Fractional-slot Machines Research Articles

A Comparative Study of Pole–Slot Combination with Fractional Slot Concentrated Winding in Outer Rotor Permanent Magnet Synchronous Generator for Hybrid Drone System

This paper is a comparative study of pole–slot combinations with fractional slot concentrated windings in an outer rotor permanent magnet synchronous generator (ORPMSG) for a hybrid drone system. Fractional slot machines have been studied for automotive applications because of their high performance and simple winding manufacturing, compared with those of integer slot machines. In this study, four pole–slot combinations of ORPMSG with fractional slot concentrated windings were selected for comparison with the performance of the hybrid drone system. Based on the results of a finite element analysis (FEA), the machines were analyzed for cogging torque, back electromagnetic force (BEMF), torque, and electromagnetic loss under the same conditions as the machine specifications. Among the four pole–slot combinations of the ORPMSM, a one pole–slot model of the ORPMSG was selected, considering the performances of the machines. The selected pole–slot model of the ORPMSG was manufactured, and experiments were conducted on the manufactured model to verify the FEA results. Finally, the effectiveness of the comparative study of pole–slot combination with fractional slot concentrated winding in ORPMSM was verified by comparing the FEA and experimental results.

Design for Reliability: The Case of Fractional-Slot Surface Permanent-Magnet Machines

Surface permanent-magnet machines are widely used in different applications, from industrial automation to home appliance and electrical traction. Among any possible machine topology, the fractional-slot surface permanent-magnet one has gained increasing importance, because of its high torque density, low cogging torque, extended flux weakening capability and high efficiency. In addition, fractional-slot machines are attractive for tooth concentrated windings, which allow some optimized manufacturing solutions such as modular stator tooth and high slot filling factor, which result in copper volume reduction; cost reduction, and lower stator parasitic resistances. The slot–pole combination is one of the most important design parameter and, as shown in this paper, it affects performances and the robustness of the machine with respect to the manufacturing imperfections. In the literature, slot–pole combinations are optimized at design phase by finite-element analysis relying on a healthy machine model. The original contribution of this paper is a design for reliability method that models manufacturing defects and includes them at design phase in the optimization process of slot–pole combinations. A method is presented that allows defining the optimal design parameters for maximum performances and robustness towards unavoidable imperfections caused by tolerances of the manufacturing process.

Novel Dual-Stator Machines With Biased Permanent Magnet Excitation

This paper proposes high-torque-density dual-stator permanent magnet machines with biased permanent magnet (PM) excitation in the inner stator. The developed machine can be geometrically considered as an outer-rotor stator PM machine plus a separate outer stator similar to the conventional fractional-slot machines. Consequently, the proposed designs feature two different stator structures. Meanwhile, two sets of armature windings are employed to improve the space utilization ratio and torque density. The machine topologies and operating principles are first described. In addition, the analytical models of the machine are introduced, which are utilized to optimize the stator/rotor pole combination as well as the power splitting ratio between two stators. This design optimization is performed in order to maximize the torque capability with the constraint of copper loss. The electromagnetic characteristics of the proposed machine with different inner stator structures are evaluated and compared by the finite-element (FE) method. Finally, an optimized dual-stator biased PM machines prototype is manufactured and tested to verify the FE analyses.

Investigation of a less rare-earth permanent-magnet machine with the consequent pole rotor

Due to the rising price of rare-earth materials, permanent-magnet (PM) machines in different applications have a trend of reducing the use of rare-earth materials. Since iron-core poles replace half of PM poles in the consequent pole (CP) rotor, the PM machine with CP rotor can be a promising candidate for less rare-earth PM machine. Additionally, the investigation of CP rotor in special electrical machines, like hybrid excitation permanent-magnet PM machine, bearingless motor, etc., has verified the application feasibility of CP rotor. Therefore, this paper focuses on design and performance of PM machines when traditional PM machine uses the CP rotor. In the CP rotor, all the PMs are of the same polarity and they are inserted into the rotor core. Since the fundamental PM flux density depends on the ratio of PM pole to iron-core pole, the combination rule between them is investigated by analytical and finite-element methods. On this basis, to comprehensively analyze and evaluate PM machine with CP rotor, four typical schemes, i.e., integer-slot machines with CP rotor and surface-mounted PM (SPM) rotor, fractional-slot machines with CP rotor and SPM rotor, are designed to investigate the performance of PM machine with CP rotor, including electromagnetic performance, anti-demagnetization capacity and cost.

Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses

The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless dc (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modeling fractional-slot machines. The inaccuracy of phase variable model of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core-loss model is developed based on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model.

Analytical Calculation of Yoke Flux Patterns in Fractional-Slot Permanent Magnet Machines

Machine design problems are often solved under the assumption of no-load when calculating iron flux densities. However, it is particularly important to account for the fluxes from the stator currents, the armature reaction, in fractional-slot machines. The fluxes from the permanent magnets and the armature reaction both vary in time with the electrical frequency. By studying the flux that flows along the stator yoke behind every slot in such a machine, it is revealed that the armature reaction flux does not have the same amplitude behind all slots. In addition, it is revealed that the time-varying no-load and armature reaction fluxes are shifted in time, with different phase shifts behind different slots. The sum of the no-load and armature reaction fluxes, namely, the load flux, depends on both the amplitudes of the fluxes and the phase shift between them. The resulting load flux behind each slot varies significantly. In four investigated machines, the ratio of the highest to the lowest load flux amplitude ranges between 1.6 and 6. The load flux can be significantly higher than the no-load flux. The flux calculations are verified through finite-element analysis in all four machines, and the error in the maximum load flux ranges between 2% and 6%.

Design and Tests of a Four-Layer Fractional-Slot Interior Permanent-Magnet Motor

This paper deals with the design and testing of an interior permanent-magnet (IPM) machine that exhibits advanced features. It adopts fractional-slot (FS) nonoverlapped coil windings that reduces the end winding length, i.e., the Joule losses and machine cost. As a consequence, higher rated current can be supplied so that higher torque density and higher efficiency in a wide operating region can be reached. The rotor saliency increases the performance in flux-weakening operating region and the fault-tolerance capability. In order to decrease the torque ripple, it is important to minimize the interaction between the magnetomotive force (MMF) harmonics due to the stator currents and the rotor anisotropy. To do that, the winding has been optimized so as to minimize the MMF harmonics, taking advantage from the higher degree of freedom of the four-layer winding. However, the so-called slot-harmonics cannot be minimized by rearranging the winding coils. Hence, the rotor geometry has been designed so as to minimize the impact of such slot-harmonics. A 12-slot 10-pole IPM FS machine has been designed and manufactured. The experimental tests confirm the expectations.

PROPER SELECTION OF NUMBER OF SLOTS AND POLES IN FRACTIONAL SLOT PERMANENT MAGNET MACHINES: LOSS REDUCTION APPROACH

Spatial harmonics of magneto motive force induces electrical current in conductive parts of rotor which causes losses in rotor. These losses in fractional slot machines due to high content of spatial harmonic are high. This article aims at introducing a method for rotor losses comparison in different combination of slot per pole in fractional slot and integral slot machines. In order to do that, first a method for winding design and then a method for analytical calculation of losses will be provided. Next a rotor loss index will be introduced by which comparison of different combination of slot per pole is achieved. This index enables one to choose the slot per pole combination that the minimum losses. Finally using the obtained information, two motor with different slot per poles combination were designed and built. The two motor losses were also comparing.

Influence of Slot and Pole Number Combinations on Voltage Distortion in Surface-Mounted Permanent Magnet Machines With Local Magnetic Saturation

The local magnetic saturation in tooth-tips of surface-mounted permanent magnet (SPM) machines generates on-load terminal voltage distortion, especially when small or closed slot openings are adopted. This paper focuses on investigating the influence of slot and pole number ( N s/2 p ) combinations on this phenomenon in both fractional slot and integer slot SPM machines. The mechanism of this phenomenon and how it is influenced by current advance angle and tooth-tip geometric parameters are introduced first. Then, voltage distortion pattern is proposed to analyze the occurring time or rotor positions of voltage ripples and their relative amplitudes according to the winding arrangements of different Ns /2 p combinations, with the influence of PM leakage flux considered. By 2-D finite-element analysis, the voltage distortion of various machines is calculated and compared, such as $N_{s} \pm 1 = 2p$ , $N_{s} \pm 2 = 2p$ , N s /2 p = 3/2 (3/4), and integer slot machines with slot number per pole per phase $q = 1$ or 2. The analysis results reveal that under the same comparison conditions, the integer slot machines have less voltage distortion than the fractional slot machines, especially when $q \geq 2$ . Meanwhile, for the same slot number, the fractional slot machines with $N_{s} > 2p$ suffer from on-load voltage distortion less than their counterparts with $N_{s} . Finally, three prototype machines with 12/10, 12/14, and 12/8 slot/pole numbers are manufactured and tested to validate the analyses.

Circulating currents of delta connected fractional slot machines for mass production

Circulating currents are a major issue in permanent magnet BLDC electric motors with delta connected windings. In 3-phase machinery they are driven by harmonics whose order is equal to a multiple of the number of phases. The harmonics occur because of special slot/pole combinations, rotor and stator asymmetries, phase imbalances and magnetic saturation inside the teeth and the yoke. In this publication all of these aspects are investigated. The advantages of delta compared to wye connection are also pointed out in terms of mass production. External sources of circulating currents like inverter operation are not part of this publication.

Design and Analysis of PM Fractional Slot Machine Considering the Fault Operation

Electromechanical actuators for automotive chassis applications such as active/semiactive suspensions, electric power steering, and electric brakes require high-performance electric machines. This paper analyzes the practicality of fractional slot permanent-magnet electric machines for these applications based on the full investigation of five candidate machines in terms of electrical, mechanical, and also fault performances. Machine designs that simultaneously achieve high torque/ampere, high torque/inertia, low torque ripple, and fast response required for these applications are presented. Two prototype machines were built and tested and found to meet the performance requirements.

Estimation of Eddy Current Loss in Semi-Closed Slot Vertical Conductor Permanent Magnet Synchronous Machines Considering Eddy Current Reaction Effect

This paper presents an analytical methodology based on subdomain field model to calculate eddy current loss in vertical conductor windings (VCWs) of surface mounted, radial flux, permanent magnet (PM) machines considering the current penetration effect. The proposed model can be used with any slot-pole combination including fractional slot machines having VCW. Initially, the model solves the two-dimensional problem based on the Laplace's and Poisson's equations using the separation of variables technique for each of the subdomains: PM, airgap, slot opening, and slot. Then, based on that obtained solution, the eddy current reaction field in the slot is calculated by solving complex Helmholtz's equation. The validity and accuracy of the model is verified using finite-element (FE) analysis. The limitations of analytical method are discussed.

Analysis of Fault-Tolerant Multiphase Power Converter for a Nine-Phase Permanent Magnet Synchronous Machine

The use of electrical drives and machines with very high number of phases is not a common topic of researchers, because of the control difficulties and the important number of switches needed to assure the operation in faulty conditions. The advantage of using a high number of legs/phases provides smooth mechanical performances (i.e., reduced torque ripples), without increasing the number of poles (this last approach, is usually applied for fractional-slot machines, increases frequency, and consequently the iron loss). The authors are proposing a nine-phase drive to supply a permanent magnet synchronous machine. A prototype of nine-phase drive machine is constructed. Its capability to operate in faulty conditions will be evaluated by numerical computation and tests. It will be proved that the proposed solution can operated even in the most severe faulted conditions (78% of the drive machine being faulted).

Faulty Operations of a PM Fractional-Slot Machine With a Dual Three-Phase Winding

The permanent-magnet (PM) machine with dual three-phase windings is proposed for applications requiring continuous operating even under a partial fault. The two windings are supplied by two separate inverters. Thus, in the event of a fault of one winding, this is disconnected, and the machine continues to be operated by means of the healthy winding. This paper investigates the PM machine with dual three-phase windings and its capabilities during faulty operating conditions. A fractional-slot interior PM machine with 12 slots and 10 poles is taken into account. Its performance is investigated according to different winding configurations. The torque behavior, overload capability, and thermal limits are evaluated under open-circuit and short-circuit faults. A finite-element analysis as well as experimental tests is carried out on a prototype of such a machine.

2-D Exact Analytical Model for Surface-Mounted Permanent-Magnet Motors With Semi-Closed Slots

This paper presents an analytical subdomain model to compute the magnetic field distribution in surface-mounted permanent-magnet (PM) motors with semi-closed slots. The proposed model is sufficiently general to be used with any pole and slot combinations including fractional slot machines with distributed or concentrated windings. The model accurately accounts for armature reaction magnetic field and mutual influence between the slots. The analytical method is based on the resolution of two-dimensional Laplace's and Poisson's equations in polar coordinates (by the separation of variables technique) for each subdomain, i.e., magnet, air gap, slot-opening, and slots. Magnetic field distributions, back-EMF, and electromagnetic torque (including cogging torque) computed with the proposed analytical method are compared with those issued from finite-element analyses.

An Accurate Subdomain Model for Magnetic Field Computation in Slotted Surface-Mounted Permanent-Magnet Machines

The paper presents an accurate analytical subdomain model for computation of the open-circuit magnetic field in surface-mounted permanent-magnet machines with any pole and slot combinations, including fractional slot machines, accounting for stator slotting effect. It is derived by solving the field governing equations in each simple and regular subdomain, i.e., magnet, air-gap and stator slots, and applying the boundary conditions to the interfaces between these subdomains. The model accurately accounts for the influence of interaction between slots, radial/parallel magnetization, internal/external rotor topologies, relative recoil permeability of magnets, and odd/even periodic boundary conditions. The back-electromotive force, electromagnetic torque, cogging torque, and unbalanced magnetic force are obtained based on the field model. The relationship between this accurate subdomain model and the conventional subdomain model, which is based on the simplified one slot per pole machine model, is also discussed. The investigation shows that the proposed accurate subdomain model has better accuracy than the subdomain model based on one slot/pole machine model. The finite element and experimental results validate the analytical prediction.

IMPROVED ANALYTICAL MODEL FOR SURFACE-MOUNTED PM MOTORS CONSIDERING SLOTTING EFFECTS AND ARMATURE REACTION

This paper presents an exact analytical method for the computation of the magnetic fleld distribution in surface-mounted permanent-magnet (PM) motors for any pole and slot combinations including fractional slot machines. The proposed model takes into account the slotting efiect and the armature reaction magnetic fleld. The analytical method is based on the resolution of the two- dimensional Laplace's and Poisson's equations in polar coordinates (by the separation of variables technique) for each subdomain, i.e., magnet, airgap and slots. Magnetic fleld distributions, back electromotive force and electromagnetic torque (cogging torque and load torque) computed with the proposed analytical method are verifled with those obtained from flnite element analyses.

Impact of MMF Space Harmonic on Rotor Losses in Fractional-Slot Permanent-Magnet Machines

The fractional-slot permanent-magnet (PM) machines are used in many applications due to their high torque density, low torque ripple, and high efficiency. However, the fractional-slot machines are characterized by high contents of space harmonics in the air-gap MMF distribution. Such harmonics cause flux variation in the air gap, and the main consequence is the induced losses in the rotor. Depending on the combination of slots and poles of the machine, there are different harmonic contents and then rotor losses. By means of a simple model of the rotor losses, this paper investigates the link between the rotor losses and the combination of the slots and the poles of the fractional-slot PM machines.

Design considerations for fractional-slot winding configurations of synchronous machines

This paper presents some design considerations for synchronous machines characterized by a fractional number of slots per pole per phase. The main advantage of this configuration is a smooth torque, which is due to the elimination of periodicity between slots and poles. A second advantage is a higher fault-tolerant capability, making the machine able to work even in faulty conditions. However, the fractional-slot configuration presents a high content of MMF harmonics that may cause an unbalanced saturation and thus an unbearable torque ripple. A method to design fractional-slot machines is illustrated in this paper, including double-layer and single-layer windings. The analytical computation is extended to determine the harmonics of MMF distribution. Their effect is highlighted in isotropic as well as anisotropic machines. Finally, some considerations are reported to avoid unsuitable configurations

The M. M. F. wave of polyphase windings: With special reference to sub-synchronous harmonics

The m. m. f. waves of fractional slot windings or other irregular windings are found to contain harmonic components having wavelengths greater than two pole pitches. These are designated as sub-synchronous harmonics since their harmonic order is lower than that of the synchronously rotating wave. They induce currents in the damper windings of synchronous machines which may produce noticeable loss. Some test data concerning losses are included. These harmonics have an effect upon reactance and, under certain conditions, they may cause vibration. An appendix covers the calculation of the m. m. f. of three-phase fractional slot machines.