Permanent magnet machine with multi-phase windings

Abstract

A permanent magnet machine is provided. The permanent magnet machine includes: a rotor including a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots. Each phase winding of the multi-phase windings comprises a plurality of coils. In particular, each pair of overlapping coils of different coil groups of the multi-phase windings are configured to have a same coil connection direction corresponding to a same current flow direction. In this regard, the above-mentioned each pair of overlapping coils overlap at least one stator slot of the plurality of stator slots. Furthermore, each coil of the plurality of coils of the above-mentioned each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil. There is also provided a corresponding method of configuring a permanent magnet machine, including configuring each pair of overlapping coils of different coil groups of the multi-phase windings to have a same coil connection direction corresponding to a same current flow direction. There is further provided a corresponding method of reconfiguring a permanent magnet machine, including: identifying each pair of overlapping coils of different coil groups of the multi-phase windings configured to have opposite coil connection directions corresponding to opposite current flow directions; and reconfiguring, for each identified pair of overlapping coils, one of the overlapping coils of the identified pair of overlapping coils such that the identified pair of overlapping coils have a same coil connection direction corresponding to a same current flow direction.

Description

PERMANENT MAGNET MACHINE WITH MULTI-PHASE WINDINGSCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of Singapore Patent Application No. 10202402834V filed on 12 September 2024, the content of which being hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] The present invention generally relates to a permanent magnet (PM) machine (c.g., a PM generator or a PM motor) with multi-phase windings, a corresponding method of configuring a PM machine with multi-phase windings, and a corresponding method of reconfiguring a PM machine with multi-phase windings.BACKGROUND

[0003] In the past several decades, direct-drive machines have undergone a renaissance to eliminate the mechanical issues associated with geared systems and achieve maintenance-free operation. Among the various types of electric machines or PM machines, for example, permanent magnet vernier machines (PMVMs) are attracting increasing attention in academia due to the distinguished torque capability and simple structure. The underlying reason for the high torque capability is attributed to field modulation, which suggests that the PMVMs can be perceived as an artful combination of a virtual gear and synchronous machine. Other types of PM machines include a permanent magnet synchronous machine (PMSM), such as a surfacemounted PMSM or an inset PMSM.

[0004] Referring to PMVMs as an illustrative example, despite the high output torque, the low power factor problem hinders the practical applications of PMVMs, leading to sharp increases in motor drive costs. To address this issue, various topologies have been investigated to enhance the PM magnetic fields. Specifically, Halbach array, V-type PMs, and U-type PMs have been adopted in PMVMs to exploit the flux-focusing effect and enhance the PM fields, thus improving the power factor. In addition, many new structures have been examined to enhance the magnetic circuit path for PM magnetic fields. Notably, the double-stator structure and the flux bridge can provide a magnetic circuit for low-pole-pair working fields, involve more PMs in contributing to the main flux, and improve power factor. On the other hand, additional research efforts have been dedicated to reducing non- working armature fields. It hasbeen reported that two-slot pitch winding (TSPW) can effectively suppress field harmonics and achieve a higher power factor. Besides, the optimal TSPW configuration has been investigated to further reduce armature harmonics and improve the power factor, hi addition, it has been disclosed that the magnetic circuits of sub-order non-working armature fields are interrupted by inserting flux barriers in the stator yoke, which contributes to improving the power factor. Moreover, the star-delta hybrid winding configuration has been investigated to reduce the nonworking inductance components and enhance the power factor. Furthermore, more endeavors have been focused on optimizing the air-gap field harmonics. In a prior work, the relationship between air-gap harmonics and power factor is established, and a coding shaped modulation tooth is specifically designed to eliminate the harmonics that adversely affect the power factor. In another prior work, the PM and armature fields arc collaboratively optimized to maximize the proportion of armature working harmonics and improve the power factor. It is noted that the majority of existing solutions are limited to a single operating point, while the analysis for improving power factor across the entire speed range is still literally absent.

[0005] Apart from the low power factor issue, another prohibiting problem of conventional PMVMs is their unsatisfactory performance during field-weakening operations due to the lack of reluctance torque. This limitation restricts their use in applications that require both low- speed crawling with high torque and highspeed cruising across a wide speed range, such as electric propulsion for electric vehicles, electric ships, and spindle drives. In conventional interior PM machines, the constant power speed range (CPSR) can be extended by exploiting reluctance torque under field-weakening operations. Numerous salient rotor structures including axially laminated designs, multilayer structure, and segmented PM have been reported to enhance the salicncy ratio and improve the field-weakening capability. However, these solutions are not feasible for PMVMs due to the negligible reluctance torque. Even when equipped with a salient rotor structure, PMVMs exhibit negligible reluctance torque because the rotor saliency in PMVMs is filtered out by the field modulation effect. The existing literature mainly focuses on improving the torque capacity and power factor of PMVMs during rated speed operation, with few efforts made to expand the operating range and field-weakening performance. In a prior work, DC excitation is employed in PMVMs to weaken the PM fields at high-speed operation. Nevertheless, the reduced slot area for AC armature windings results in impaired output torque, and the additional DC supply limits the practical applications. The pole-changing concept is introduced in PMVMs to expand the speed range, allowing the armature windings to be connected in two modes to couple with different pole-pair PM fields.However, this method intentionally introduces additional PM field harmonics, which induces high losses especially in high-speed operations, and the substantially increased complexity of power converter impedes its application in cost-sensitive scenarios. Based upon the above reasoning, there have been concerns regarding the field-weakening capability of PMVMs.

[0006] The armature winding configuration is typically designed by star of slots method (e.g., disclosed in N. Bianchi el al., “Design considerations for fractional- slot winding configurations of synchronous machines,” IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 997 - 1006, July / August 2006). To achieve the highest winding factor and symmetrical three-phase windings, the coils of each phase winding are distributed in a concentrated manner, with a 120° spatial interval among the three-phase windings. As a result, the phase mutual coupling of the conventional winding layout is typically negative (herein referred to as negative-mutual- coupling (NMC) winding). As will be illustrated later in the detailed description, NMC winding indicates that a positive phase current tends to produce negative flux linkage in the adjacent phase windings, which means that the <y-axis self- and mutual flux linkages are superimposed. This results in an increased terminal voltage, placing an extra burden on PMVMs and further deteriorating both the power factor and field-weakening performance.

[0007] A need therefore exists to provide a PM machine (e.g., a PM generator or a PM motor) with multi -phase windings, as well as a corresponding method of configuring or reconfiguring a PM machine with multi-phase windings, that seeks to overcome, or at least ameliorate, one or more deficiencies in conventional PM machines with multi-phase windings, and more particularly, having improved power factor and field-weakening performance. It is against this background that the present invention has been developed.SUMMARY

[0008] According to a first aspect of the present invention, there is provided a permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots, wherein each phase winding of the multi-phase windings comprises a plurality of coils, each pair of overlapping coils of different coil groups of the multi-phase windings are configured to have a same coil connection direction corresponding to a same current flowdirection, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots, and each coil of the plurality of coils of said each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

[0009] According to a second aspect of the present invention, a method of configuring a permanent magnet machine, the permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets; and a stator having a plurality of stator slots, the stator being arranged to house the rotor therein, the method comprising: installing multi-phase windings on the stator through the plurality of stator slots, wherein each phase winding of the multi-phase windings comprises a plurality of coils, said installing the multi-phase windings on the stator comprises configuring each pair of overlapping coils of different coil groups of the multi-phase windings to have a same coil connection direction corresponding to a same current flow direction, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots, and each coil of the plurality of coils of said each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

[0010] According to a third aspect of the present invention, a method of reconfiguring a permanent magnet machine, the permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots, wherein each phase winding of the multi-phase windings comprises a plurality of coils, and the method comprises: assigning each coil of the plurality of coils of said each phase winding to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil;identifying each pair of overlapping coils of different coil groups of the multiphase windings configured to have opposite coil connection directions corresponding to opposite current flow directions, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots; and reconfiguring, for each identified pair of overlapping coils, one of the overlapping coils of the identified pair of overlapping coils such that the identified pair of overlapping coils have a same coil connection direction corresponding to a same current flow direction.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments of the present invention will be better understood and readily apparent to one of ordinary skill in the art from the following written description, by way of example only, and in conjunction with the drawings, in which:FIGs. 1A to 1C depict schematic drawings of topologies (cross-sections) of permanent magnet (PM) machines configured as a permanent magnet vernier machine (PMVM), a surfacemounted permanent magnet synchronous machine (PMSM) and an inset PMSM, respectively, according to various embodiments of the present invention;FIG. 2 depicts a schematic diagram of a method of configuring a PM machine, according to various embodiments of the present invention;FIG. 3 depicts a schematic diagram of a method of reconfiguring a PM machine, according to various embodiments of the present invention;FIG. 4 depicts a schematic drawing of a topology (or cross section) of a PMVM with conventional negative mutual coupling (NMC) winding (which may herein be referred to as the conventional NMC PMVM);FIG. 5 shows a Table (Table I) presenting example main geometric parameters of the PMVM shown in FIG. 1 A with positive mutual coupling (PMC) winding according to various example embodiments of the present invention (which may herein be referred to as the PMC PMVM) and the conventional NMC PMVM;FIGs. 6A and 6B show a comparison of phasor diagrams under rated and fieldweakening conditions for the conventional NMC winding (FIG. 6A) and for the PMC winding (FIG. 6B);FIGs. 7 A and 7B depict star of slots phasor diagrams of the NMC PMVM (FIG. 7 A) and the PMC PMVM (FIG. 7B), respectively;FIGs. 8 A and 8B show Tables (Table II and Table III) presenting the detailed coil distributions of the conventional NMC winding (Table II) and the detailed coil distributions of the PMC winding (Table III), respectively;FIGs. 9A to 9C depict schematic drawings illustrating a method of converting NMC winding to PCM winding, according to various example embodiments of the present invention;FIGs. 10A and 10B show the on-load armature flux linkage with single-phase current injection for the conventional NMC PMVM (FIG. 10A) and the PMC PMVM (FIG. 10B), respectively;FIGs. 11A and 11B show a ratcd-load field distribution comparison between the conventional NMC PMVM (FIG. 11 A) and the PMC PMVM (FIG. 1 IB), respectively;FIGs. 12A and 12B show the output torque and synergistic on-load three-phase armature flux linkage for the conventional NMC PMVM (FIG. 12A) and the PMC PMVM (FIG. 12B), respectively;FIG. 13 depicts a Table (Table IV) presenting a summary of the analysis and comparison between the conventional NMC PMVM and the PMVM with the PMC winding;FIGs. 14A and 14B show the control strategy for maximum power under limited voltage and current for the conventional NMC winding (FIG. 14A) and the PMC winding (FIG. 14B), respectively;FIG. 15 shows a comparison of output torque and power factor between the conventional NMC PMVM and the PMC PMVM;FIG. 16 shows a comparison of d-axis and r / -axis currents between the conventional NMC PMVM and the PMC PMVM;FIG. 17 shows a comparison of output power capability and CPSR ratio between the conventional NMC PMVM and the PMC PMVM;FIG. 18 shows a comparison of the losses and efficiency between the conventional NMC PMVM and the PMC PMVM;FIG. 19 shows a Table (Table V) presenting the comprehensive loss and efficiency comparisons between the conventional NMC PMVM and the PMC PMVM;FIGs. 20A and 20B show a comparison of efficiency maps and torque-speed curves between the conventional NMC PMVM and the PMC PMVM;FIG. 21 depicts a Table (Table VI) presenting the detailed field-weakening performance comparison between the conventional NMC PMVM and the PMC PMVM;FIGs. 22A to 22D show an example stator and rotor lamination (FIG. 22A), an example stator (FIG. 22B), an example rotor (FIG. 22C), an example prototype (FIG. 22D) of the PMC PMVM, according to various embodiments of the present invention;FIG. 22E shows an example control system for the PMC PMVM, according to various embodiments of the present invention;FIG. 22F shows an example test rig for the PMC PMVM, according to various embodiments of the present invention;FIGs. 23A and 23B show simulation results and experimental waveform, respectively, for validation of the PMC winding;FIGs. 24A and 24B show the measured steady-state torque and current waveforms at 200 r / min and 600 r / min (10 Nm / div, 10 A / div), respectively;FIG. 25 shows the measured power factor at 200 r / min (50 V / div, 10 A / div);FIGs. 26A to 26D illustrate the validation of field-weakening performance for electromagnetic torque (FIG. 26A), output power (FIG. 26B), power factor (FIG. 26C) and efficiency (FIG. 26D);FIG. 27 depicts a schematic drawing of a topology (or cross section) of a surface PMSM with conventional NMC winding (which may herein be referred to as the conventional surface NMC PMSM);FIG. 28 shows a comparison of output torque and power factor between the surface PMC PMSM and the conventional surface NMC PMSM);FIG. 29 depicts a schematic drawing of a topology (or cross section) of an inset PMSM with the conventional NMC winding (which may herein be referred to as the conventional inset NMC PMSM); andFIG. 30 shows a comparison of output torque and power factor between the inset PMC PMSM and the conventional inset NMC PMSM.DETAILED DESCRIPTION

[0012] Various embodiments of the present invention provide a permanent magnet (PM) machine, such as a PM generator or a PM motor, with multi-phase windings, a corresponding method of configuring a PM machine with multi-phase windings, and a corresponding method of reconfiguring a PM machine with multi-phase windings. In various embodiments, the PM machine may be configured as a permanent magnet vernier machine (PMVM) or a permanentmagnet synchronous machine (PMSM). For example, the PMSM may be a surface-mountedPMSM or an inset PMSM. room As discussed in the background, in conventional PM machines (e.g., a PM generator or a PM motor) with multi-phase windings, conventional winding layout typically presents negative-mutual-coupling (NMC) among the multi-phase windings, such as NMC amongst three-phase windings due to the 120° spatial phase shift. In this regard, it will be illustrated later below according to various example embodiments of the present invention that in the conventional NMC winding, the negative phase-mutual inductance leads to increasing ( -axis inductance and amplifying armature reaction, which deteriorates both the power factor and field- weakening performance. In this regard, various embodiments of the present invention provide a PM machine with multi-phase windings, as well as a corresponding method of configuring or reconfiguring a PM machine with multi-phase windings, that seeks to overcome, or at least ameliorate, one or more deficiencies in conventional PM machines with multi-phase windings, and more particularly, having improved power factor and field-weakening performance.

[0014] FIG. 1A depicts a schematic drawing of a topology (cross-section) of a PM machine 100-1, according to various embodiments of the present invention. For illustration purpose, FIG. 1A depicts the PM machine 100-1 configured as a PMVM. However, it will be appreciated by a person skilled in the art that the present invention is not limited to a PM machine in the form of a PMVM and the PM machine may be configured as other types of PM machine, such as but not limited to, a PMSM. For illustration purpose, FIGs. IB and 1C depict schematic drawings of topologies (cross-sections) of a PM machine 100-2 configured as a surfacemounted PMSM and a PM machine 100-3 configured as an inset PMSM, respectively, according to various embodiments of the present invention. In addition, it will be appreciated by a person skilled in the art that the topologies of the PM machines 100-1, 100-2, 100-3 shown in FIGs. 1 A to 1 C are for illustration purpose and, for example, the number of stator slots at the stator 120-1, 120-2, 120-3 and the number of permanent magnets (PMs) 114-1, 114-2, 114-3 are not limited to that illustrated in FIGs. 1A to 1C.

[0015] In various embodiments, the PM machine 100-1, 100-2, 100-3 comprises: a rotor 110-1, 110-2, 110-3 comprising a plurality of permanent magnets 114-1, 114-2, 114-3; a stator 120-1, 120-2, 120-3 having a plurality of stator slots 124-1, 124-2, 124-3, the stator 120-1, 120- 2, 120-3 being arranged to house the rotor 110-1, 110-2, 110-3 therein; and multi-phase windings 130-1 , 130-2, 130-3 installed on the stator 120-1 , 120-2, 120-3 through the pluralityof stator slots 124-1, 124-2, 124-3. Each phase winding of the multi-phase windings 130-1, 130-2, 130-3 comprises a plurality of coils. In particular, each pair of overlapping coils of different coil groups of the multi-phase windings 130-1, 130-2, 130-3 are configured to have a same coil connection direction corresponding to a same current flow direction (e.g., a pair of overlapping coils having a same coil connection direction may be referred to exhibiting positive mutual coupling (PMC), and thus may be referred to as PMC winding). In this regard, the above-mentioned each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots 124-1, 124-2, 124-3. Furthermore, each coil of the plurality of coils of the above- mentioned each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

[0016] Accordingly, the multi-phase windings 130-1, 130-2, 130-3 of the PM machine 100- 1, 100-2, 100-3 according to various embodiments of the present invention are advantageously configured to exhibit positive mutual coupling (PMC), which has been found to improve power factor and field-weakening performance. In particular, the PMC winding according to various embodiments of the present invention exhibits positive phase-mutual inductance, cancellation effect on the -axis flux linkage, and brings the characteristic current closer to the current limit. That is, the PMC winding exhibits counteracted effect between r / -axis self-flux linkage and phase-mutual flux linkage, leading to reduced t / -axis inductance and facilitating the approach of the characteristic current to the current limit. This contributes to suppressing armature reaction, improving the power factor, reducing the terminal voltage, and enhancing the fieldweakening performance. These advantages or technical effects, and / or other advantages or technical effects, will become more apparent to a person skilled in the art as the PM machine 100-1, 100-2, 100-3, as well as the corresponding method of configuring a PM machine with multi-phase windings (to exhibit PMC) and the corresponding method of reconfiguring a PM machine with multi-phase windings (to exhibit PMC), is described in more detail according to various embodiments and example embodiments of the present invention.

[0017] For illustration purpose and without limitation, in FIGs. 1A to 1C, each coil is labelled by a letter and a number shown at a periphery of the stator 120-1, 120-2, 120-3 over a middle of the corresponding coil. The letter (e.g., ‘A’, ‘B’, ‘C’) indicates a phase of the coil (e.g., phase ‘A’, phase ‘B’ or phase ‘C’) and the number indicates a coil number of the coil of a phase winding. As an illustrative example and without limitation, in the case of a phase winding comprising four coils, these four coils may be labelled by coil numbers ‘ 1’, ‘2’, ‘3’ and ‘4’, respectively. Accordingly, as can be seen in FIGs. 1 A to 1C, each pair of overlappingcoils of different coil groups of the multi-phase windings 130-1, 130-2, 130-3 are configured to have a same coil connection direction, corresponding to a same current flow direction, to exhibit PMC. For example, the pair of overlapping coils Al and C3 are of different coil groups and are configured to have a same coil connection direction to exhibit PMC.

[0018] In various embodiments, the multi-phase windings 130-1 , 130-2, 130-3 are configured on the stator 120-1, 120-2, 120-3 through the plurality of stator slots 124-1, 124-2, 124-3 with a regular spatial interval among the multi-phase windings 130-1, 130-2, 130-3 to form symmetrical multi-phase windings.

[0019] In various embodiments, the multi-phase windings 130-1, 130-2, 130-3 arc three- phase windings and the above-mentioned each coil of the plurality of coils belongs to one of two different coil groups based on the phase angle of the magnetomotive force associated with the coil.

[0020] In various embodiments, the PM machine 100-1 is configured as a PMVM. In this regard, the rotor 110-1, the stator 120-1 and the multi-phase windings 130-1 are configured such that the number of stator slots 124-1 at the stator 120-1 is equal to a sum of the number of PM rotor pole pairs and the number of armature pole pairs of the PM machine 100-1.

[0021] In various embodiments, the PM machine 100-2, 100-3 is configured as a PMSM. In this regard, the rotor 110-2, 110-3, the stator 120-2, 120-3 and the multi-phase windings 130- 2, 130-3 are configured such that the number of PM rotor pole pairs is equal to the number of armature pole pairs of the PM machine 100-2, 100-3.

[0022] In various embodiments, the PM machine 100-1, 100-2, 100-3 is a PM generator or a PM motor.

[0023] FIG. 2 depicts a schematic diagram of a method 200 of configuring a PM machine, according to various embodiments of the present invention. The PM machine comprises: a rotor comprising a plurality of permanent magnets; and a stator having a plurality of stator slots, the stator being arranged to house the rotor therein. As described hereinbefore, the PM machine may be any type or form of PM machine as desired or as appropriate as long as the PM machine has multi-phase windings installed on the stator, such as but not limited to PMVM or PMSM (e.g., a surface-mounted PMSM or an inset PMSM). Accordingly, in various embodiments, the method 200 may correspond to configuring any one of the above-mentioned PM machines 100- 1, 100-2, 100-3 with multi-phase windings as described hereinbefore with reference to FIGs. 1 A to 1C, according to various embodiments of the present invention.

[0024] In various embodiments, the method 200 comprises: installing (at 202) multi-phase windings 130-1, 130-2, 130-3 on the stator 120-1, 120-2, 120-3 through the plurality of stator slots 124-1, 124-2, 124-3. Each phase winding of the multi-phase windings 130-1, 130-2, 130- 3 comprises a plurality of coils. In particular, the above-mentioned installing (at 202) the multiphase windings 130-1 , 130-2, 130-3 on the stator 120-1 , 120-2, 120-3 comprises configuring each pair of overlapping coils of different coil groups of the multi-phase windings 130-1, 130- 2, 130-3 to have a same coil connection direction corresponding to a same current flow direction. In this regard, the above-mentioned each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots 124-1, 124-2, 124-3. Furthermore, each coil of the plurality of coils of the above-mentioned each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

[0025] In various embodiments, the method 200 is for configuring any one of the above- mentioned PM machines 100-1, 100-2, 100-3 as described hereinbefore with reference to FIGs. 1A to 1C, according to various embodiments of the present invention, therefore, step(s) or operation(s) of the method 200 may correspond to forming, providing or configuring various components, parts or portions of a corresponding one of the PM machines 100-1, 100-2, 100-3 as described herein according to various embodiments of the present invention, and thus such corresponding step(s) or operation(s) need not be described or repeated with respect to the method 200 for clarity or conciseness. In other words, various embodiments described herein in the context of any one of the PM machines 100-1, 100-2, 100-3 are analogously valid for the method 200 (e.g., for configuring a corresponding one of the PM machines 100-1, 100-2, 100- 3 having various components, pails, portions and / or configurations as described hereinbefore according to various embodiments), and vice versa.

[0026] Accordingly, the method 200 advantageously configures a PM machine with multiphase windings to exhibit PMC, which has been found to improve power factor and fieldweakening performance.

[0027] FIG. 3 depicts a schematic diagram of a method 300 of reconfiguring a PM machine, according to various embodiments of the present invention. The PM machine comprising: a rotor comprising a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots. Each phase winding of the multi-phase windings comprises a plurality of coils. Similarly, as described hereinbefore, the PM machine may be any type or form of PM machine as desired or as appropriate, as long as the PM machine has multi-phasewindings installed on the stator, such as but not limited to PMVM or PMSM (e.g., a surfacemounted PMSM or an inset PMSM). Accordingly, in various embodiments, the method 300 may correspond to reconfiguring a PMVM or a PMSM (e.g., a surface-mounted PMSM or an inset PMSM) with multi-phase windings that exhibit NMC to PMC.

[0028] In various embodiments, the method 300 comprises: assigning (at 302) each coil of the plurality of coils of the above-mentioned each phase winding to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil; identifying (at 304) each pair of overlapping coils of different coil groups of the multi-phase windings configured to have opposite coil connection directions corresponding to opposite current flow directions (e.g., a pair of overlapping coils having opposite coil connection directions may be referred to exhibiting negative mutual coupling (NMC), and thus may be referred to as NMC winding), the above-mentioned each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots 124-1, 124-2, 124-3; and reconfiguring (at 306), for each identified pair of overlapping coils (i.e., having NMC), one of the overlapping coils of the identified pair of overlapping coils such that the identified pair of overlapping coils have a same coil connection direction corresponding to a same current flow direction (i.e., to exhibit PMC). That is, each pair of overlapping coils of different coil groups identified to exhibit NMC is reconfigured, or converted, to exhibit PMC.

[0029] Accordingly, the method 300 advantageously reconfigures a PM machine with multi-phase windings that exhibit NMC to exhibit PMC, which has been found to improve power factor and field- weakening performance. In particufar, by reconfiguring the PM machine with multi-phase windings that exhibit NMC to exhibit PMC, the method 300 advantageously overcomes the negative phase-mutual inductance associated with the conventional NMC winding which leads to increasing < -axis inductance and amplifying armature reaction. In contrast, as described hereinbefore, the PMC winding according to various embodiments of the present invention exhibits positive phase-mutual inductance, cancellation effect on the -axis flux linkage, and brings the characteristic current closer to the current limit. This contributes to suppressing armature reaction, improving the power factor, reducing the terminal voltage, and enhancing the field-weakening performance.

[0030] In various embodiments, the above-mentioned reconfiguring (at 306) one of the overlapping coils of the identified pair of overlapping coils comprises: maintaining a first coil side of the above-mentioned one of the overlapping coils at a stator slot of the plurality of stator slots 124-1 , 124-2, 124-3 where the identified pair of overlapping coils overlap; andrepositioning a second coil side, opposite to the first coil side, of the above-mentioned one of the overlapping coils to another stator slot of the plurality of stator slots 124-1, 124-2, 124-3 such that the identified pair of overlapping coils have the same coil connection direction.

[0031] In various embodiments, the above-mentioned another stator slot of the plurality of stator slots 124-1 , 124-2, 124-3 is determined based on a coil pitch of the above-mentioned one of the overlapping coils and is located in a direction from the above-mentioned stator slot opposite to that of an original stator slot of the second coil side.

[0032] In various embodiments, the method 300 further comprises swapping coil sides, including the first coil side of the above-mentioned one of the overlapping coils, between different layers at the above-mentioned stator slot for maintaining a same magnetomotive force direction in the above-mentioned stator slot.

[0033] Accordingly, in various embodiments, the method 300 may correspond to reconfiguring a PM machine (e.g., a PMVM, a surface-mounted PMSM or an inset PMSM) with multi-phase windings that exhibit NMC to any one of the PM machines 100-1, 100-2, 100- 3 with multi-phase windings exhibiting PMC as described hereinbefore with reference to FIGs. 1A to 1C, according to various embodiments of the present invention. Therefore, in various embodiments as described hereinbefore, the multi-phase windings 130-1, 130-2, 130-3 are configured on the stator through the plurality of stator slots 124-1, 124-2, 124-3 with a regular spatial interval among the multi-phase windings 130-1 , 130-2, 130-3 to form symmetrical multi-phase windings. In various embodiments as described hereinbefore, the multi-phase windings 130-1, 130-2, 130-3 are three-phase windings. In this regard, the above-mentioned each coil of the plurality of coils is assigned to one of two different coil groups based on the phase angle of the magnetomotive force associated with the coil. In various embodiments as described hereinbefore, the PM machine is configured as a PMVM. In this regard, the rotor 110-1, 110-2, 110-3, and the stator 120-1, 120-2, 120-3 and the multi-phase windings 130-1, 130-2, 130-3 are configured such that the number of stator slots at the stator is equal to a sum of the number of permanent magnet rotor pole pairs and the number of armature pole pairs of the permanent magnet machine. In various embodiments as described hereinbefore, the PM machine is configured as a PMSM. The rotor 110-1, 110-2, 110-3, the stator 120-1, 120-2, 120- 3 and the multi-phase windings 130-1, 130-2, 130-3 are configured such that the number of permanent magnet rotor pole pairs is equal to the number of armature pole pairs of the PM machine.

[0034] It will be appreciated by a person skilled in the art that the terminology used herein is for the purpose of describing various embodiments only and is not intended to be limiting of the present invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and / or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0035] Any reference to an element or a feature herein using a designation such as “first”, “second” and so forth does not limit the quantity or order of such elements or features, unless stated or the context requires otherwise. For example, such designations may be used herein as a convenient way of distinguishing between two or more elements or instances of an element. Thus, a reference to first and second elements does not necessarily mean that only two elements can be employed, or that the first element must precede the second element, unless stated or the context requires otherwise. In addition, a phrase referring to “at least one of’ a list of items refers to any single item therein or any combination of two or more items therein.

[0036] In order that the present invention may be readily understood and put into practical effect, various example embodiments of the present invention will be described hereinafter by way of examples only and not limitations. It will be appreciated by a person skilled in the art that the present invention may, however, be embodied in various different forms or configurations and should not be construed as limited to the example embodiments set forth hereinafter. Rather, these example embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art.

[0037] In particular, for better understanding of the present invention and without limitation or loss of generality, various example embodiments of the present invention will now be described with respect to a PM machine in the form of a PMVM as illustrated in FIG. 1A for clarity and conciseness. However, as explained hereinbefore, it will be appreciated by a person skilled in the art that the present invention is not limited to a PM machine in the form of a PMVM and may be configured as other types of PM machine, such as but not limited to, a PMSM (e.g., a surface-mounted PMSM 100-2 as illustrated in FIG. IB or an inset PMSM 100- 3 as illustrated in FIG. 1C).

[0038] Various example embodiments provide a new winding design for PMVM, namely, Positive-Mutual-Coupling (PMC) winding for improved power factor and higher fieldweakening capability. In particular, various example embodiments provide and investigate a PMVM equipped with PMC winding. For example, the conventional winding layout typically presents negative-mutual-coupling (NMC) among the three-phase windings due to the 120° spatial phase shift. As will be illustrated later below, in the conventional NMC winding, the negative phase-mutual inductance leads to increasing -axis inductance and amplifying armature reaction. On the contrar y, the investigated PMC winding according to various example embodiments of the present invention (which may herein be referred to as the present PMC winding) exhibits positive phase-mutual inductance, cancellation effect on the ( / -axis flux linkage, and brings the characteristic current closer to the current limit. That is, the investigated PMC winding exhibits counteracted effect between ( ax is self-flux linkage and phase-mutual flux linkage, leading to reduced ( / -axis inductance and facilitating the approach of the characteristic current to the current limit. This contributes to suppressing armature reaction, improving the power factor, reducing the terminal voltage, and enhancing the field-weakening performance. According to various example embodiments, based upon winding function theory, an example design methodology to obtain PMC winding is described and exemplified on a 24-slot, 5-armature pole pair, and 19-rotor pole pair PMVM. Finite element analysis (FEA) and experimental results show that the PMC PMVM according to various example embodiments of the present invention may improve the rated power factor and widen the constant torque region. In particular, FEA and experimental results demonstrate that the constant torque region and CPSR are substantially extended with the adoption of PMC winding. Furthermore, with reduced q-axis inductance and suppressed armature reaction, the power factor and output torque across the whole speed range are enhanced. In particular, with reduced terminal voltage and more voltage margins, the PMC PMVM can employ a higher ( / -axis current to generate torque, thus significantly enhancing the output torque and power factor during field- weakening operations. As a result, the output power capability and constant power speed range (CPSR) are improved dramatically. In addition, a PMC PMVM prototype according to various example embodiments is manufactured to validate the efficacy of PMC winding in improving field-weakening and power factor. Accordingly, in various example embodiments, a new PMC winding design is employed in PMVMs to improve power factor and field- weakening performance. The PMC winding design according to various exampleembodiments validates that the PMVMs can be viable solutions to applications that require high torque capability at low-speed operation and high output power across a wide speed range.INVESTIGATED VERNIER MACHINE TOPOLOGY AND WORKING PRINCIPLE

[0039] Based on field modulation theory, the large-pole PM rotor magnetic field of PMVM is modulated by the stator teeth to generate a low-pole modulated field. As a consequence, the armature pole pair of PMVM can be designed as a low value. It can be derived from winding function theory that with identical electrical loading, the amplitude of armature field is inversely proportional to armature pole pair. Therefore, as compared to conventional PM synchronous machine with same PM rotor arrangement, the armature field of PMVM exhibits lower pole pair and higher amplitude, contributing to higher output torque capability. To obtain the highest torque production capability, the stator slot number Zs, PM rotor pole pair pr, and armature pole pair psmay be configured to satisfy the following equation:Zs— Pr+ Ps(Equation 1)

[0040] FIG. 1A depicts a schematic drawing of a topology (or cross section) of the investigated PMVM 100-1 with PMC winding (which may herein be referred to as PMC PMVM 100-1). For comparison, FIG. 4 depicts a schematic drawing of a topology (or cross section) of a PMVM 300-1 with conventional NMC winding (which may herein be referred to as NMC PMVM 300-1). For example, with reference to FIG. 1A or FIG. 4, the number of PM magnets or pieces corresponds to the pole number, and half of that value is defined as the PM rotor pole-pair number. On the other hand, to determine the armature pole-pair number, the winding function theory or the star-of-slots method may be employed. These approaches may be utilized to identify the dominant harmonic order of the armature field, i.e., the one with the highest amplitude, based on the spatial distribution of the winding. As can be seen, the V-type PM arrangement with flux focusing effect is employed to enhance magnetic loading, and alternate flux bridge is provided for the low-polc-pair armature fields to improve field modulation and output torque. FIG. 5 shows a Table (Table I) presenting example main geometric parameters of the PMVMs 100-1, 300-1. As listed in Table I shown in FIG. 5, the geometric parameters are optimized by commercial FEA software JMAG 23.0, targeting high output torque and power factor. Taking into account the conflicting effects of pole ratio on output torque and power factor, the investigated PMVMs 100-1, 300-1 each incorporate 24- stator slot, 5-armature pole pair, and 19-rotor pole pair. As a result, the two-slot pitch windingwith an electrical slot pitch angle (i.e., ae) of 150° is adopted. This design reduces the bulky end-winding volume of distributed windings and suppresses the abundant field harmonics of concentrated windings. In addition, the single-layer winding is utilized to increase the slot filling factor, improve fault-tolerant capability, and reduce manufacture complexity.

[0041] The conventional NMC winding, as depicted in FIG. 4, is designed using the star of slots phasor diagram by allocating the adjacent MMF / EMF phasors to the same phase to obtain the highest fundamental winding factor. As will be illustrated later below, the negative phase mutual inductance tends to increase q-axis flux linkage and armature reaction, leading to deteriorated power factor, and sacrificed field-weakening performance. To address the adverse effect of negative phase-mutual coupling on q-axis flux linkage and inductance, a PMC winding method or configuration is provided according to various example embodiments of the present invention. The PMC winding configuration is illustrated in FIG. 1A, where the slot pitch is identical and winding allocation is varied to produce positive coupling between different phases. The geometric parameters of the two PMVMs 100-1, 300-1 have been kept constant to achieve a fair comparison and clear demonstration of the benefit with positive phase-mutual coupling effect according to various example embodiments of the present invention.PHYSICAL INSIGHTS AND DESIGN METHODOLOGY OF POSHTVE-MUTUAL-COUPLING (PMC) WINDINGPhysical Insights of PMC Winding: Counteracted q-axis Flux Linkage and Reduced Terminal Voltage

[0042] To reveal the physical insights of positive-mutual-coupling (PMC), the current and inductance in the de / - ax is frame arc obtained as:(Equation 3) where Kcdenotes the Clarke Transformation from the stationary ahc-axis frame to the stationary <z / »-axis frame, and KPdenotes the Park Transformation to the rotatory t / q-axis frame, expressed as:(Equation 4)(Equation 5) where 0edenotes the electrical angle of the PM rotor, and (L)3sdenotes the inductance matrix in the stationary afec-axis frame, which is expressed as:(Equation 6) where Mxy(x = a, b, c) represents the mutual inductance of phase x due to the excitation of phase y.

[0043] Then the g-axis flux linkageis calculated as:(Equation 7)

[0044] Substituting (2) and (3) into (7), and neglecting the pulsating inductance components, 'Pq can be derived as:—Lphlm SIH P ~ MphlmSin ft — W^ph + 'Pq(Equation 8) where Imdenotes phase current amplitude, p denotes the spatial electrical angle between the stator flux linkage and the permanent magnet flux linkage (i.e., the angle by which stator current vector leads the d- axis), Lphand Mphdenote phase self- and mutual inductance components, respectively.

[0045] As can be seen from Equation (8), the ( / -axis flux linkagellJqis composed of armature phase self- and mutual flux linkages, denoted as Vq^h andrespectively. For conventional NMC winding with negative mutual inductance, the armature phase self- and mutual flux linkages are superimposed on each other. On the contrary, the PMC winding (i.e., with positive phase mutual inductance) according to various example embodiments of the present invention exhibits counteracted < / -axis phase self- and mutual flux linkages, contributing to reduced terminal voltage.

[0046] FIGs. 6A and 6B show a comparison of phasor diagrams under rated and fieldweakening conditions for the conventional NMC winding (FIG. 6A) and for the PMC winding (FIG. 6B),is the -axis armature flux linkage generated by the demagnetizing current (i.e., Id), and Eo is the no-load back EMF.

[0047] With identical geometric parameters and comparable magnet flux linkage, the PMC PMVM 100-1 exhibits comparable output torque but decreased terminal voltage as compared with the conventional NMC PMVM 300-1 underrated conditions. Therefore, the PMC winding can increase the corner speed and rated power factor, extending the constant-torque operating range. When operating speed exceeds the corner speed, the two investigated PMVMs 100-1, 300-1 operate in the field-weakening region, where both the voltage and current limits are reached. Benefiting from the counteracted ( / -axis armature flux linkage and reduced terminal voltage, the PMC PMVM 100-1 can fulfil the voltage limit in a wider speed range, leading to a wider constant power speed range (CPSR). With further increases in operating speed, the PMVMs 100-1, 300-1 operate in the deep field-weakening region, where the phase current is reduced to meet the voltage limit. In this situation, the armature reaction is significant, and the < / -axis armature flux linkage is dominant as most of the magnet flux linkage is compensated by the ( / -axis demagnetizing current. Under such condition, the PMC PMVM 100-1 can employ a higher ( / -axis current within the same voltage limit, contributing to improved output torque in the deep field-weakening region.

[0048] In summary, positive phase-mutual coupling effect indicates counteracted ( / -axis armature flux linkage and reduced terminal voltage. As compared with the conventional NMC PMVM 300-1, the investigated PMC PMVM 100-1 can widen the constant torque region, improve output torquc / powcr in the field-weakening operating region, and extend the constant power speed range.Design Methodology of PMC Winding Through Winding Funct ion Theory

[0049] Based on winding function theory' (e.g., disclosed in Novotny etal., “Vector Control and Dynamics of AC Drives”, Oxford, U.K.: Clarendon, 1998), the phase self- and mutual inductances can be calculated as:(Equation 10) among whic are the air-gap permeance and winding functions, expressedas:(Equation 11)(Equation 12) where Asand Arare the permeance functions that represent the stator and rotor slotting effect. Ni is the number of turns in series per phase. kw his the winding factor of hth-order MMF harmonic. tc— GCD(ZS, ps~) is the machine periodicity.

[0050] Equation (10) suggests that the phase mutual inductance is closely related to the winding function and the coil spatial distribution of each phase winding. FIGs. 7A and 7B depict the star of slots phasor diagrams of the conventional NMC winding and the PMC winding, respectively, indicating the magnetomotive force (MMF) phasor induced in each individual coil side. The solid and dash lines represent the upper- and lower- layer coil sides of the single-layer windings, and each phase winding is classified into multiple coil groups. Accordingly, various example embodiments include assigning each coil of the plurality of coils of each phase winding to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil. For example, for the example 24-slot / 5-pole-pair armature windings, each phase winding has four coils and is classified into two coil groups based on the phase angle of the MMF generated by each coil. For example, each phase of theexemplified PMVMs 100-1, 300-1 has four coils (i.e., coil I+, I-, II+, and II ), where “F and “II” refer to coil groups, and “+”indicate the coil connection direction (i.e., current flow direction). It should be noted that, although the MMF phasors of coil 1+ and coil I- exhibit opposite polarities, the generated MMFs have the same phase angle due to the reversed current direction. Therefore, coils 1+ and I- (and similarly, coils 11+ and IT-) are categorized as the same coil group. Furthermore, in FIGs. 7A and 7B, the phase of each coil is indicated by a letter (e.g., ‘A’, ‘B’, ‘C’ indicating phase ‘A’, phase ‘B’, phase ‘C’, respectively) at a periphery of the phasor diagram. To differentiate each coil side, the lower coil side is highlighted with an underline, while the upper coil side shares the same name as the coil. To facilitate better understanding, the detailed coil distributions are listed in Table II shown in FIG. 8 A and Table III shown in FIG. 8B. It will be appreciated by a person skilled in the art that each phase winding is not limited to having four coils and being classified into two coil groups. In this regard, in general and according to various example embodiments, the number of coils per phase (Nc)Z may be formulated as: Nc= — -k . The number of coil groups, i.e., q, can be calculated as: 2mZ -k q = — - — , where Z, denotes the number of stator slots, m denotes the number of phases, k 4m -tcdenotes equal to the number of winding layers, and tcdenotes the machine periodicity, defined as the greatest common divisor of stator slot number and armature pole-pair number.

[0051] Regarding the coil groups, for example, from the star of slots illustrated in FIGs. 7A and 7B, the phase angles (electrical degrees) for corresponding coil groups are defined as (taking phase A as an example): conventional NMC winding (FIG. 7A): Coil group I: 0°; Coil group II: -15°; and PMC winding (FIG. 7B): Coil group I: 0°; Coil group II: -45°. For example, as can be seen in FIG. 7A, for the conventional NMC winding, phase A has 4 coils. In this regard, Coil I + is wound around teeth 1 (starting coil side) and 3 (ending coil side); coil I- is wound around teeth 13 and 15; coil 11+ is wound around teeth 20 and 22, and coil II- is wound around teeth 8 and 10. For simplicity, the MMF phasor shows where the starting coil side is placed to represent the whole coil. As can be seen in FIG. 7A, the phase angle between adjacent MMF phasors is 15°. Accordingly, the MMF angles of coil 1+ and coil 11+ are 0° and -15°, respectively. In addition, the phasor angles of coil I- and coil II- are 180° and 165°, respectively. It should be noted thatmeans oppositive current direction. As a result, the MMF angle of coil I- is 0° (and thus, coil I- and coil 1+ are classified / assigned into coil group I), and that of coil II- is -15° (thus coil II- and coil 11+ are classified / assigned as coil group II). For the PMCwinding, as illustrated in FIG. 7B, each coil is similarly classified / as signed to coil group I or II, based on a phase angle of a magnetomotive force associated with the coil.

[0052] The armature MMF distribution of the conventional NMC winding is illustrated in FIG. 9A. It can be seen that the NMC winding exhibits negative phase mutual coupling, which is to be converted to positive phase mutual coupling (PMC winding) according to various example embodiments of the present invention, as indicated by the dashed box. A method for converting the NMC winding to PMC winding according to various example embodiments is shown in FIGs. 9 A to 9C and is summarized as follows:

[0053] 1) Step 1: Identify negatively-coupled coil groups. As shown in FIG. 9A, coil groupI of phase A and coil group II of phase C exhibit negative phase mutual coupling, while the other coils present minimal mutual coupling. In various example embodiments, this step may include: assigning each coil of the plurality of coils of each phase winding to one of a plurality of different coil groups (e.g., coil groups I and II) based on a phase angle of a magnetomotive force associated with the coil; and identifying each pair of overlapping coils of different coil groups of the multi-phase windings configured to have opposite coil connection directions corresponding to opposite current flow directions (i.e., identifying each pair of overlapping coils exhibiting NMC). In this regard, a pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots 124-1, 124-2, 124-3.

[0054] 2) Step 2: Construct the positively-coupled coil groups by rearranging the coil spatial distribution. This step may include reconfiguring, for each identified pair of overlapping coils (i.e., having NMC), one of the overlapping coils of the identified pair of overlapping coils such that the identified pair of overlapping coils have a same coil connection direction corresponding to a same current flow direction (i.e., PMC). That is, each pair of overlapping coils of different coil groups identified to exhibit NMC is reconfigured, or converted, to exhibit PMC.

[0055] 3) Step 3: validating the symmetry among the three-phase windings. If the three- phase windings are not in symmetry, obtain the remaining coil distribution by following symmetrical three-phase restrictions to maintain the three-phase symmetrical relationship.

[0056] Accordingly, FIGs. 9A to 9C show an example design methodology of PMC winding through winding function, where FIG. 9A shows the conventional NMC winding, FIG. 9B shows the intermediate winding with positively -coupled coil groups and FIG. 9C shows the configured PMC winding according to various example embodiments of the present invention.

[0057] Regarding Step 2, although a number of approaches are possible to achieve a positive-coupling relation by rearranging the coils, it is preferable to make as few changes as possible to the original coil positions. This is because the conventional NMC winding is designed by assigning the most adjacent phasors (i.e., the phasors within the two opposite 60° phase belts) to the same phase to obtain the highest winding factor, as shown in FIG. 7 A. Nevertheless, rearranging the coil spatial positions can deteriorate the winding factor. Therefore, according to various example embodiments of the present invention, the number of reconfigured coils and the deviation angle between the MMF phasors of the new and original coils is minimized. For example, the most straightforward approach to achieve positive coupling is to directly flip the coil group II of phase C (which forms negative-coupling with coil group I of phase A), as can be seen in FIG. FIG. 9A. However, various example embodiments note that this will result in a 180° deviation angle in MMF phasors between the new and original coil group II. As a result, the MMF of the new coil group II will be in antiphase with the MMFs of the other remaining coils, causing them to cancel each other, which substantially deteriorates the winding factor.

[0058] As illustrated in FIG. 9A, negative-coupling occurs when two coils overlap and have opposite connection directions. For example, the coil 1+ of phase A (i.e., with the positive upper layer coil side placed in slot 1, and the negative lower coil side in slot 3) and coil II- of phase C (i.e., with the negative upper layer coil side placed in slot 24 and the positive lower coil side in slot 2) cross over in slot 2 and have opposite directions, thus exhibiting negative-coupling. To convert it to positive-coupling coil group, in various example embodiments, the overlapped slot (i.e., slot 2) is reserved for the new coil. To maintain the same MMF direction in the overlapped slot (so that it adds up to composite phase MMF), and considering that the new and original coils have opposite connection directions (to convert negative-coupling (NMC) to positive-coupling (PMC)), in various example embodiments, the coil side sequence placed in the overlapped slot is reversed for the new and original coils. In other words, the coil sides in the overlapped slot is swapped between the lower and upper layers. Then, the other coil side of the new coil is determined by coil throw. Consequently, the minimum deviation angle in MMF phasors of the new and original coils equals the difference between 180° and the electrical coil pitch angle, i.e., jr-cie.

[0059] Accordingly, in various example embodiments, in Step 2, the above-mentioned reconfiguring one of the overlapping coils of the identified pair of overlapping coils comprises: maintaining a first coil side of the above-mentioned one of the overlapping coils at a stator slotof the plurality of stator slots 124-1, 124-2, 124-3 (i.e., keeping the first coil side at the stator slot) where the identified pair of overlapping coils overlap; and repositioning a second coil side, opposite to the first coil side, of the above-mentioned one of the overlapping coils to another stator slot of the plurality of stator slots 124-1, 124-2, 124-3 such that the identified pair of overlapping coils have the same coil connection direction. The above-mentioned another stator slot of the plurality of stator slots 124-1, 124-2, 124-3 is determined based on a coil pitch of the above-mentioned one of the overlapping coils and is located in a direction from the above- mentioned stator slot opposite to that of an original stator slot of the second coil side. Furthermore, in various example embodiments, the method further comprises swapping coil sides, including the first coil side of the above-mentioned one of the overlapping coils, between different layers (c.g., between the lower and upper layers) at the above-mentioned stator slot for maintaining a same magnetomotive force direction in the above-mentioned stator slot.

[0060] The above procedure is applied and exemplified in FIGs. 9A and 9B, with new coils labelled with As can be seen, the new positive-coupling coil (e.g., coil 11*+) occupies one slot of its own (the overlapped slot, i.e., slot 2) and another slot that belongs to other phases (i.e., slot 4), while one slot is discarded (i.e., slot 24). Therefore, in order to obtain symmetrical three-phase windings, the discarded slot is to be used by other phases when constructing positive-coupling coil groups. This indicates that the discarded and newly occupied slots have symmetrical positions in the phasor diagram, as exemplified by slot 24 (i.e., discarded) and slot 4 (i.e., newly occupied) in FIG. 7B. This adds additional constraints on the pole-pair combinations of single-layer windings that can convert NMC to PMC:(Equation 13) where m is the number of phases, ki is any integer but not a multiple of m, and n / m is the phase belt angle.

[0061] For PMVMs that can be designed with a minimum deviation angle (i.e.,= n — ae), Equation (13) can be rephrased as:(Equation 14) where [X] represents the largest integer not exceeding X, and [Zs / 2ps] is the coil pitch / span in units of slot number.

[0062] Equation (14) can be used to examine whether a traditional NMC winding with a specific slot / pole combination can be converted to the corresponding PMC winding, with minimal MMF phasor deviation angle between the new and original coils, thereby minimizing the adverse effects on winding factor. It is worth noting that for winding configurations that do not satisfy Equation (14), positive-mutual coupling may still be achievable, but at a considerable expense to the winding factor and output torque. Under such circumstances, according to various example embodiments, a comprehensive analysis may be conducted to choose between the conventional NMC winding and the present PMC winding. From the above analysis, the detailed design approach can be easily extended to other situations, such as different slot / pole combinations, coil pitches, winding layer numbers, and phase numbers, etc.Effects of the PMC Winding and Comparison with Conventional NMC Winding

[0063] Based on the aforementioned design procedures, the PMC winding is obtained, and the star of slots phasor diagram is illustrated in FIG. 7B. To validate the design methodology and effectiveness of the PMC winding, the phase mutual coupling of the two investigated PMVMs 100-1, 300-1 is examined. FIGs. 10A and 10B show the phase mutual coupling of the conventional NMC winding and the present PMC winding when only phase A current is injected, while PM excitation and the other phase currents are removed. It should be noted that the frozen permeability (FP) method is adopted to account for magnetic saturation caused by the PM fields. In particular, FIGs. 10A and 10B show the on-load armature flux linkage with single-phase current injection for the conventional NMC PMVM 300-1 and the PMC PMVM 100-1.

[0064] As can be seen from FIGs. 10A and 10B, the conventional NMC winding exhibits negative-mutual-coupling while the investigated PMC winding demonstrates positive-mutualcoupling. In addition, the vth-order harmonic winding factors of the NMC and PMC windings can be calculated as:(Equation 15) where ft denotes the mechanical slot pitch angle (i.e., ft —y denotes the mechanical coil span / pitch angle, and q denotes the number of coil groups, which can be expressed as:q =^T2(Equation 16)where &2=1 for double-layer winding and C=2 for single-layer winding.

[0065] From Equations (15) and (16), it can be obtained that the PMC winding exhibits a lower fundamental winding factor than the traditional NMC winding (i.e., 0.892 vs. 0.958). This is not unexpected because the original NMC winding is designed by assigning the most adjacent phasors to the same phase to achieve the highest winding factor, while rearranging the coil spatial positions will inevitably deteriorate the winding factor. However, FIGs. 10A and 10B show that the PMC PMVM 100-1 presents a higher phase-self flux linkage than the conventional NMC PMVM 300-1 (i.e., 83.37 mWb vs. 74.36 mWb), albeit with a lower winding factor. This is attributed to the reduced sub-harmonic content and mitigated magnetic saturation level in the PMC PMVM 100-1, as validated in FIGs. 11A and 11B. In particular, FIGs. 11A and 11B show a ratcd-load field distribution comparison between the conventional NMC PMVM 300-1 (FIG. 11A) and the PMC PMVM 100-1 (FIG. 11B). Consequently, the output torque of the PMC PMVM 100-1 is maintained despite the slightly deteriorated winding factor, attributed to the alleviated magnetic saturation and increased phase self-flux linkage.

[0066] When the three-phase symmetrical currents are injected, the synergistic on-load armature flux linkage is obtained using the FP method, as shown in FIGs. 12A and 12B. In particular, FIGs. 12A and 12B show the output torque and synergistic on-load three-phase armature flux linkage for the conventional NMC PMVM 300-1 (FIG. 12A) and the PMC PMVM 100-1 (FIG. 12B). One can see that for traditional NMC winding, the composite three- phase flux linkage is the summation of phase self- and mutual flux linkages. In contrast, the phase self- and mutual flux linkages cancel out in the investigated PMC winding, which contributes to reduced q-axis flux linkage and terminal voltage. It should be mentioned that due to alleviated magnetic saturation, the cancellation effect of PMC winding (i.e., decreased from 83.37 mWb to 64.16 mWb) is more prominent than the summation effect of NMC winding (i.e., increased from 74.36 mWb to 86.85 mWb).

[0067] The above analysis and comparison are presented in Table IV in FIG. 13, where 3D FEA simulation is used to account for the leakage inductances. With counteracted <7- ax is phase self- and mutual flux linkages, the PMC winding possesses lower terminal voltage than the traditional NMC winding (i.e., 86.34V vs. 105.55 V), which improves the rated power factor from 0.70 to 0.81 and enhances the field-weakening performance. Further details will be illustrated later below.MECHANISM FOR FIELD-WEAKENING AND POWER FACTOR IMPROVEMENT

[0068] Neglecting transient state and winding resistance, the control strategy should satisfy the voltage and current constraints as:;2 , ;2 <- ;2 ' d ' — Him(Equation 17)(Equation 18)

[0069] For PMVMs with negligible saliency, i.e., Ldis close to Lq, the voltage limit can be perceived as a circle and the d-q current operation region shrinks as speed increases, as shown in FIGs. 14A and 14B. In particular, FIGs. 14A and 14B show the control strategy for maximum power under limited voltage and current for the conventional NMC winding (FIG. 14 A) and the PMC winding (FIG. 14B). It is well known that optimal field-weakening control can be achieved when the characteristic current Ich equals the current Emit. Ich indicates the center of voltage limit circles and can be calculated as:(Equation 19)

[0070] As shown in Equation (19) and validated in FIGs. 14A and 14B, the PMC winding demonstrates a counteracted c / -axis flux linkage and reduced q-axis inductance, which brings the characteristic current closer to the current limit, thereby improving field-weakening capability. It should be mentioned that for the two investigated PMVMs 100-1, 300-1, the characteristic current remains within the current limit circle, suggesting that they could theoretically be operated at infinite speed. This scenario is due to the fact that the PMVMs generally possess low magnet flux linkage and large inductances. A comprehensive evaluation of the PMC PMVM 100-1 across the entire operating range will be conducted to demonstrate its potential.

[0071] When operating below base speed, the maximum torque per ampere (MTPA) control strategy is adopted in region I, which is denoted as constant torque operation region. With negligible reluctance torque, the electromagnetic torque of PMVMs can be expressed as 3Te= - Pr ^PM iq (Equation 20)

[0072] According to Equation (20), id= 0 control is generally adopted in Region I for MTPA operation. Thereby, below the corner speed, the maximum g-axis current is injected to obtain the highest output torque, and the operating point is fixed at point A, as shown in FIGs. 14A and 14B. The terminal voltage remains within the voltage limits until the operating speed reaches the corner speed a>1, calculated as:(Equation 21)

[0073] As can be seen, with identical voltage and current limits (i.e., 190 V and 14.5 A), the corner speed of constant torque region can be increased by the PMC winding, which exhibits a lower ( / -axis inductance. This is validated in FIG. 15 and FIG. 16, showing that the corner speed is increased from 600 r / min to 695 r / min. In particular, FIG. 15 shows the comparison of output torque and power factor between the PMC PMVM 100-1 and the conventional NMC PMVM 300-1. FIG. 16 shows the comparison of d-axis and ( / -axis currents between the PMC PMVM 100-1 and the conventional NMC PMVM 300-1. Furthermore, with counteracted q- axis flux linkage and suppressed armature reaction, the ratio of ( / -axis inductance to magnet flux linkage is reduced in the PMC PMVM 100-1, which substantially improves the power factor. FIG. 15 indicates that when operating in the constant torque region, the power factor of the PMC PMVM 100-1 is improved from 0.70 to 0.81, compared to the conventional NMC PMVM 300-1. In summary, the PMC PMVM 100-1 broadens the constant torque region and improves the operating power factor.2 ) Region II: constant power region (to-t < co < <z>2)

[0074] When speed increases above the base speed, field-weakening control is required, and negative d-axis demagnetizing current is injected to weaken the magnet flux linkage. As illustrated in FIGs. 14A and 14B, the currents are controlled by following track AB. In this region, both voltage and current limits are reached. The input apparent power remains maximum and constant, and the two PMVMs 100-1, 300-1 provide constant output power, when the variation of power factor and losses are neglected. Therefore, region II is also denoted as constant power region. When the magnet flux linkage is fully weakened by the negative d- axis armature flux, the operating speed reaches the boundary' of region II, and the boundary speed u>2 can be calculated as:(Equation 22)

[0075] At speed m2, the achievable maximum power is derived as:(Equation 23)

[0076] As can be seen from Equations (22) and (23), the PMC PMVM 100-1 can increase boundary speed m2and maximum output power. This is validated in FIG. 16 and FIG. 17, showing that the boundary speed a>2is improved from 1086 r / min (i.e., when the ( / -axis current reaches the maximum value) to 2524 r / min, and the maximum output power is increased from 1580 W to 1950 W. Moreover, with reduced d / q-axis inductance, a higher ( / -axis current is applied in the PMC PMVM 100-1 during field-weakening operation, as shown in FIG. 16. Superimposing the effect of counteracted ( / -axis flux linkage, the angle between voltage and current phasors (i.e., power factor angle) is smaller in the PMC PMVM 100-1, thereby leading to a higher power factor. In summary, with counteracted ( / -axis flux linkage and more voltage margins, the investigated PMC PMVM 100-1 can employ a higher ( / -axis current to generate torque, thereby extending the constant power region and improving maximum output power capability.3) Region III: deep field-weakening region (<D > a)2j

[0077] With speed further increased beyond m2, the two investigated PMVMs 100-1, 300- 1 enter deep field-weakening region, denoted as region III in FIGs. 14A and 14B. In this region, the current amplitude is decreased to fulfil the voltage limitations. To fully utilize the DC bus voltage, the maximum torque per voltage (MTPV) control strategy is adopted, which can be expressed as:(Equation 23)

[0078] It can be seen that the magnet flux linkage is fully compensated by the negative d- axis current, and the terminal voltage is solely determined by the ( / -axis armature flux linkage. As a result, the PMC PMVM 100-1 can employ a higher ( / -axis current to generate torque, due to the counteracted ( / -axis flux linkage, as validated in FIG. 15 and FIG. 16. In deep fieldweakening region (region III), the current phasor leads the voltage phasor, and the current angletends to increase as the d-axis current remains constant while the y-axis current decreases with the increasing speed, resulting in reduced power factor at higher speeds. FIG. 15 illustrates that the PMC PMVM 100-1 exhibits a slower decrease in the -axis current and a higher overall power factor compared to the conventional NMC PMVM 300-1. The output power capability of the PMC PMVM 100-1 can also be improved substantially. FIG. 17 shows that the CPSR of the conventional NMC PMVM 300-1 ranges from 600 r / min to 1800 r / min with a base power of 1510 W, whereas the PMC exhibits a wider CPSR ranging from 695 r / min to 4200 r / min with a base power of 1747 W. In specific, with the employment of PMC winding, the CPSR ratio is improved from 3 to 6, and the output power is increased by 15.70 %.

[0079] The core losses tend to become more troublesome at highspeed operations because the eddy current loss is proportional to the square of operating frequency, and the working magnetic field is overwhelmed by harmonic components in deep field-weakening operations. FIG. 18 shows that the PMC PMVM 100- 1 presents substantially lower core losses as compared to conventional NMC PMVM 300-1, owing to the suppressed sub-order field harmonics, which has been validated in FIGs. 11A and 1 IB. The comprehensive loss and efficiency comparisons between the conventional NMC and PMC PMVMs 300-1, 100-1 are provided in Table V in FIG. 19. It can be seen that despite higher <A / -axis currents and increased copper losses, the PMC PMVM 100-1 presents higher operating efficiency due to reduced core losses and higher output torque.

[0080] The efficiency maps of the two investigated PMVMs 100-1, 300-1 are compared in FIGs. 20A and 20B to take into account various load and speed conditions. As can be seen, the investigated PMC PMVM 100-1 can extend the constant torque region, enhance output torque and power capability during field-weakening operating conditions, and improve operating efficiency especially under high-speed operations. The detailed field-weakening performance comparison is listed in Table VI shown in FIG. 21, indicating that the PMC PMVM 100-1 exhibits an improved power factor and comparable output torque at rated conditions. Moreover, with counteracted -axis armature flux linkage and reduced terminal voltage, the investigated PMC PMVM 100-1 can widen the constant torque region from 600 r / min to 695 r / min, and achieve a wider CPSR ranging from 695 r / min to 4200 r / min, with the base power increased from 1510 W to 1747 W. It should be noted that if the base speed and power of the CPSR are set identical to the conventional NMC PMVM 300-1 (i.e., 600 r / min and 1510 W), the PMC PMVM 100-1 shows a substantially increased CPSR ratio from 3 to higher than 10.EXPERIMENTAL VALIDATION

[0081] To validate the concept of PMC winding and its ability to improve power factor and field-weakening, the investigated PMC PMVM 100-1 is fabricated and shown in FIGs. 22A to 22D, with the main geometric design parameters listed in Table I in FIG. 5. In particular, FIGs. 22A to 22D show the example stator and rotor lamination (FIG. 22A), the example stator (FIG. 22B), the example rotor (FIG. 22C), the example prototype (FIG. 22D) of the PMC PMVM 100-1. FIG. 22E shows the example control system for the PMC PMVM 100-1 and FIG. 22F shows an example test rig for the PMC PMVM 100-1. As illustrated in FIGs. 22E and 22F, the prototype is driven by a three-phase full-bridge voltage source inverter (VSI), and a servo motor coupled with a mechanical gearbox acts as the load. The torque signal is measured by a high- precision HBM torque transducer T21WN, while the voltage and current signals arc measured by a high-performance LECROY motor drive analyzer (i.e. , model MDA 8058HD).

[0082] Firstly, to validate the concept of the PMC winding, the voltages induced in the three-phase windings are examined, with only phase A current injection. It should be noted that the rotor is latched by the servo motor to eliminate the back-EMF induced by the PM rotor, and the injected current frequency is set as 190 Hz (corresponding to 600 r / min operation) so that the effect of winding resistance is overwhelmed by the reactance. Even though the magnetic circuit is affected by the presence of PMs, the PMC concept can still be validated, as illustrated in FIGs. 23A and 23B, indicating that the induced voltages in phases B and C are aligned with phase A. This confirms that the phase mutual inductance / coupling is positive for the proposed PMC PMVM.

[0083] When operating speed is lower than the comer speed, MTPA control (i.e., id=0 control for PMVM) is implemented with a rated phase current amplitude of 14.5 A. The measured steady-state torque and current waveforms at 200 r / min and 600 r / min (10 Nm / div, 10 A / div) are shown in FIGs. 24A and 24B, respectively. The experimental output torque is 22.8 Nm, exhibiting a 5.0% discrepancy with the simulation results. The error is acceptable and attributed to fabrication imperfections. The power factor is measured at 200 r / min (50 V / div, 10 A / div) as depicted in FIG. 25, where Vallais the phase voltage / current generated by the VSI, and Va IIRis the filtered fundamental voltage component using the built-in infinite impulse response (IIR) filter of the motor drive analyzer. The measured power factor is 0.82, showing a good consistency with the simulated results.

[0084] As speed increases beyond the corner speed, field-weakening control is adopted, with the DC bus voltage limit set to 190 V. The key performance metrics including averagetorque, output power, power factor, and operating efficiency are measured and illustrated in FIGs. 26 A to 26D. In particular, FIGs. 26 A to 26D illustrates validation of field- weakening performance for electromagnetic torque (FIG. 26A), output power (FIG. 26B), power factor (FIG. 26C) and efficiency (FIG. 26D). It should be noted the maximum operating speed is limited to 3000 r / min, considering the high operation frequency of the prototype (i.e., 950 Hz at 3000 r / min) and the limited switching frequency of the VSI (i.e., 10 kHz). As can be seen, the experimental results exhibit the same variation trend and good agreement with the FEA predicted results. FIG. 26B indicates that the experimental error in output power tends to increase with speed due to the increased friction at high speeds. Despite this issue, the discrepancy in output torque and power across the entire testing range is lower than 10%. It is worth noting that even though the boundary speed of CPSR (i.e., 4200 r / min) is beyond the testing range, the output power measured in FIG. 26B shows no sign of drop even under the highest testing speed. In particular, the prototype exhibits an output power of 1429. 9 W and 1693.5 W when operating at 600 r / min (rated) and 3000 r / min (highest in experiments), respectively. The experimental results validate the PMC PMVM can extend the CPSR, with the tested CPSR ratio being higher than 5. This is superior to the conventional PMVM 300- 1 , which typically exhibits a CPSR ratio of less than 2.

[0085] Accordingly, various example embodiments investigate the concept and feasibility of PMC PMVM 100-1 , with primary focus on improving field-weakening and power factor. Distinct from the conventional NMC PMVM 300-1, in which the -axis phase self- and mutual armature flux linkages are superimposed on each other, the PMC PMVM 100-1 exhibits counteracted q-axis flux linkages and reduced terminal voltage. As a result, the field-weakening and power factor can be improved dramatically. The design methodology to realize PMC winding according to various example embodiments of the present invention is illustrated based on winding function theory and exemplified on a PMVM with 24-slot, 5-armature pole pair, and 19-rotor pole pair. The simulation and experimental results validate that the investigated PMVM 100-1 exhibits an improved power factor, enhanced torque capability, and expanded constant torque and power speed regions than the conventional NMC PMVM 300-1. In specific, the rated power factor is improved from 0.70 to 0.81, and the corner speed of constant torque region is increased from 600 r / min to 695 r / min. Moreover, the CPSR ratio is improved from 3 to 6, with the base power improved by 15.70%. As a result, the PMC PMVM 100-1 exhibits great potential in application scenarios that require both high torque density at low-speed operation and high-power capability across a wide speed range.

[0086] As explained hereinbefore, it will be appreciated by a person skilled in the art that the present invention is not limited to a PM machine in the form of a PMVM and may be in the form of other types of PM machine, such as but not limited to, a PMSM (e.g., a surface-mounted PMSM 100-2 as illustrated in FIG. IB or an inset PMSM 100-3 as illustrated in FIG. 1C). As further illustrative examples, benefits of employing the PMC winding to surface and inset PMSMs 100-2, 100-3 will now be described according to various example embodiments of the present invention.

[0087] The main distinction between PMSMs and PMVMs lies in the operating principle that PMVMs rely on the field modulation effect, where the rotor PM field is modulated by the stator teeth to produce a new field that interacts with the armature field to generate steady torque. Therefore, for any given PMSM (whether with a surface -mounted or inset PM rotor), a corresponding PMVM counterpart exists, differing only in the number of PM pole-pairs. In other words, the stator structure and winding configuration are identical in both PMSMs and PMVMs Accordingly, the multi-phase PMC winding design described hereinbefore with respect to PMVM can also be directly applied to PMSMs, such as surface -mounted and inset PMSMs.

[0088] To validate the above analysis, the multi-phase windings for the surface-mounted and inset PMSMs 100-2, 100-3 are configured in the same way as for the PMVM 100-1, while the main difference i the PM rotor structure. In particular, due to field modulation, the number of stator slots at the stator is equal to a sum of the number of permanent magnet rotor pole pairs and the number of armature pole pairs in PMVMs 100-1. In contrast, the number of permanent magnet rotor pole pairs should be equal to the number of armature pole pairs in surface and inset PMSMs 100-2, 100-3. As a result, the main difference between PMVM and PMSM is the PM rotor configuration and PM pole -pair numbers.

[0089] For comparison with the surface PMSM 100-2 with PMC winding, FIG. 27 depicts a schematic drawing of a topology (or cross section) of a surface PMSM 2700 with conventional NMC winding. FIG. 28 shows the comparison of output torque and power factor between the surface PMC PMSM 100-2 and the conventional NMC PMSM 2700. With the present PMC winding, the surface PMSM 100-2 can employ a higher ( / -axis current to generate output torque and power, due to the counteracted ( / -axis flux linkage. As validated in FIG. 28, during fieldweakening operation, the PMC PMSM 100-2 exhibits a slower decrease in output torque and power when compared to the conventional NMC PMSM 2700. In specific, the constant torque range is extended from 1400 r / min to 1600 r / min. Furthermore, the CPSR of the conventionalNMC PMSM 2700 ranges from 1400 r / min to 5600 r / min with a base power of 3773 W, whereas the PMC PMSM 100-2 demonstrates a wider CPSR, ranging from 1600 r / min to over 8000 r / min with a base power of 4101 W.

[0090] For comparison with the inset PMSM 100-3 with PMC winding, FIG. 29 depicts a schematic drawing of a topology (or cross section) of an inset PMSM 2900 with conventional NMC winding. FIG. 30 shows the comparison of output torque and power factor between the inset PMC PMSM 100-3 and the conventional inset NMC PMSM 2900. With the present PMC winding, the inset PMSM 100-3 can employ a higher ( / -axis current to generate output torque and power, due to the counteracted ( / -axis flux linkage. As validated in FIG. 30, during fieldweakening operation, the inset PMC PMSM 100-3 exhibits a slower decrease in output torque and power when compared to the conventional inset NMC PMSM 2900. In specific, the constant torque range is extended from 1200 r / min to 1400 r / min. Furthermore, the CPSR of the conventional inset NMC PMSM 2900 ranges from 1200 r / min to 4000 r / min with a base power of 2482 W, whereas the inset PMC PMSM 100-3 demonstrates a wider CPSR, ranging from 1400 r / min to over 5200 r / min with a base power of 2698 W.

[0091] While embodiments of the invention have been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced.

Claims

1. CLAIMS1. A permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots, wherein each phase winding of the multi-phase windings comprises a plurality of coils, each pair of overlapping coils of different coil groups of the multi-phase windings arc configured to have a same coil connection direction corresponding to a same current flow direction, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots, and each coil of the plurality of coils of said each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

2. The permanent magnet machine according to claim 1 , wherein the multi -phase windings are configured on the stator through the plurality of stator slots with a regular spatial interval among the multi-phase windings to form symmetrical multi-phase windings.

3. The permanent magnet machine according to claim 1 or 2, wherein the multi -phase windings are three-phase windings and said each coil of the plurality of coils belongs to one of two different coil groups based on the phase angle of the magnetomotive force associated with the coil.

4. The permanent magnet machine according to any one of claims 1 to 3, configured as a permanent magnet vernier machine or a permanent magnet synchronous machine, the permanent magnet synchronous machine being a surface-mounted permanent magnet synchronous machine or an inset permanent magnet synchronous machine.

5. The permanent magnet machine according to claim 4, wherein the permanent magnet machine is configured as the permanent magnet vernier machine, andthe rotor, the stator and the multi-phase windings are configured such that the number of stator slots at the stator is equal to a sum of the number of permanent magnet rotor pole pairs and the number of armature pole pairs of the permanent magnet machine.

6. The permanent magnet machine according to claim 4, wherein the permanent magnet machine is configured as the permanent magnet synchronous machine, and the rotor, the stator and the multi-phase windings are configured such that the number of permanent magnet rotor pole pairs is equal to the number of armature pole pairs of the permanent magnet machine.

7. The permanent magnet machine according to any one of claims 1 to 6, wherein the permanent magnet machine is a permanent magnet generator or a permanent magnet motor.

8. A method of configuring a permanent magnet machine, the permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets ; and a stator having a plurality of stator slots, the stator being arranged to house the rotor therein, the method comprising: installing multi-phase windings on the stator through the plurality of stator slots, wherein each phase winding of the multi-phase windings comprises a plurality of coils, said installing the multi-phase windings on the stator comprises configuring each pair of overlapping coils of different coil groups of the multi-phase windings to have a same coil connection direction corresponding to a same current flow direction, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots, and each coil of the plurality of coils of said each phase winding belongs to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil.

9. The method according to claim 8, wherein said installing the multi-phase windings on the stator further comprises configuring the multi-phase windings on the stator through the plurality of stator slots with a regular spatial interval among the multi-phase windings to form symmetrical multi-phase windings.

10. The method according to claim 8 or 9, wherein the multi-phase windings are three-phase windings and said each coil of the plurality of coils belongs to one of two different coil groups based on the phase angle of the magnetomotive force associated with the coil.1 1. The method according to any one of claims 8 to 10, the permanent magnet machine is configured as a permanent magnet vernier machine or a permanent magnet synchronous machine, the permanent magnet synchronous machine being a surface-mounted permanent magnet synchronous machine or an inset permanent magnet synchronous machine.

12. The method according to claim 11, wherein the permanent magnet machine is configured as the permanent magnet vernier machine, and the rotor, the stator and the multi-phase windings are configured such that the number of stator slots at the stator is equal to a sum of the number of permanent magnet rotor pole pairs and the number of armature pole pairs of the permanent magnet machine.

13. The method according to claim 11, wherein the permanent magnet machine is configured as the permanent magnet synchronous machine, and the rotor, the stator and the multi-phase windings are configured such that the number of permanent magnet rotor pole pairs is equal to the number of armature pole pairs of the permanent magnet machine.

14. The method according to any one of claims 8 to 13, wherein the permanent magnet machine is a permanent magnet generator or a permanent magnet motor.

15. A method of reconfiguring a permanent magnet machine, the permanent magnet machine comprising: a rotor comprising a plurality of permanent magnets; a stator having a plurality of stator slots, the stator being arranged to house the rotor therein; and multi-phase windings installed on the stator through the plurality of stator slots,wherein each phase winding of the multi-phase windings comprises a plurality of coils, and the method comprises: assigning each coil of the plurality of coils of said each phase winding to one of a plurality of different coil groups based on a phase angle of a magnetomotive force associated with the coil; identifying each pair of overlapping coils of different coil groups of the multiphase windings configured to have opposite coil connection directions corresponding to opposite current flow directions, said each pair of overlapping coils overlap at at least one stator slot of the plurality of stator slots; and reconfiguring, for each identified pair of overlapping coils, one of the overlapping coils of the identified pair of overlapping coils such that the identified pair of overlapping coils have a same coil connection direction corresponding to a same current flow direction.

16. The method according to claim 15, wherein said reconfiguring one of the overlapping coils of the identified pair of overlapping coils comprises: maintaining a first coil side of said one of the overlapping coils at a stator slot of the plurality of stator slots where the identified pair of overlapping coils overlap; and repositioning a second coil side, opposite to the first coil side, of said one of the overlapping coils to another stator slot of the plurality of stator slots such that the identified pair of overlapping coils have the same coil connection direction.

17. The method according to claim 16, wherein said another stator slot of the plurality of stator slots is determined based on a coil pitch of said one of the overlapping coils and is located in a direction from said stator slot opposite to that of an original stator slot of the second coil side.

18. The method according to claim 16 or 17, further comprising swapping coil sides, including the first coil side of said one of the overlapping coils, between different layers at said stator slot for maintaining a same magnetomotive force direction in said stator slot.

19. The method according to any one of claims 15 to 18, wherein the multi-phase windings are configured on the stator through the plurality of stator slots with a regular spatial interval among the multi-phase windings to form symmetrical multi-phase windings.

20. The method according to any one of claims 15 to 19, wherein the multi-phase windings are three-phase windings and said each coil of the plurality of coils is assigned to one of two different coil groups based on the phase angle of the magnetomotive force associated with the coil.

21. The method according to any one of claims 15 to 20, wherein the permanent magnet machine is configured as a permanent magnet vernier machine, or a permanent magnet synchronous machine, the permanent magnet synchronous machine being a surface-mounted permanent magnet synchronous machine or an inset permanent magnet synchronous machine.

22. The method according to claim 21, wherein the permanent magnet machine is configured as the permanent magnet vernier machine, and the rotor, and the stator and the multi-phase windings are configured such that the number of stator slots at the stator is equal to a sum of the number of permanent magnet rotor pole pairs and the number of armature pole pairs of the permanent magnet machine.

23. The method according to claim 21, wherein the permanent magnet machine is configured as the permanent magnet synchronous machine, and the rotor, the stator and the multi-phase windings are configured such that the number of permanent magnet rotor pole pairs is equal to the number of armature pole pairs of the permanent magnet machine.

24. The method according to any one of claims 15 to 23, wherein the permanent magnet machine is a permanent magnet generator or a permanent magnet motor.

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