A Systematic Approach for Developing Electric Machine Windings with Suppressed MMF Space Harmonics

This paper studies the design of electric machine windings with reduced magnetomotive force (MMF) space harmonic content by adjusting the slot distribution and coil turns. Closed-form expressions for the winding factor and harmonic magnitudes established from a mathematical representation of winding functions are used to formulate the MMF space harmonic suppression problem. The framework is applicable to both distributed windings and fractional-slot concentrated windings (FSCWs) and can be solved with different techniques. No special requirements on the slot/pole combination and the number of layers are necessary. One example uses a linear algebraic technique to solve simultaneous equations and the result is a mixed-layer distributed winding. The process also reveals the criterion when multiple requirements on the winding factor and harmonic magnitudes can be satisfied concurrently. Contour plots are included to provide additional graphical insight. Another example designs a 24-slot 22-pole FSCW subset with numerical optimization. The resultant winding is a four-layer FSCW with two subsets and 3/4 of the harmonic orders are eliminated. The performance improvement of this winding is verified with finite-element simulations.

Research into electric machine windings with reduced magnetomotive force (MMF) space harmonic content has a long history. However, attention has often been confined to lower order harmonics with larger magnitudes. To more clearly and easily visualize the MMF space harmonic spectrum, this paper will explain the phenomenon of harmonic “families” intrinsic to a majority of electric machine windings. With a concise proof, it will be shown that within each family, the harmonic components have magnitudes that are inversely proportional to their orders. As a consequence, harmonics of the same family have the same winding factor. The number of families and, hence, different winding factors is found to be only a fraction of the number of slots of a unit machine. The family phenomenon greatly simplifies the determination of an MMF harmonic spectrum, envisions the behavior of higher order components, and predicts how a design change can improve the winding harmonic profile. When the family phenomenon disappears and the special cases with enlarged periods are also discussed. Two examples, both eliminating the 5th- and 7th-order harmonics but with very different harmonic spectra, are analyzed and compared to illustrate the power of the family phenomenon to aid the design of windings with improved electromagnetic performance.

Alternating current (ac) windings in electrical machines basically have a twofold purpose. In electrical generators ac windings are place where electromotive force (EMF) should be induced. In electrical motors, primarily ac windings goal is to produce rotating magneto-motive force (MMF) wave. In any case, ac windings should be designed in such a manner that induced EMF or generated rotating MMF wave consists predominantly of the fundamental sinusoidal component. Therefore, the starting point of an induction machine study is the analysis of MMF waves in the air gap of such machines. This assumes knowledge of winding distribution along the air gap from stator as well as from rotor side. The magnetic flux is analogous to the electric current. The MMF which sets up the magnetic flux is analogous to the EMF. The MMF is equivalent to a number of turns of wire carrying an electric current. If either the current through a coil (as in an electromagnet) or the number of turns of wire in the coil is increased, the MMF will be higher; and if the rest of the magnetic circuit remains the same, the magnetic flux increases proportionally [1]. At least two different approaches exist for describing winding distribution.

Modularity technique is desirable in large permanent magnet synchronous machines (PMSMs) because it facilitates manufacture, assembly, and maintenance. Although the PMSMs with fractional-slot concentrated windings (FSCWs) allow their stators to be modularized, they usually suffer from high nonworking space harmonic content. The PMSMs with various reported two-slot pitch windings (TSPWs) show much lower nonworking space harmonic content, but they do not support stator modularity. This paper proposes a modular PMSM with a special dual three-phase (DTP) TSPW, which exhibits quite low nonworking space harmonic content. First, the topology of the proposed machine is described in detail. Then, the mechanism of reducing the nonworking space harmonic content of the machine is expounded through winding magnetomotive force (MMF) analysis. Finally, the electromagnetic characteristics of a specific proposed modular PMSM and a conventional modular PMSM with DTP-FSCW are compared by finite element method (FEM), in terms of electromotive force (EMF), armature reaction field, torque performance, efficiency and power factor. The FEM results demonstrate that the proposed machine can realize low space harmonic content while retaining stator modularity.

Purpose The purpose of this paper is to investigate advantages of multiphase permanent magnet synchronous motors (PMSM) with fractional slot concentrated windings (FSCW). The investigation is based on comparative analysis and assessment of FSCW PMSM wound as 3, 6, 9 and 12 phase machines suited for low speed applications. Design/methodology/approach The investigations are focussed on distortions of back electromotive (emf) and magnetomotive force (mmf) with the torque ripples and motors’ performance taken into account. The finite element models with the aid of customized computer code have been adopted for motor winding design and back emf, mmf and motor performance analyses. Findings The novel multiphase winding layouts were found to offer lower content of sub-harmonics in the mmf waveforms compared with the traditional three-phase machine designs. Moreover, the investigated multiphase machines exhibited higher average value of the electromagnetic torque, while the multiphase PMSM machines with FSCW were further characterized by significantly lower torque pulsations. Originality/value The analyses presented in this paper demonstrate that PMSM with FSCW are advantageous to their counterpart three-phase machines. Specifically, they offer higher performance and are more suitable to work with multiple drives supplying segmented winding system. This ability of using multi-drive supply for one motor offers flexibility and cost reduction while increasing fault tolerant power train system.

PurposeThe purpose of this paper is to analyse and compare the functional parameters of three- and six-phase permanent magnet synchronous motors (PMSM) with fractional-slot concentrated windings (FSCW).Design/methodology/approachThe investigations are focused on the comparison of the distortions of back electromotive force (emf) and magnetomotive force (mmf) waveforms, as well as torque ripples, radial force spatial harmonics and motor performance studies. The finite element models of the test machine and a personally developed computer code have been used to calculate motor characteristics and analyse and synthesise multiphase winding layouts, respectively.FindingsCompared with the traditional three-phase PMSM designs, the proposed six-phase machines are characterized by a significantly lower content of sub-harmonics in mmf waveform distribution. Moreover, the investigated six-phase machines exhibited a higher average value of electromagnetic torque, significantly lower torque ripples and a reduced value of low-order harmonics of the radial component of the electromagnetic force in the air-gap of the machine.Originality/valueThe analyses presented in this paper show that six-phase PMSM with FSCWs are advantageous to their counterpart three-phase machines. Specifically, they are more suited to working with multiple drives supplying a segmented winding system while simultaneously offering higher performance. This suitability to the use of a multi-drive supply for one motor offers flexibility and cost reduction while increasing the fault tolerance of a power train system.

This paper proposes a novel winding layout for the electric machines with fractional‐slot concentrated windings (FSCW) using a stator shifting concept, with which all the non‐working harmonics can be completely cancelled or significantly reduced and the non‐overlapping winding can be kept. First, the basic winding layout with a 24‐slot 14‐pole machine to reduce the significant 1st sub‐harmonic will be presented for machines with single‐layer (SL) windings. From this, a novel double layer (DL) winding layout using the stator‐shifting concept will be introduced. By adopting two SL winding sets with a 105° mechanical angle shift with respect to each other, it is not necessary to use overlapping windings. With this configuration, the 1st sub‐harmonic will be completely cancelled and the parasitic 5th harmonic will be significantly reduced. Hence, the rotor losses, specifically magnet loss will be significantly reduced. Finally, two PM machines with different DL winding layout, namely, conventional 12‐slot 14‐pole and 24‐slot 14‐pole machine, will be designed and compared to validate the advantages of this winding topology.

The Fractional Slot Concentrated Winding (FSCW) configuration increases spatial harmonics of the magneto motive force (MMF) waveform of an electric machine. Therefore, saturation level in such machines is typically higher than that of the conventional machines with distributed windings. Since the characteristic of Interior Permanent Magnet (IPM) machine principally depends on inductances variation, this paper attempts to investigate the effect of saturation on the machine inductances in a FSCW IPM machine. Variations of apparent, incremental and cross-magnetization inductances were measured by flux-linkage calculation method and the dq-axis voltage equations were modified to take into account for these variations. The effect number of slot and pole combinations in the variations of the inductances was also investigated. Experimental test was carried out in a prototype machine to verify the finite element results.

Due to the high content of sub- and super- stator MMF components of Fractional-Slot Concentrated-Windings (FSCW) Permanent Magnet Machine, high eddy current losses will be induced inevitably. To diminish the eddy current losses, a simple multi-layer winding design method for FSCW is presented. The proposed method is derived from winding function, and both winding factor and loss factor are considered. Three different multi-layer windings are designed by the proposed method for an 18 slots-16 poles FSCW. Finite element analysis is employed to validate the proposed method.

Flux-switching permanent magnet machines (FSPMMs) with fractional-slot concentrated windings (FSCWs) are good candidates for electric vehicle applications due to their simple construction and strong robustness. Although the FSCW can reduce the end-winding overlap and deliver near-sinusoidal back-EMF, it contains a large amount of harmonics, so as to result in, more losses. In this paper, the effect of number of winding layer on key electromagnetic indexes of FSPMMs with FSCW is analyzed based on finite element analysis (FEA). Comprehensive simulations demonstrate that significant reduction can be got on torque ripple, total harmonic distortion (THD) of back-EMF and losses with higher number of winding layer.

I. IntroductionThere are many studies on axial flux permanent magnet machines (AFPMMs) due to their compactness [1]. The conventional AFPMMs comprise a stator and two rotors. In general, the stator with toroidal windings or overlapping windings is sandwiched between two rotors [2][3]. Toroidal windings have shorter ends than overlapping windings, which can reduce copper loss and ending effect. However, this structure also wastes the ends of windings, which means that the windings are not utilized sufficiently. To some extent, it reduces the torque density of the machine.This paper proposes a novel axial-radial flux permanent magnet machine (ARFPMM) to solve the problem. In the ARFPMM, the endings of windings are also used to produce torque with little increase of volume, which results in the improvement of torque density.II. Structure of ARFPMMThe proposed ARFPMM integrates both axial-flux and radial-flux machines in a compact space, which improves the torque density. As shown in Fig. 1(a), the ARFPMM is composed of one stator, two axial rotors and one radial rotor. Because the end of overlapping windings is useless, the machine adopts toroidal windings. Thus, the stator is equipped with opening slots on three faces. Permanent magnets are mounted on the surface of rotors. The radial rotor is fixed and aligned with two axial rotors, which can avoid the tilt of axial rotors and generation of harmonics in flux density per phase. The inner and outer diameters of permanent magnets on axial rotors are the same as those of stator. Similarly, the height of permanent magnets on radial rotor is equal to that of stator.In order to suppress air-gap flux density harmonics and get more sinusoidal waveform of air-gap flux [4], the permanent magnets are arranged as Halbach-array. It can also increase the flux density in the air gap. The magnetization direction of PMs is related to the number of segments per pole pair. As shown in Fig. 1(b), each pole pair is divided into six segments, so the magnetization direction of each segment varies 60° in turn.III. Design and AnalysisCompared with integer-slot concentrated windings, fractional-slot concentrated windings can enhance flux-weakening capability and reduce cogging torque [5]. Therefore, a 20 pole 24 slot fractional-slot concentrated-winding machine is chosen. In the case, the winding factor is 0.966. It is related to the no load back electromotive force (EMF) which can be calculated as equation (1). E0=4.44fkwNΦ10 (1)Where f is the electric frequency of the machine, kw is the winding factor, N is the number of coils per phase in series, Φ10 is the magnetic flux. In the ARFPMM, three rotors are used to increase the magnetic flux in air gap. The result of 3D FEA for back EMF is shown in Fig. 2(a). Fig. 2(b) is the fast Fourier transform of back EMF. It shows that the maximum harmonic is the third order harmonic, which can be neglected due to the star-connection of three phase windings.Because the magnetic flux in air gap is increased under the same operating state, the torque of ARFPMM is also increased. Fig. 2(c) shows the torque of the machine at rated conditions when the current is 7 A and rotor speed is 600 rpm. In the condition, the average torque is 41.63 Nm and the torque density is 28.58 Nm/L. The torque ripple is 3.4 Nm, 8.1% of the rated torque. As shown in Fig. 2(c), the peak-peak value of cogging torque is 3.26 Nm.IV. ConclusionThis paper proposes a novel ARFPMM with a unique structure of two axial rotors and one radial rotor, and implements its design and FEA. Due to the Halbach-array PMs, the main harmonics of back EMF is the third order harmonic, which is negligible when the windings are connected in star-connection. Compared with conventional AFPMM, the structure increases the torque through increasing the magnetic flux through windings per phase. Thus, the ARFPMM reaches an extremely high torque density of 28.58 Nm/L. On the other hand, fractional-slot concentrated winding configuration reduces the cogging torque, of which the peak-peak value is only 3.26 Nm.AcknowledgeThis work is supported in part by NSFC (52077186&51677159), in part by STIC of Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK. **

Interior PM machines equipped with fractional-slot concentrated-windings are good candidates for high-speed traction applications. This is mainly due to the higher power density and efficiency that can be achieved. The main challenge with this type of machines is the high rotor losses at high speeds/frequencies. This paper will thoroughly investigate the effect of number of winding layers on the performance of this type of machines. It will be shown that by going to higher number of layers, there can be significant improvement in efficiency especially at high speeds mainly due to the reduction of the winding factor/magnitude of the most dominant stator mmf subharmonic component. It will also be shown that there is significant improvement in torque density. Even though there is reduction in the winding factor of the stator synchronous torque-producing mmf component, this is more than offset by increase in machine saliency and reluctance torque. The paper will provide general guidelines regarding the optimum slot/pole/phase combinations based on torque density and efficiency. Sample designs of various slot/pole combinations are used to quantify the benefit of going to higher number of layers in terms of torque density, efficiency, and torque ripple.

This paper describes an original approach dealing with AC/DC winding design in electrical machines. A research software called “ANFRACTUS Tool 1.0”, allowing automatic generation of all windings in multi-phases electrical machines, has been developed using the matrix representation. Unlike existent methods, where the aim is to synthesize a winding with higher performances, the proposed method provides the opportunity to choose between all doable windings. The specificity of this approach is based on the fact that it take only the slots, phases and layers number as input parameters. The poles number is not requested to run the generation process. Windings generation by matrix representation may be applied for any number of slots, phases and layers. The software do not deal with the manner that coils are connected but just the emplacement of coils in each slot with its current sense. The waveform and the harmonic spectrum of the total magnetomotive force (MMF) are given as result.

Under the effects of alternating current (AC), the resistance and reactance of electric machine windings are different from their static state. As electric machine windings usually comprise many conductors, it makes the modeling and analysis very cumbersome using the finite element method. This paper presents an analytical method for computing AC resistance and reactance of electric machine windings placed in ferromagnetic slots, which is more convenient and efficient, and could be extended to the slots with different complex structures. First, the slot is divided into a number of layers based on the concept of discretization. Then, the magnetic field governing equation is established, and the distributions of magnetic field intensity and the current density of conductors under AC conditions are solved. By Poynting's theorem, the complex power flowing into the conductors is calculated, and then the effective resistance and reactance of the windings are obtained. Finally, the deduced analytical solutions are compared with the finite element method, and the results show that they have a good agreement for both single-layer winding and the double-layer windings with current phase difference. The presented analytical model is useful for understanding the AC effects and optimization of electric machine windings placed in ferromagnetic slots.

This paper presents the design of an interior permanent magnet synchronous motor (IPMSM) with fractional-slot concentrated winding (FSCW). The study determines the number of poles and slots considering the winding factor and unbalanced magnetic force. Conventional calculation method is used to obtain the initial dimensions and finite element analysis (FEA) is adopted to acquire the performance of the motor. The study optimizes the rotor structure, adjusting the eccentric length and the angle of pole shoe, so as to improve the torque quality. Finally, the finite element results verify the effectiveness of the optimization.