Magnetomotive Force Distribution Research Articles

Analysis and Comparison of Even-Order Back EMF Harmonics of Fractional-Slot Concentrated-Winding Consequent Pole Permanent Magnet Vernier Machines

Fractional-slot concentrated-winding (FSCW) consequent pole (CP) permanent magnet vernier (PMV) machines have received increasing attention due to their less magnet consumption but larger torque capability. However, the PM magnetomotive force (MMF) distribution is asymmetric in the CP structure. Thus, even-order air-gap flux density and back-electromotive force (back-EMF) harmonics are generated, which increases torque ripples. In this paper, to eliminate the even-order back-EMF harmonics and the resulting torque ripples, a comprehensive investigation on even-order flux density and back-EMF harmonics of five-phase FSCW CP PMV machines was presented, and then the general design rules without even-order back-EMF harmonics were summarized. Firstly, considering single- and double-layer windings, the effects of slot/pole number combination and flux modulator distribution on even-order flux density and back-EMF harmonics were analyzed. Secondly, the optimal slot/pole number combinations were selected, and then the rules for eliminating even-order back-EMF harmonics of CP PMV machines were summarized. As an extension, it was revealed that the harmonic elimination mechanism of CP PMV machines is applicable to CP-Halbach PMV machines. According to the summarized general design rules, the five-phase CP and CP-Halbach PMV machines with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> =20/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_r</i> =21/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_f</i> =10 were proposed. Their detailed performance has been comparatively analyzed and then the optimal one was selected for prototyping. Both finite element analysis (FEA) and experiments were carried out to validate theoretical analyses.

Winding Characteristics and Magnetization State Regulations of Variable Flux Memory Machines With Segregated Distributed Windings

The variable flux memory (VFM) machine with segregated multiple three-phase windings is investigated, with particular reference to its winding characteristics and magnetization state (MS) regulations. The overlapped distributed windings are separated into multiple three-phase winding sets with each set non-overlapped, which contributes to the independent relationship between the winding set and corresponding permanent magnet (PM) pole-pairs. Consequently, the single winding set can independently complete the MS regulation, and thus the overall current requirement is reduced. Moreover, it is revealed that the amplitude of de/re-magnetizing magneto-motive force (MMF) with single winding set operation is actually higher than those with multiple winding sets operation thanks to the asymmetric winding layout, resulting in the enhanced de/re-magnetizations and thus the further reduced de/re-magnetizing currents. The winding function, MMF distribution, inductance, and torque of the machine are analyzed, and intentional MS regulations with different methods are compared. A prototype machine is fabricated and tested for experimental validations.

D-Q Axis Inductance Analytical Calculation for Fractional-Slot Distributed Winding IPM Motor Based on Big-Small Pole Space Method

The d-q axis inductance is the crucial parameter for the interior permanent magnet (IPM) motor. In order to facilitate the design, analysis, and optimization of IPM motors, it is of great significance to develop an accurate and simplified inductance analytical calculation method. Among the existing calculation methods, the magnetic equivalent circuit (MEC) has advantages in the inductance calculation of the IPM motor due to the simple modeling, the fine processing of the saturation region and the visualization of the magnetic field distribution. However, the traditional MEC method is only applicable to the IPM motor with integer-slot distributed winding (ISDW) or fractional-slot concentrated winding (FSCW), while lacking of in-depth research on fractional-slot distributed winding (FSDW). The magnetic circuit topology of FSDW IPM motors is not as single as that of FSCW/ISDW IPM motors. It leads to problems in the traditional MEC method when dividing the d/q axis flux path in FSDW motors. To solve this problem and expand the applications of MEC method, a big-small pole space (BSPS) method is proposed after fully considering the common characteristics of MMF distribution and reluctance distribution in FSDW motors, which fills the gap of MEC method applied to FSDW motors. The BSPS method divides the d-axis flux path according to the asymmetry of the d-axis magnetomotive force (MMF). Based on the divided flux paths, an improved nonlinear MEC model that considers the saturation of stator and rotor is established to calculate d- and q-axis inductances. The results of finite element analysis (FEA) verify the validity of the proposed MEC model with different geometry parameters. Experimental results of an 84-pole/360-slot FSDW I-type IPM wind generator further confirm the validity of the proposed MEC model

AC Copper Loss Reduction in Planar Inductors With Magnetic Building Blocks-Based Gapless Parallel Symmetrical Magnetoresistance Structure

Fringing and proximity effects are the main reasons for serious ac copper loss in high-frequency planar inductors. In this article, a novel air-gapless core structure based on magnetic building blocks with magnetoresistance parallel and symmetrically distributed relative to the windings is proposed, in which two magnetic building blocks parallel to the PCB windings are made of metal soft magnetic material with low relative permeability and three magnetic building blocks perpendicular to windings are made of ferrite with high relative permeability. Equivalent magnetic circuit models and theoretical analysis for the proposed core structure reveal that even if the interleaved winding structure fails in the inductor, a better distribution of magnetomotive force can be obtained by optimizing the distribution of magnetoresistance. Compared with the conventional inductors using stand airgaps, both the fringing and proximity effects can be weakened by the designed parallel symmetrical magnetoresistance core structure, which has been verified in three-dimensional finite element analysis (FEA)-based simulations. The FEA calculated results show that the proposed optimized core structure can achieve a 46% reduction in ac resistance, and this advantage will extend with increasing frequency over a certain frequency range. The experimental validation includes converter efficiency test and inductor loss test on a high-frequency critical conduction mode Boost converter has been carried out, the maximum efficiency improvement was 1.4% and the inductor loss reduction is also verified.

Characteristic Analysis of Coreless-Type Linear Synchronous Motor With the Racetrack Coils as Secondary for EDS Maglev Train

The characteristics of coreless-type linear synchronous motor, which is applied in the propulsion system of electrodynamic suspension maglev train are calculated and analyzed by the more accurate analytical model. First, the magnetomotive force distribution model of the vehicle coils is proposed according to their racetrack shape. Then, on the basis of the space harmonic method, the characteristic analysis formula of coreless-type linear synchronous motor with single-layer and double-layer armature winding are presented. Second, the air-gap flux density, back electrodynamic force, and thrust of the coreless-type linear synchronous motor are analyzed by the three-dimensional finite element simulation method and the analytical methods. Then, the relationship of efficiency, power factor, and power angle with the number of feeder units is obtained. Finally, the accuracy of the analytical model and numerical result are experimentally validated by comparing with the transient operation data on Yamanashi and Miyazaki test line.

A Rotor Winding Internal Short-Circuit Fault Protection Method for Variable-Speed Pumped Storage Units

In electrical machinery, the rotor windings’ internal short-circuit faults are addressed by the instantaneous over-current protection of the power electronic excitation device, which has low sensitivity and has difficulty meeting the safety requirements. In this paper, a rotor windings’ internal short-circuit fault protection method is proposed based on the harmonic characteristics of the circulating current between stator branches. The magnetomotive force distribution of the short-circuit coils in the rotor windings is theoretically deduced, and the characteristic frequencies of the circulating current between stator branches are analyzed. On this basis, the protection criterion of the rotor windings’ internal short-circuit fault is constructed by using the harmonic component of the circulating current. Then, an analytic model of the variable-speed pumped storage unit is established based on the multi-loop method, and the finite element method is used to verify the correctness of the proposed modeling method. An actual large variable-speed pumped storage unit is taken as an example, and the possible faults under different slip ratios are simulated. In the simulation results, the stator branch circulation has the obvious characteristic frequency harmonic components, which is consistent with the theoretical analysis. It verifies the effectiveness of the proposed protection method. Finally, it is analyzed and verified that the proposed protection has a strong maloperation prevention ability under other kinds of faults.

A Novel High-Order-Harmonic Winding Design Method for Vernier Reluctance Machine With DC Coils Across Two Stator Teeth

Vernier reluctance machine (VRM) with dc field coils in stator is a competitive rare-earth-free design for variable-speed industrial applications due to its robust structure and controllable excitation, while its torque density is relatively disadvantageous. To address this issue, this article proposes a new armature winding design method for VRM with dc field coils across two stator teeth. The key is to break the traditional winding design principle based on the flux modulation effect of fundamental dc field harmonic, and instead, reconstruct a novel harmonic winding to enhance the utilization factor of the modulated high-order dc field harmonics arising from the unique magnetomotive force distribution of dc field coils across two stator teeth. By this means, the torque density can be improved by 75.6% against the existing poor counterpart. In this article, the machine structure and operation principle are introduced, with emphasis on the high-order dc field harmonics distribution rule and its influence on the armature winding design. By finite element design and optimization, a comparative study is performed to evaluate the electromagnetic performance of VRMs using two different winding configurations with variable slot pole combinations. A prototype is fabricated and tested, and the results agree well with finite element analysis, which verifies the feasibility and advantages of the proposed winding design method.

Asymmetrical six-phase induction motor drives based on Z-source inverters: Modulation, design, fault detection and tolerance

Multiphase machines are becoming one of the mainstream research topics during the last decade, especially in high-reliability based systems. Among the different configurations of the multiphase machines, Asymmetrical Six-Phase Induction Motor (ASPIM) with a spatial displacement of 30° is popular as it has a better magnetomotive force (MMF) distribution. This paper therefore concerns with detecting and mitigating the operation of ASPIM during healthy and faulty modes. Recently, the Z-source Inverter (ZSI) technology has attracted great concerns of the researchers. The key idea of this paper is to combine together the technologies of ASPIM and ZSI. This combination produces a very high reliable drive system. Traditional modulation methods associated with the ZSI are modified in this paper to be convenient for ASPIM drives. Besides, the impedance network design procedures are introduced. Moreover, the Vector Space Decomposition Fault Detection (VSDFD) method has been applied to detect open-circuit faults and used to select the proper post-fault operation. An experimental setup has been established in the laboratory to validate the proposed ideas. Finally, the actual machine parameters are measured and used to investigate the system performance via simulation and experimental results in both healthy and faulty conditions.

Comparative Study of Torque Production Mechanisms in Stator and Rotor Consequent-Pole Permanent Magnet Machines

This article presents a comparative study of torque production mechanisms in stator and rotor consequent-pole permanent magnet (CPM) machines. Due to the CPM design, a unipolar PM magnetomotive force (MMF) distribution can be observed in both stator CPM (S-CPM) and rotor CPM (R-CPM) machines. As a consequence, more resultant air-gap field harmonics are responsible for torque production due to the double-side slotting effect. The PM MMF-permeance-based model is employed to identify and reveal the difference of sources and patterns of the working air-gap field harmonics in the two investigated CPM machines. The torque contributions of the main-order working harmonics of the two studied machines are analytically quantified by a unified torque equation and compared with the corresponding finite-element (FE) results. Finally, some experimental measurements are carried out on a 12-slot/14-pole R-CPM machine prototype to validate the theoretical and FE analyses.

Asymmetrical Four-Phase Combined Winding Arrangement for Bearingless PM Motors

Conventional bearingless motors typically comprise two sets of independent windings in the stator to produce torque and suspension force, denoted by a separated winding in this study. However, several approaches to combine suspension and rotation windings into one set of windings, known as combined winding, have been investigated for torque density improvement and for increasing the instantaneous suspension force production at start-up. This study proposes a method to convert a typical three-phase brushless dc motor into a four-phase bearingless motor with combined winding, based on the magnetomotive force (MMF) distribution. As an example, a 12-slot/10-pole surface-mounted permanent magnet motor was investigated. The calculation results demonstrate that the suspension force cannot be generated at certain rotational angles when the four phases are symmetrically located. This study introduces torque and force current factors based on the MMF distribution to select several asymmetrical four-phase winding arrangements. The radial force trajectory calculated by the finite element method was evaluated to determine the final model. To verify the proposed method, the prototype was built and tested, and the test results showed that the rotor was levitated successfully and could be driven up to 5000 r/min.

A Novel Combined Winding and Test Result of a 20-Pole/24-Slot Consequent-Pole Bearingless Motor With Parallel Motor Winding

A novel consequent-pole bearingless motor is proposed with a unique combined winding structure of parallel motor windings for mixing applications, such as agitators used to mix fluids in the pharmaceutical or food industry. Bearingless motors can be used to achieve high purity and no contamination in these mixing applications. The principles of the magnetic suspension force and torque generation are presented by calculating the magnetomotive force (MMF) distributions with two different magnetic field. In addition, the error angle of the suspension force is evaluated in several pole/slot combinations with the proposed combined winding using 3-D finite element analysis. As a result, 20-pole/24-slot was found to be the best configuration, because it has the least direction and amplitude variations in the radial suspension force generation. A prototype of the proposed 20-pole/24-slot bearingless motor was built and tested. The stable magnetic suspension start-up and rotation can be successfully achieved in the experiment. The measured waveforms of the rotor displacement and the U-phase current while the rotor is magnetically suspended and rotated are shown. It is confirmed by calculations and experiments that the proposed combined winding is effective for stable radial magnetic suspension and rotation.

Influence of Pole and Slot Combination on Torque Characteristics and Radial Force of Fractional Slot Permanent Magnet Machines

The fractional slot concentrated winding structure effectively solves the difficulty of low‐speed and high‐torque permanent magnet (PM) machines with a large number of poles and slots, but it also brings a wealth of magnetomotive force (MMF) harmonic. The winding function method is used to compare and analyze the stator MMF distribution and harmonic content of the fractional slot PM machines with different pole and slot combinations, and the cogging torque waveform and torque ripple are calculated by the finite element method. The influence of pole and slot combination on radial force and vibration modes of fractional slot PM machines is studied. The main vibration mode can be determined from the lowest order of radial force harmonics. The results show that in a fractional slot PM motor, the radial force is the main cause of noise and vibration, rather than the cogging torque and torque ripple. The dominant radial force is mainly produced by the interaction of rotor field harmonics and armature reaction field harmonics, and the vibration and noise will significantly increase with the decrease of the dominant vibration mode order, which largely depends on the pole and slot combination. This paper provides a certain reference for the selection of pole and slot combination in the electromagnetic design process of low speed high torque fractional slot PM motors. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Comparative study of stator consequent‐pole permanent magnet machines

A comparative investigation is made of stator consequent-pole (SCP) machines with different permanent magnet (PM) arrangements. Compared with conventional surface-mounted PM (SPM) configurations, SCP configurations produce more orders of air-gap field harmonics. Due to asymmetrical PM magnetomotive force (MMF) distributions and the double-side slotting effect, SCP machines exhibit multiple air-gap field harmonics, especially relatively enhanced low-order field harmonics, for torque production. As a consequence, improved torque capability can be obtained over that of conventional SPM counterparts. Machine topologies and operating principles are described. The design parameters of four SCP machines with different magnet arrangements are globally optimised. The key electromagnetic performances, including open-circuit performance, torque quality, field-weakening capability, and efficiency, are comprehensively investigated and compared by the finite element (FE) method. Finally, some experimental measurements on an optimally selected SCP machine prototype are carried out to validate the theoretical and FE analyses.

Fault Operation Analysis of a Triple-Redundant Three-Phase PMA-SynRM for EV Application

Due to the uninterrupted operation capability in the fault conditions, fault-tolerant machine drives are being favored by the safety-critical applications, such as the electric vehicles (EVs). Understanding the machine drive fault behavior is of key importance to facilitate the fault diagnosis, control law design, and avoid further damage. In this article, the fault operation behavior of a triple-redundant three-phase permanent magnet-assisted synchronous reluctance machine (PMA-SynRM) is analyzed in detail. The mutual-coupling mechanism of different three-phase modules is explained by analyzing the magnetomotive force (MMF) distribution. It is found that the three-phase set module affects each other via an MMF offset component, causing second harmonics in the dq -axis currents, voltages, and torque. Both the open- and short-circuit fault operation behaviors are investigated. The correctness of the analysis is validated by finite element (FE) simulations and experimental tests in different fault modes. It indicates that the machine drive requires an advanced control technique to enhance the current tracking capability in postfault operation conditions.

Analysis of Airgap Field Modulation Principle of Flux Guides

The flux guides are adopted in a number of electric machines, such as the synchronous reluctance machine (SynRM) and the brushless doubly fed reluctance machine (BDFRM). This article further develops a novel and unified theoretical approach for the category of machines with flux guides. Specifically, the magnetomotive force (MMF) modulation operator of variable flux guides is proposed based on the general airgap field modulation theory, to describe the modulation behavior on the source magnetizing MMF distribution in detail. Both machine topologies with flux guides, namely, the SynRM and BDFRM, are addressed in detail from the perspective of airgap field modulation mechanism. It is proven that, three kinds of harmonic components with pole pairs of $p_{f}$ and $(lN_{MB}\pm p_{f})$ correspond to $p_{f}$ pole-pair source magnetizing MMF and their relative amplitudes can be characterized by three magnetic field conversion factors. The magnetic field modulation effects of flux guides and simple salient poles are compared in terms of the torque production ability. In addition, electromagnetic performances such as airgap flux density, torque density, and inductance characteristics are correlated with their initial key topological parameters by certain analytical expressions and compared fairly between the SynRM and BDFRM. The agreement among the theoretical analysis and the two-dimensional (2-D) finite element analysis together with experimental test verifies the effectiveness of the proposed analysis.

Unified Analysis of Induction Machine and Synchronous Machine Based on the General Airgap Field Modulation Theory

This paper investigates the natures of induction machine (IM) and synchronous machine (SM) from a new point of view based on the general airgap field modulation theory. The equivalent airgap model containing three critical elements is proposed to expound their modulation principles and common features in a unified way, thus the electromagnetic performance analysis, i.e., back-electromotive force (EMF) and torque, of IM and SM can be put together from the perspective of airgap field modulation principle while the only difference exists in the modulators. The modulators are optimized by considering the nonlinearities like rotor coils resistance and leakage inductance of IM and the actual magnetomotive force (MMF) distribution of SM. Theoretical expressions of airgap flux density distribution, flux linkage and EMF, general average torque, torque density comparison, and inductance characteristics are developed to reveal the relation between the performances and initial key topological parameters systematically and verify the model feasibility entirely. The iron saturation is treated as a constant discount on the airgap MMF to provide general mechanism comprehension and reasonable parameters calculation. All the theoretical predictions are verified by two-dimensional (2-D) finite element analysis together with experiment achieving good agreement.

Analytical Analysis and Performance Characterization of Brushless Doubly Fed Machines With Multibarrier Rotors

The brushless doubly fed reluctance machine (BDFRM) with a multibarrier rotor has shown great promise in applications where high reliability and low maintenance cost are required, such as offshore wind turbines. This paper presents a systematic analytical analysis and performance characterization of the BDFRM with a multibarrier rotor. First, the airgap magnetomotive force distributions under both open circuit and loaded condition are detailed, based on which a more practical rule than the widely accepted | p 1 − p 2|≠1 is derived to effectively avoid the unbalanced magnetic pull in such machines. Analytical formulas different from those for slip-ring doubly fed induction machines are then obtained to estimate inductance parameters for circuit modeling and control purposes. Design equations for initial sizing and torque density comparison are also developed, with achievable torque density discussed. Both finite-element analysis and experimental tests are conducted to validate the effectiveness of the presented analysis.

Investigation of Different Winding Configurations and Displacements of a Nine-Phase Permanent-Magnet-Synchronous Motor With Unbalanced AC Winding Structure

Integral-slot electrical machines require modifications and optimization of both stator and rotor to maximize the machine performance. In addition, sub-harmonics in magneto-motive force distributions is an important issue in motors with fractional-slot concentrated windings. These additional sub- and super-harmonics increase iron losses, which becomes an even bigger challenge in high speed/frequency applications. A permanent-magnet (PM) motor with unbalanced winding (UBW) and unconventional slot numbers is a good option for applications that require smooth torque output and low back electromotive force voltage harmonics. In this paper, different winding configurations and displacements of an unconventional nine-phase PM motor with both balanced fractional-slot winding and UBW structures have been investigated. The focus has been on 117-slot with 12-pole (for the balanced winding motor) and 36-pole (for the UBW motor) combinations. Motor prototypes with UBW configurations have been manufactured. The finite-element analyses results have been validated with experimental results and it is shown that such unconventional slot/pole combinations can be a good option for some high-power applications.

Analysis of Airgap Field Modulation Principle of Simple Salient Poles

This paper models a huge family of electrical machines featuring simple salient poles in a unified way based on the general airgap field modulation theory. The modulation principle is analyzed by introducing the magnetomotive force (MMF) modulation operator, which characterizes the influence of a variable reluctance block on the primitive magnetizing MMF distribution established by field winding. Popular machine topologies are investigated in detail from the perspective of an airgap field modulation mechanism. The iron core magnetic potential drop due to the finite slot opening depth and the impact of iron saturation on the parameters are considered by proper theoretical indication. In addition, the modulation effect of salient poles highly depends on the slot-opening-width-to-pole-pitch ratio ϵ . The effect can be neglected when ϵ ϵ = 0.5. It is also found that mainly three different harmonics parts modulated by salient poles contribute to airgap flux density and torque production. Straightforward relations between the frequency-domain or amplitude information of performances indexes and topological parameters can be obtained obviously by certain analytical expressions without heavy finite-element analysis (FEA). Analytical results are verified by two-dimensional FEA and experiments measurements.

Combination Traction and Lateral Stabilisation System for Magnetic Levitation Transport

The problems of improvement of modern types of transport and creation of new ones are important and topical for the human society development. One of the most promising and environmentally-friendly modes of transport is the high-speed maglev transport, moving at speeds of approximately 500 km/h. Objective. Justification of linear induction motor, development and research of various constructions of this type of motors. Methods. Description of linear induction motor with longitudinal and transverse magnetic flux for combined traction and lateral stabilisation system of maglev transport, having increased lateral stabilisation forces. The mathematical modelling of magnetomotive force (MF) in the air gap of traction linear motor of this type has been conducted. To analyse the MF the assumption has been made about even distribution of magnetic induction in the air gap in transverse direction and its sinusoidal longitudinal direction, making it possible to develop new mathematical model of MF distribution in the air gap of linear induction motor with longitudinal and transverse magnetic flux Results. The developed mathematical model for calculation of MF on traction linear machine will enable increasing accuracy of traction and lateral stabilisation combined system forces for maglev transport. The same relates to mutual location of inductor to the secondary element. All this proves the successful ten-year commercial operation experience of magnetically suspended train carrying passengers from an airport to Shanghai, P.R. China. The values of traction and lateral stabilisation forces of linear induction motor with longitudinal and transverse magnetic flux is greatly influenced by the character of current distribution in the secondary element. The character itself is influenced by MF distribution in the air gap.