Permanent Magnet Vernier Machine Research Articles

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.

Permanent Magnet Vernier Machines for Direct-Drive Offshore Wind Power: Benefits and Challenges

Permanent magnet Vernier (PM-V) machines, at low power levels (few kWs), have shown a great potential to improve the torque density of existing direct-drive PM machines without much compromising on efficiency or making the machine structure more complicated. An improved torque density is very desirable for offshore wind power applications where the size of the direct-drive machine is an increasing concern. However, the relatively poor power factors of the PM-V machines will increase the power converter rating and hence cost. The objective of this paper is to review the benefits and challenges of PM-V machines for direct-drive offshore wind power applications. The review has been presented considering the system-level (direct-drive generator + converter) performance comparison between the surface-mounted permanent magnet Vernier (SPM-V) machines and the conventional SPM machines. It includes the indepth discussion on the challenges facing the PM-V machines when they are scaled up for multi-MW offshore wind power application. Other PM-V topologies discussed in literature have also been reviewed to asses their suitability for offshore wind power application.

Experimental Verification of Dual Airgap PMVM Having Yokeless Rotor for Extended Speed Application

Permanent magnet vernier machines (PMVM) are recently proven to be a good candidate for extended-speed operation in the constant power region. In this paper, a dual-airgap PMVM having a yokeless rotor has been presented for extended-speed operation. The PMVM model is designed with two stators and a sandwiched rotor without an iron yoke. To achieve the extended speed operation, the yokeless structure of dual airgap PMVM benefits from the increased inductance which makes it possible to operate at higher speeds. For this purpose, the prototype of this machine is built, and experimental testing is performed to verify its performance in a constant power region. Electromagnetic performance such as back EMF and output torque at high speeds are analyzed. The experimental results are compared with those obtained using finite element analysis which confirms the ability of dual airgap PMVM having a yokeless rotor to perform well at higher speeds in a constant power region.

Split Pole Permanent Magnet Vernier Machine With Halbach Array Magnets in Stator Slot Opening and Consequent Pole Rotor

Due to simpler mechanical structure and magnetic gearing effects, Permanent Magnet Vernier Machines (PMVMs) attract researcher interest because of their higher torque density for direct drive applications. However, regular PMVMs utilize more rare earth Permanent Magnet (PM), which increases machine cost and weight. Moreover, the PMs are mounted on the rotor surface, which enhances flux leakage and flux circulation, which degrade electromagnetic performance that ultimately decreases average torque, torque density, power density and efficiency. A new Split Pole PMVM (SP-PMVM) with Halbach PM arrangement in the stator slot opening and consequent pole rotor is proposed to overcome the issues above. The proposed SP-PMVM enhanced flux modulation phenomena to improve electromagnetic performance. Comparing the proposed machine with the existing designs reveals that the proposed design reduces the PM utilization by 22.2% and improves the flux linkage by 41.3% due to suppression of leakage flux and flux circulation. Moreover, the average torque is boosted by 42.35%. Furthermore, torque and power densities are increased by 83.01% and 44.84%, respectively. In addition, in comparison with the existing conventional design, the efficiency of the proposed model is enhanced by 25.01% at the cost of 19.75% cogging torque.

Modeling and detection of demagnetization fault in permanent magnet vernier machine using flexible magnetic equivalent circuit method

In this paper, an analytical model is proposed for evaluating electromagnetic performances of permanent magnet vernier machines (PMVMs) under healthy and faulty conditions. The proposed model employs flexible magnetic equivalent circuit (MEC) method, which its accuracy can be selected by tunable parameters. The model is capable of considering the influence of saturation effect, skewed slots, slot leakage fluxes, and various winding arrangements for the machines with desired properties. First, the proposed model is used to predict the no-load performance of machine at healthy condition. Then, the machine loading behaviors under healthy and demagnetization fault conditions are analyzed by the MEC model. Moreover, the results of the proposed model are compared and validated with those of 2-D finite element method (FEM) and 3-D FEM. Eventually, a specific pattern is extracted from the stator current spectrum to detect the demagnetization fault.

Modelling and analysis of permanent magnet vernier machine using flexible magnetic equivalent circuit method

This paper develops a new model with adjustable accuracy to evaluate performance of permanent magnet Vernier machine (PMVM) based on flexible magnetic equivalent circuit (MEC) method. The desired machine parameters such as number of flux modulation poles (FMPs), winding pole-pairs, and geometrical dimensions can be chosen in the presented model. By utilizing nonlinear core magnetization curve, saturation effect is taken into account. There are two main contributions in this study. First, the flexible MEC model is developed to predict the machine performance accurately. The second contribution is that the developed model can be used to evaluate the performance of the machine under no-load and loading conditions at the same time. The results of MEC model under no-load and loading conditions are compared with 2D-finite element method (FEM) and 3D-FEM in terms of accuracy and simulation time. The results indicate acceptable accuracy and suitable processing time of the proposed MEC model.

Featured Cover

The cover image is based on the Review Article Single stator-single rotor permanent magnet Vernier machine topologies for direct-drive applications: Review and case study by Jawad Faiz et al., https://doi.org/10.1002/2050-7038.13240.

Single stator‐single rotor permanent magnet Vernier machine topologies for direct‐drive applications: Review and case study

Stator and rotor structures, arrangement of permanent magnets (PMs), and type of coils of PM Vernier machines are reviewed and classified. Then, electromagnetic performance and the energy conversion process in the machine are described. Determination of magnetic field distribution and air-gap permeance of the machine is very complicated than that of other PM machines. Impacts of variations of dimensions in the machine such as the number of modulators on the modulus width and the rotor PMs thickness on the load characteristics (cogging torque, back-EMF, and power factor) are investigated. In addition, principles of flux modulation machines operation are presented and the shape and dimensions of the modulators are optimized. The two-phase and four-phase winding types are used to improve the output power of the machine. Finally, a 150 W PM Vernier generator is designed and prototyped to feed the road speed camera.

Intern-turn fault modeling and diagnosis in permanent magnet vernier machine using modified magnetic equivalent circuit method

PurposeThe aim of this paper is to propose the model for analyzing the electromagnetic performances of permanent magnet vernier machines (PMVMs) under healthy and faulty conditions.Design/methodology/approachThe model uses interconnected reluctance network formed based on the geometrical approximations to predict magnetic performances of the machine. The network consists of several types of reluctances for modeling different parts of machine. Applying Kirchhoffs laws in the network and the machine windings, magnetic and electrical equations are obtained, respectively. To construct the model system of equations, the electrical equation is converted into algebraic form by using the trapezoidal technique. Moreover, the system of equations must be solved by Newton–Raphson method in each step-time because of considering the core saturation effect.FindingsThe proposed model is developed based on the modified magnetic equivalent circuit (MEC) method, in which the number of flux paths in different parts of the machine can be arbitrary selected. The saturation effect, skewed slots, the desired machine geometrical parameters and various winding arrangements are included in the proposed model; therefore, it can evaluate the time and space harmonics in modeling the PMVMs. Furthermore, a pattern for inter-turn fault detection is extracted from the stator current spectrum. Finally, 2 D-finite element method (FEM) and 3 D-FEM analysis are carried out to evaluate and verify the results of the proposed MEC model.Originality/valueGenerally, the element numbers have important role in modeling the machine and calculating its performance. Hence, the proposed MEC model’s capability to choose desired number of flux paths is advantage of this paper. Moreover, the developed MEC can be used for analyzing several electrical machines, including other types of vernier machines, with simple modification.

Design and Analysis of a Permanent Magnet Vernier Machine with Non-Uniform Tooth Distribution

To improve the torque performance of the permanent magnet vernier machine in the direct-drive system for Unmanned Aerial Vehicle (UAV), this paper proposes the topology of non-uniform tooth distribution. This distribution, considering the additional flux harmonics, aims to contribute to torque improvement, whereas the cogging torque also increases at the same time. A phasors method is proposed to solve the issue caused by the non-uniform structure, adjusting the mechanic angle of each tooth reasonably to restrict the cogging torque. In addition, the non-uniform design is illustrated in detail, which includes the method of grouping the teeth, considering the factors of series pole ratio and winding layout. By using the three-dimensional finite element method, torque is significantly increased without additional torque ripple, which satisfies the desired design target.

A Novel Consequent-Pole Modular-Mover Linear Permanent Magnet Vernier Machine for Thrust Ripple and Cost Reduction

Recently, linear permanent magnet vernier machine (LPMVM) is attracting more and more attention due to its high thrust density, high efficiency, and simple structure at low-speed operation, which makes it a preferable solution for direct-drive linear motion applications. In order to further reduce the thrust ripple and the cost of LPMVM, a novel consequent-pole modular-mover LPMVM (CM-LPMVM) is proposed and analyzed in this article. Due to the dual-flux-modulation effect, the proposed CM-LPMVM can exhibit a low thrust ripple (∼3.2% of the average thrust) and high thrust density (∼387 kN/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) at a low current density of 3 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , as well as reduce nearly half of the PM usage at the same time. The performance improvement of the proposed CM-LPMVM is verified by the comparison to a regular modular-mover LPMVMs, using the finite-element method. Finally, three prototypes are built and tested. The experimental results match well with the analytical data, showing the superiority of the proposed CM-LPMVM.

Robustness optimization of fault-tolerant permanent magnet vernier machine under multimode operation

<p indent=0mm>To enhance the electromagnetic torque of permanent magnet vernier machine parameters, a multi-objective optimization method considering the parameter uncertainty is proposed under multifault tolerant control modes. The proposed method solves the problem of uncertain parameters, which affects this machine. First, according to different open-circuit conditions under the fault-tolerant control mode, the optimization objectives and constraints are set up. Second, the torque and its ripple under different fault-tolerant operation modes are optimized using a deterministic genetic algorithm. Finally, the robustness of the machine is optimized using the 6<italic>σ</italic> quality optimization method. The results showed that the optimized permanent magnet vernier machine has excellent torque performance under multimode operation and significantly improved robustness.

Analysis and detection of turn‐to‐turn short circuit fault in a permanent magnet Vernier generator based on modified winding function

Operation of Vernier machines is based on flux modulation. They have some advantages including maintaining the rated torque in motor applications and the rated output power in generator applications at low speeds, high torque density and relatively low torque ripple due to their magnetic gear property and fault-tolerance. In recent years, the motor with various topologies has been developed for different applications. Therefore, analysing and monitoring different faults is essential in the design and implementation stages. This study has two main purposes. First, to introduce an accurate frequency index independent of load variations for detecting the turn-to-turn short circuit (TTSC) faults in the stator windings of a permanent magnet Vernier machine. Second, modelling the machine in a healthy condition and in the presence of TTSC faults to investigate its effect on machine performance and output characteristics. An analytical model is presented using the modified winding function theory under the TTSC fault by taking into account the effect of stator slots which enhances the accuracy of the air-gap permeance function estimation. In the process of calculating the fault index, frequency components of the output characteristics of the machine are obtained from the mathematical equations of the magnetic field. It is shown that the proposed indicators are robust against load variations.

Study of the Influence of the Armature Number of Phases on the Electromagnetic Torque Quality in PM Vernier VRM

This paper aims at dimensioning and studying three examples of PM Vernier machines with different number of armature phases to analyze, under the same conditions, the influence of the number of phases on the electromagnetic torque quality. An analytical energy model is first introduced along with the pre-design procedure which leads to a first three phase prototype (VRM_1). The performance of the latter is then studied using analytical approach and numerical modeling based 2 D FEM. Two other prototypes of 5 and 7 phases are sized using the same procedure and constraints as the first machine. Their performances are studied using the same approaches and the electromagnetic torques of the three structures are compared.

Analysis and Design of a Fault-Tolerant Permanent Magnet Vernier Machine With Improved Power Factor

This article aims to analyze and design a fault-tolerant permanent magnet Vernier (FTPMV) machine with improved power factor. Different from the existing FTPMV machine with uniform distributed split-teeth stator, hybrid stator and multiple working harmonics designs are adopted in this proposed machine. With these designs, the proposed machine can obtain not only improved power factor but also higher torque and good fault-tolerant performance. First, the topologies, fault-tolerant design and working principle of the proposed machine are introduced. Then, accurate permeance and equivalent magnetic circuit analytical models are established for investigating the mechanism of power factor improvement. And the influences of some key design parameters on power factor and torque of the proposed machine are analyzed by finite element analysis. Finally, a FTPMV prototype is manufactured and tested to validate the designs and analyses.

Design and Analysis of Fractional Pole-Pair Linear Permanent Magnet Machine

A novel concept of fractional pole-pair linear permanent magnet machine (FP-LPM) has been proposed recently. It is found that using fractional pole-pair number in linear permanent magnet machine(LPM) could effectively reduce slot cogging force as well as back EMF unbalance. Thus thrust ripple is curtailed which improves its thrust quality and enhances its application potential. However, some issues of FP-LPM still remain unsolved, such as phase split, current phase adjustment, plus structure optimization is different from the traditional topology due to extra auxiliary tooth, etc. This paper contributes to giving a detailed designing methodology including winding arrangement, regulations of choosing slot/pole combination and effective end optimization method of FP-LPM. Thus, this paper can give helpful guidance in designing FP-LPM to satisfy different application demands. Finally, an 18slots/29poles fractional pole-pair linear permanent magnet vernier machine (FP-LPMVM) is designed and constructed using the proposed method and the test results verifies the research conclusions.

Design and Analysis of a Dual Airgap Radial Flux Permanent Magnet Vernier Machine with Yokeless Rotor

This paper presents a novel topology of dual airgap radial flux permanent magnet vernier machine (PMVM) in order to obtain a higher torque per magnet volume and similar average torque compared to a conventional PMVM machine. The proposed machine contains two stators and a sandwiched yokeless rotor. The yokeless rotor helps to reduce the magnet volume by providing an effective flux linkage in the stator windings. This effective flux linkage improved the average torque of the proposed machine. The competitiveness of the proposed vernier machine was validated using 2D finite element analysis under the same machine volume as that of conventional vernier machine. Moreover, cogging torque, torque ripples, torque density, losses, and efficiency performances also favored the proposed topology.

Characteristics Analysis of Consequent-Pole Ferrite Magnet Vernier Machine Using Novel Equivalent Magnetic Circuit

This study deals with a consequent-pole (CP) vernier motor with low-cost ferrite magnets. To investigate the magnetic behavior of the CP permanent magnet vernier machine (CP-PMVM) quantitatively, two magnetic equivalent models are newly proposed which are applied to estimate the main and the modulation flux densities in air gap, respectively. Using the proposed models, it is revealed that the CP structure substantially reduces the effective air-gap length, and thus, a CP-PMVM with half number of magnets has much higher modulation flux density than that of a regular surface PM vernier machine (SPMVM). Consequently, the CP-PMVM is expected to able to keep the vernier effect high even with thick ferrite magnets, producing higher back electromotive force (EMF) than the SPMVM does. Moreover, large variation of air-gap length due to thick magnet thickness leads to a considerable advantage of reluctance torque. For a proto-designed CP-ferrite PMVM, the electromagnetic characteristics, such as main and modulation flux densities, back EMF, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> inductances, and torque, have been investigated by using the proposed method as well as finite-element (FE) method. In addition, through the demagnetization analysis, it is proved that the proposed CP-PMVM has certainly enough antidemagnetization capability, whereas an SPMVM with ferrite magnets loses its magnetism. From the analysis results, it is confirmed that the proposed machine with less magnet volume and low-cost ferrite magnets has higher torque compared with its SPM vernier counterpart. Finally, to validate the analytical and numerical analyses, experimental results are provided.

Design and Comparison of Vernier Permanent-Magnet Machines With Different Winding Types Based on Fractional-Slot Windings

Vernier permanent-magnet (VPM) machines which have high torque density and high efficiency have been extensively used in direct drive. This article attempts to propose a new winding form and compare it with a traditional winding form as a part of fractional slot winding in the VPM machines to provide a design guideline in the aspect. Different winding forms are compared with the same copper loss and the same design. The design guideline of winding forms is provided by multiobjective generation algorithm (GA) optimization. Maximum torque value and minimum torque ripple are the optimization objectives in the GA optimization process. In addition, several models of the modularized motor with the new winding form based on the fractional-slot windings are compared, and the suitable application range of these models are discussed.

A Hybrid Analytical Model for Permanent Magnet Vernier Machines Considering Saturation Effect

This article proposes a new hybrid analytical model combining subdomain model and equivalent magnetic network for permanent magnet vernier machines, which are easy to get saturated due to the air-gap field modulation effect. The key is representing saturation effect by iterating equivalent surface current as part of interface conditions in the proposed subdomain model. First, five subdomains are divided to calculate magnetic field distribution. The equivalent surface current is utilized as the boundary constraint between subdomains and iron core. Second, the equivalent magnetic network is established based on stator structure, and the fluxes flowing into flux modulation poles are equivalent as the magnetic flux sources. Node magnetic potentials can be achieved with the application of Kirchhoff's law of current. Then, the equivalent surface current is updated for convergence by node magnetic potential to accurately predict saturated performance. Finally, a prototype is manufactured, and the effectiveness of the proposed hybrid model is verified by the finite-element analysis (FEA) and experimental results. The hybrid model combines the subdomain model and the equivalent magnetic network model to complement each other and it is demonstrated to be more efficient than the FEA model while maintaining high accuracy.