Surface-mounted Permanent Magnet Vernier Machine Research Articles

Analytical calculation of magnetic field in surface-mounted permanent-magnet vernier motors

This paper proposes an analytical method to calculate the on-load magnetic field, Back electromotive force (BEMF) and torque of the surface-mounted permanent-magnet vernier machine (SMPMVM) accounting for slots, tooth-tips, flux modulation pole slots (FMPS) and the shape of magnet. The on-load magnetic field is predicted according to the surface-current method of permanent magnet, subdomain model and the superposition principle. BEMF and torque are calculated based on the magnetic field. The results show that THD of open-circuit and on-load radial flux density in the SMPMVM with concentric magnet poles is smaller than that in the conventional SMPMVM with eccentric magnet poles. 30th and 50th harmonic orders are obvious between two motors. Moreover, the peak cogging torque of the motor with concentric magnet poles is almost six times of the peak cogging torque of motor with eccentric magnet poles. The finite-element and experimental results confirm that the developed analytical method has high accuracy for predicting the magnetic field, BEMF, cogging torque and on-load electro-magnetic torque of SMPMVM with different shape of magnet.

Design Trade-Off Between Torque Density and Power Factor in Surface-Mounted PM Vernier Machines Through Closed-Form Per-Unit Equations

Benefited from flux modulation effects, surface-mounted permanent magnet vernier machines (SPMVMs) present the high-torque low-speed properties, which can become the potential candidates for direct-drive applications. However, their power factor is inferior to conventional PM machines due to the large inductance caused by parasitic no-working harmonics. This paper is devoted to propose some design considerations of SPMVMs to make a good compromise between torque density and power factor. Via constructing closed-from per-unit equations, the cross-coupling influences of slot/pole combinations and normalized geometric variables on machine performances are revealed. It is found that there is a tradeoff between torque density and power factor. The high magnet thickness to air-gap length ratio is beneficial to decrease inductance, while the flux modulation effect under the large equivalent air-gap length would be impaired. Moreover, the pole-pair ratio, i.e., the PM pole-pair to armature winding pole-pair, should be carefully selected, where the SPMVMs with high pole-pair ratio have the relatively high magnetic loading owing to the strong flux modulation effects, whereas they suffer from the low power factor due to serious harmonic leakage inductance. In particular, taking the end-winding length into consideration, the high torque advantages of high pole-pair ratio SPMVMs under the same copper losses can be well performed with high length-radius ratio. Combined with the analysis, the preferable selections of critical parameters to satisfy various technical indexes are determined. Then, the general design approach is proposed, and two design examples are built and compared. Meanwhile, finite element analysis (FEA) and prototype experiments are carried out to verify the feasibility.

Reduction of Unipolar Leakage Flux and Torque Ripple in Consequent-pole PM Vernier Machine

This paper proposes a new consequent-pole permanent magnet vernier machine (CPMVM), which can be regarded as a combination of two conventional CPMVM with opposite polarities. Based on the simplified axial magnetic circuit model, it is verified that the proposed CPMVM can reduce the unipolar leakage flux. In order to reduce the torque ripple of machine and improve the output torque of machine, the flux barrier is placed on the rotor of the proposed machine. Then, the parameters of the proposed CPMVM are optimized and determined. Moreover, the electromagnetic performance, including no-load air-gap flux density, average torque and torque ripple, flux linkage, back-electromotive force, cogging torque, average torque, torque ripple, power factor and loss, is compared with conventional surface-mounted permanent magnet vernier machine (SPMVM) and CPMVM. Finally, it is demonstrated that proposed CPMVM with flux barrier can effectively reduce the unipolar leakage flux and greatly reduce the torque ripple of machine. Also, compared with the SPMVM, the proposed CPMVM with flux barrier saves more than 45% of the permanent magnet material without reducing output torque.

AC Losses in Form-Wound Coils of Surface Mounted Permanent Magnet Vernier Machines

Surface mounted permanent magnet Vernier (SPM-V) machines, because of their high torque density and multi-pole structure, are promising candidates for low-speed direct-drive applications. To achieve high torque density, the SPM-V machines are generally designed with high gear ratios. Therefore, their operating frequencies can be much higher than those of the conventional SPM machines. This potentially increases the alternating current (AC) winding losses, especially those with form-wound coils proposed for high-power applications. This article investigates the AC losses (including skin effect, proximity effect, rotor PM induced, and circulating current losses) in form-wound stator coils of a 3 MW direct-drive SPM-V machine with different slot/pole number combinations. The study reveals that the SPM-V machines have significantly higher AC winding losses than their conventional SPM counterparts for similar operating conditions. To reduce the AC winding losses in SPM-V machines, a novel flux shunt concept is proposed along with other conventional techniques such as increasing the number of turns/coil (with terminal voltage being kept constant) and parallel strands/turn, providing extra clearance at slot opening. With the loss reduction techniques implemented, the SPM-V machines can achieve comparable efficiency but much higher torque density than their conventional counterparts. Moreover, the proposed flux shunt was also found to be very effective in reducing the potential risk of permanent magnet (PM) irreversible demagnetization, a key issue for SPM-V machines at high power ratings.

Effect of Airgap Length on Electromagnetic Performance of Permanent Magnet Vernier Machines With Different Power Ratings

This article investigates the effect of airgap length on the electromagnetic performance of direct-drive surface mounted permanent magnet Vernier (SPM-V) machines with different power ratings. Using 3 kW machine as an example, its performance is comprehensively compared with a conventional SPM machine with the same airgap lengths using two-dimensional finite-element analysis. For each airgap length, the slot&#x002F;pole number combination for the SPM-V machine is investigated to achieve the optimal performance compared to the conventional SPM machine. In order to make the study more generic, the slot&#x002F;pole number and the airgap length variations are expressed as normalized pole pitch, i.e., <inline-formula><tex-math notation="LaTeX">$\overline {{{\boldsymbol{\tau }}_{\boldsymbol{r}}}} $</tex-math></inline-formula> (ratio of rotor pole pitch to electromagnetic airgap length). The results show that for 3 kW machines, <inline-formula><tex-math notation="LaTeX">$\overline {{{\boldsymbol{\tau }}_{\boldsymbol{r}}}} $</tex-math></inline-formula> &gt;2.2 is a good design criterion for the SPM-V machines to achieve higher average torque and efficiency than the conventional SPM machines. In addition, a reasonably good power factor (&gt;0.9 in this case) can be achieved. Although the power factor of SPM-V machines drops significantly at multi-MW power level, i.e., 3 and 10 MW, the criterion <inline-formula><tex-math notation="LaTeX">$\overline {{{\boldsymbol{\tau }}_{\boldsymbol{r}}}} $</tex-math></inline-formula> &gt;2.2 still results in achieving a performance closest to their optimal capability. However, when <inline-formula><tex-math notation="LaTeX">$\overline {{{\boldsymbol{\tau }}_{\boldsymbol{r}}}} $</tex-math></inline-formula> &gt;2.2, special consideration should be paid to avoid potential irreversible magnet demagnetization at multi-MW power levels.

Multicriteria Optimal Latin Hypercube Design-Based Surrogate-Assisted Design Optimization for a Permanent-Magnet Vernier Machine

This article proposes an efficient surrogate-assisted design optimization method based on a multicriteria optimal Latin hypercube design (LHD) for multi-objective optimization of a surface-mounted permanent-magnet vernier machine (SPMVM). An improved iterated local search (ILS) method is proposed to optimize the spatial distribution uniformity and orthogonality of LHDs so that the data feature over the wide ranges of optimization variables can be captured more efficiently. Using the optimal LHD, a highly generalizable surrogate model can be trained with fewer samples, thus greatly reducing the required number of finite element analysis (FEA) cases and improving the optimization efficiency. A prototype corresponding to the optimal design is built and measured to validate the proposed method.

Investigation of scaling effect on power factor of permanent magnet Vernier machines for wind power application

This study investigates the scaling effect on power factor of surface mounted permanent magnet Vernier (SPM-V) machines with power ratings ranging from 3 kW, 500 kW, 3 MW to 10 MW. For each power rating, different slot/pole number combinations have been considered to study the influence of key parameters including inter-pole magnet leakage and stator slot leakage on power factor. A detailed analytical modelling, incorporating these key parameters, is presented and validated with two-dimensional finite-element analysis for different power ratings and slot/pole number combinations. The study has revealed that with scaling (increasing power level), significant increase in electrical loading combined with the increased leakage fluxes, i.e. (i) magnet leakage flux due to large coil pitch to rotor pole pitch ratio, (ii) magnet inter-pole leakage flux and (iii) stator slot leakage flux, reduces the ratio of armature flux linkage to permanent magnet flux linkage and thereby has a detrimental effect on the power factor. Therefore, unlike conventional SPM machines, the power factor of SPM-V machines is found to be significantly reduced at high power ratings.

Scaling Effect on Electromagnetic Performance of Surface-Mounted Permanent-Magnet Vernier Machine

This article investigates the impact of scaling on the electromagnetic performance of surface-mounted permanent-magnet Vernier (SPM-V) machines with a main focus on open-circuit induced Electro Motive Force (EMF). Three different power ratings, i.e., 3 kW, 500 kW, and 3 MW, have been chosen for this article. For each power rating, the SPM-V machines are analyzed for different slot/pole number combinations to compare their optimal performance with a conventional SPM machine. Step-by-step development of an analytical equation is presented for the prediction of induced EMF taking into account the interpole leakage of rotor permanent-magnets. 2-D finite-element analysis (FEA) has been used to validate the analytical equation across different power ratings. The analytical equation is thereafter utilized to study the influence of different geometric parameters on the performance of the SPM-V machines. It reveals that the back EMF and torque of SPM-V machines, for a given normalized pole pitch (rotor pole pitch to magnetic airgap length), are unaffected by the increase in airgap length due to scaling. However, the power factor of SPM-V, unlike the conventional SPM, reduces significantly with the increase in electrical loading due to the scaling effect. The analytical model for induced EMF and the 2-D FEA predicted results are validated by experiments using conventional SPM and SPM-V machine prototypes.

System-Level Investigation of Multi-MW Direct-Drive Wind Power PM Vernier Generators

Surface mounted permanent magnet Vernier (SPM-V) machines are known for their high torque density but relatively poor power factor compared to conventional SPM machines. The high torque density feature of the SPM-V machines is desirable for direct-drive offshore wind power applications as it leads to reduced generator size, mass and cost. However, their poor power factor can negatively affect the converter cost and efficiency. This paper compares the system-level performance, including generator active and structural components and converter, between the SPM-V and the conventional SPM generator systems. Four different power ratings, i.e. 0.5MW, 3MW, 5MW and 10MW, have been considered to study the trend of system-level performance with increasing power rating. The study shows that the SPM-V generators can be lighter and cheaper than their conventional SPM counterparts. However, after the consideration of converter cost and efficiency, the conventional SPM generator exhibited slightly better overall performance. Nonetheless, with the development of novel Vernier topologies and reduction in converter costs in the future due to emerging technologies, the Vernier generators can still be competitive for direct-drive offshore wind power applications.

Design and Analysis of Surface-Mounted PM Vernier Machines Considering Harmonic Characteristics of Winding MMF

This paper proposes a design method for the flux modulation poles (FMPs) formed on the stator of surface-mounted permanent magnet vernier machines (SPMVM) considering the winding configurations. In three types of the SPMVM with the different winding configurations, the FMP shapes to maximize the output torque are optimized by employing the analytical equations for the magneto-motive force (MMF) due to the windings, permeance, and flux density in the air-gap. Then, the validity of the optimal shapes for the FMPs is verified by the finite element analysis. It is found that the optimal FMP shapes are designed differently in the three types of the SPMVM and increase the output torque by different ratios according to the winding configurations. In addition, the experimental results for the prototype show that the proposed method can optimally design the FMP shape by analyzing mathematically the effects of the winding configuration and the FMP shape on the output torque of the SPMVM.

Investigation of Spoke Array Permanent Magnet Vernier Machine With Alternate Flux Bridges

In recent years, permanent magnet vernier (PMV) machines are attracting more and more attentions owing to their high torque density feature, which is mainly benefited from its special operation principle called flux modulation effect. Nevertheless, It is found that its working flux density is low, viz., ∼0.3T for modulated flux density in the surface mounted PMV machines. Hence, there is a really large space to further improve the torque density of PMV machine. The spoke array magnet is widely used in the regular PM machine to improve working flux density. However, the flux barrier effect of spoke array magnet for the PMV machine has been proved, and a large torque reduction would be introduced in the high pole ratio spoke array PMV machine. In this paper, a novel spoke array PMV machine is proposed to improve working flux density and the torque density of PMV machines. The alternate magnetic bridges are added in the rotor core to connect iron pieces with same polarity and provide magnetic circuit for the low-pole number working magnetic field, hence the no-load back EMF and output torque of the proposed machine can be significantly improved. Moreover, analytical airgap flux density distribution based on equivalent magnetic circuit is presented to reveal the mechanism of working flux density improvement, and finite element analysis is used to investigate the performance features and structure parameter influence on the key performances, viz., back EMF and torque, of the proposed machine. Finally, a 25 N·m prototype has been built and tested to validate these analyses.

A Novel Design Method for the Geometric Shapes of Flux Modulation Poles in the Surface-Mounted Permanent Magnet Vernier Machines

This paper presents a novel approach to determine geometric shapes of flux modulation poles (FMPs) by using the analytical equations for flux density distribution due to armature windings. The magnetic field by the windings is modulated by the FMPs. Then, the resulting magnetic field produces the torque by interacting with the rotor permanent magnets (PMs). Thus, to improve the output power of the machine, the FMP shape should be optimized in terms of the magnetic flux modulation. To do so, the permeance function which can consider the changes of the geometric parameters for the FMPs is defined using the Fourier series analysis method. Consequently, the working harmonic, which is the spatial harmonic of the air-gap magnetic field due to the windings and creates the torque, is given as the function of the geometric variables. The optimal set of design variables to maximize the working harmonic in the analytical equation is obtained by employing the genetic algorithm. The finite element analysis results show that the proposed method improves the output torque of the surface-mounted permanent magnet vernier (SPMV) machines up to 31%. In addition, the torque ripple can be minimized by regulating the harmonic components of the permeance in the analytical equations.

Influences of Winding MMF Harmonics on Torque Characteristics in Surface-Mounted Permanent Magnet Vernier Machines

This paper presents the influences of winding magneto-motive force (MMF) harmonics on the torque characteristics in surface-mounted permanent magnet vernier (SPMV) machines. Based on the magnetic gearing effects, the armature magnetic field of the SPMV machines is modulated by flux modulation poles (FMPs). In the modulated magnetic field, a working harmonic which corresponds to the number of the rotor pole pairs generates torque. Unlike regular PM machines, the winding MMF harmonics in the SPMV machines can produce the working harmonic by adjusting the FMP shapes. In order to investigate the effects of the winding MMF harmonics, the operating principle of the SPMV machines is elaborated by an analytical method using the winding MMF distribution and air-gap permeance function. After that, the design method of the FMP shapes that can improve the output torque by using the winding MMF harmonics is proposed. For the SPMV machine having 6 slots and 24 FMPs, the effects of the winding MMF harmonics and the validity of the proposed design method are confirmed by the finite element analysis method. It is shown that the proposed design method can improve the performances of the SPMV machine in terms of the torque density, induced electromagnetic force, and efficiency.

Dual-stator Interior Permanent Magnet Vernier Machine Having Torque Density and Power Factor Improvement

—An improved topology for a low-speed permanent magnet vernier machine, called a dual-stator interior permanent magnet vernier machine, is introduced to significantly increase torque density and power factor. A dual-stator is adopted in the design for more torque and improving space utilization. An interior spoke-type magnet array in the rotor is designed for magnet flux focusing, which can effectively increase useful flux and force flux lines to pass through the entire machine during operation as opposed to two separate torque components as in a normal dual-stator permanent magnet machine. To clearly place the advantages of the proposed topology in perspective, the proposed dual-stator interior permanent magnet vernier machine is compared to a well-known dual-stator surface-mounted permanent magnet vernier machine. This article discusses the operation principle and magnetic field analysis of the proposed machine and reports comparison simulation results taken from the finite-element method. In addition, the stator tooth is optimized for further better performance on torque density and power factor.