methods of winding factors for all spatial harmonics and the harmonic leakage factor. The results of winding function approach and symmetrical components of electromotive forces (EMFs) are perfectly in compliance with each other, provided that the fast Fourier transform (FFT) analysis is sufficiently accurate. The results obtained from measurements on an unskewed electrically excited synchronous machine are applied for validating the results given by the sum of EMFs and the proposed calculation formula. The sum of EMFs, considering just one set of a multiple topology, can give the same results as the proposed winding analysis methods for the fundamental or the slot harmonic winding factors.

Effects of Harmonics Into Magnet Shape and Current of Dual Three-Phase Permanent Magnet Machine on Output Torque Capability

The harmonics can be utilized in the outer frame of a permanent magnet and phase current waveform in a multiphase machine to improve the output torque capability. The relationship between the output torque and harmonics in both the shape of the permanent magnet and phase current waveform is mathematically established in this paper. Consequently, the optimum harmonics are quantitatively identified and verified by the finite-element (FE) method. It is found that the incremental output torque decreases with the order of the harmonics. However, the output torque does not increase when the harmonic order is higher than seventh. It is also shown that the harmonics in the shape of the permanent magnet and phase current waveform influenced each other. The optimum of the interacted harmonics is dependent on the fundamental and harmonic winding factors. For the dual three-phase surface-mounted permanent magnet (SPM) machines with tile rotors, sinusoidal field rotor, and sinusoidal with third harmonic field rotor, their airgap flux density, back electromotive forces, and torque characteristics are compared. It is demonstrated that the average torque with the optimal harmonics into both the shape of the permanent magnet and phase current waveforms can be enhanced while the torque ripple remains similar to that of the one with the sinusoidal field rotor. Finally, the prototype machine is built and measured to verify the analytical and FE analysis.

Design and Analysis of a Five-Phase SPM Machine Considering Third Harmonic Current Injection

This paper analytically derives the optimal third harmonic current to improve the output torque in five-phase surface-mounted permanent magnet (SPM) machines under the constraints of the same peak/rms value. The relationship between the output torque and the third harmonic current is established and its optimal value for maximizing the output torque is derived. It is found that the optimal third harmonic current is dependent on the ratio of the third harmonic back electromotive force (EMF) to the fundamental one but it is not 1/6 of the fundamental one as pulse width modulation in an inverter. In order to improve the output torque by increasing the fundamental and third harmonic winding factors and the third harmonic airgap flux density, the unequal width tooth and permanent magnet (PM) segmentation are employed in the 10-slot/8-pole five-phase SPM machine. The optimal unequal tooth dimensions and the number of PM segmentations are analyzed for maximizing the output torque. The airgap flux density, back EMF, cogging torque, and output torque of the machine with equal/unequal tooth width and unsegmented/segmented PM are compared. Finally, the experiments on the prototype 10-slot/8-pole PM machine with unequal tooth width and segmented rotor are given to verify the analytical and finite element analyses.

Design of Optimal Winding Configurations for Symmetrical Multiphase Concentrated-Wound Surface-Mount PMSMs to Achieve Maximum Torque Density Under Current Harmonic Injection

Torque density of multiphase PMSMs can be enhanced by using current harmonic injection (CHI) techniques that utilize potential torque-producing nonfundamental spatial harmonics of the stator winding function (SWF) to produce an additional average torque. This possibility is ignored in the existing multiphase winding design methods that only aim at maximizing the fundamental spatial SWF harmonic, thus neglecting the remaining torque-producing spatial harmonics. These methods are also restricted by the number of machine phases. Motivated by these drawbacks in the existing methods, this paper proposes a novel heuristic algorithm for designing symmetrical multiphase concentrated windings with maximized average torque by considering all the nonfundamental torque-producing spatial SWF harmonics. The proposed approach is valid for any number of phases. Accordingly, an index is proposed to evaluate the multiphase winding performance in terms of its torque density under the CHI technique. The proposed method is formulated by using analytical treatment of the SWF, based on which, a systematic approach for calculating harmonic winding factors and evaluating the average torque is synthesized. The proposed approach is validated through case studies and experimental tests.

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

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.

Analysis of a Novel Linear Doubly Salient Slot Permanent Magnet Motor

A novel linear doubly salient slot permanent magnet motor (LDSSPMM) is proposed in this paper. First, the topology and geometric parameters of the LDSSPMM with 12 slots (12s) are proposed and the basic operating principle is investigated. By analyzing the feasible slot/pole combinations and harmonic winding factors, 11 poles and 13 poles (11p/13p) are proved to have higher winding factor for working harmonic. In addition, the LDSSPMMs with 12s/11p and 12s/13p are optimized by global optimization with genetic algorithm. It is shown that 12s/13p is the optimal slot/pole combination. Finally, the electromagnetic performance of the 12s/13p LDSSPMM is investigated by 2-D finite-element analysis (FEA) and validated by 3-D FEA.

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

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.

Harmonic Winding Factors and MMF Analysis for Five-phase Fractional-slot Concentrated Winding PMSM

To enhance torque density by harmonic current injection, optimal slot/pole combinations for five-phase permanent magnet synchronous motors (PMSM) with fractional-slot concentrated windings (FSCW) are chosen. The synchronous and the third harmonic winding factors are calculated for a series of slot/pole combinations. Two five-phase PMSM, with general FSCW (GFSCW) and modular stator FSCW (MFSCW), are analyzed and compared in detail, including the stator structures, star of slots diagrams, and MMF harmonic analysis based on the winding function theory. The analytical results are verified by finite element method, the torque characteristics and phase back-EMF are also taken into considerations. Results show that the MFSCW PMSM can produce higher average torque, while characterized by more MMF harmonic contents and larger ripple torque.

Design of phase-change 2-speed windings for induction motors, using pole-amplitude modulation techniques

Pole-amplitude/modulation is a well known technique for obtaining two speeds from an induction motor with a single stator winding. In PAM windings, pole changing is achieved by reversing coils. It has been shown that pole changing can also be achieved in a 3-phase motor by connecting coils to a different phase. Combining this principle with a technique devised for the design of PAM windings leads to the development of 2-speed windings with low harmonic content and high winding factors.

A.C. machine windings with reduced harmonic content

This paper describes a type of double-layer winding known as an interspersed winding, which may be used in a.c. machines to reduce harmonic components of induced e.m.f. or load m.m.f. The principles underlying the design of interspersed windings are described and compared with the standard analysis of conventional windings in terms of harmonic winding factors. Design and performance details are then given for a complete range of 3-phase interspersed windings covering equivalent values of slots/pole per phase from 4 to 9. It is shown that control of the largest low-order harmonics may be achieved with insignificant alteration to manufacturing methods, and this type of winding should therefore find useful application in large generators and motors where the reduction of stray load losses is an important consideration.