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The objective of this article isto developa comprehensive mathematical model of a three-phase induction motor to facilitate stator interturn (SIT) fault related study. A detailed analytical model that includes accurate inductance modeling considering rotor slot harmonics (RSH) under healthy as well as SIT faults is described. The proposed model is developed analytically in a step-by-step manner incorporating the features of RSH. A detailed but simplified analysis considering both magnetomotive force harmonics and air-gap flux harmonics has been presented. An asymmetric model is proposed, including SIT faults, in a single phase of the induction motor in the next stage of the modeling. The effect of saturation has also been considered in the model. The proposed model is validated by comparing the simulation results in transient, steady state, and frequency domain with the experimental results. Comparison shows a high degree of correlation with the results of the actual motor. The contributions of this work are justified by comparing the proposed model with the existing models. This article also shows that a frequency signature related to RSH present in the line current is capable of characterizing the SIT faults. [ABSTRACT FROM AUTHOR]

This article proposes a quantitative analysis model for the electromagnetic forces in rotor-permanent-magnet (rotor-PM) machines, decoupling the air-gap field modulation and the force modulation. First, a unified analytical model of the equivalent concentrated forces (ECFs) is deduced based on the air-gap flux density (AFD) harmonics. Second, the air-gap field modulation and the force modulation are decoupled by the ECF coefficient. Then, to determine the contributions of the modulated AFD harmonics, a quantitative analytical method is proposed. On this basis, the vibration performance of a 12-slot/10-pole (12s/10p) interior PM machine is investigated considering the modulation effect. The results reveal that the influences of rotation speed, PM-excited field, and armature field on the vibration can be clearly represented by the proposed method. Finally, the modal test and the acceleration measurement are conducted to validate the analysis. [ABSTRACT FROM AUTHOR]

Due to the enhanced air gap flux density and eddy currents in the favorable path, eddy current brakes with slotted conductors have attracted more attention in recent years. However, due to the increased difficulty in analytical modeling, there is currently no suitable analytical model available for the optimization design of eddy current brakes with slotted conductor. To solve this problem, an improved analytical model is provided based on the subdomain model and the least squares method in this article. The proposed analytical model considers slotted conductor disk, magnetic saturation of primary core and actual path of eddy currents in the conductor disk. The accuracy of the proposed analytical model is verified by finite-element method (FEM) and experimental measurement. The results show that the improved analytical model has good accuracy in the entire speed range. As the analytical model takes less computational time than three-dimensional FEM, it can be used as an effective tool for the optimization design. [ABSTRACT FROM AUTHOR]

Compared with the conventional permanent magnet (PM) machines, the flux-switching permanent magnet (FSPM) machine exhibits higher torque ripple due to its special doubly salient structure and high air-gap flux density, leading to the deterioration of smooth operation. In this article, the output torque ripple suppression methods of FSPM machines from both rotor and stator sides are proposed with the aid of general air-gap field modulation theory. According to harmonic modulation mechanism, air-gap PM field can be modified by revising harmonic content of rotor and stator modulation functions and, consequently, three concepts, including cos-shaped edge rotor (CSER), cos-shaped edge stator, and double cos-shaped edge, are proposed and implemented to suppress the output torque ripple due to the cogging torque and electromagnetic torque ripple of FSPM machines. Finally, finite-element analysis and experiments are conducted to verify the proposed approaches. The results reveal that the CSER method exhibits the most effective suppression effect. [ABSTRACT FROM AUTHOR]

Permanent magnet Vernier motors (PMVMs) possess the advantage of high torque density for high-performance applications. However, the low power factor challenge makes it unacceptable for direct-drive applications. A lack of accurate modeling method based on the motor sizing law, i.e., air-gap flux density, linear current density, and motor geometry parameters, raises difficulties for machine designers to further conduct research on the performance metrics. This article presents a deep investigation into the analytical modeling technique for surface PMVMs (SPMVMs). It can identify an accurate approach to obtain the performance metrics, including electromagnetic torque and power factor. The modeling technique is developed based on the conformal mapping method. By using this, both radial and tangential permeability functions can be calculated to obtain the motor magnetic loading accurately, considering the leakage flux. The slotting effect on both air-gap flux density and armature-winding function is analyzed to achieve a precise formula for torque and power factor computations. The new modeling technique is applied to integral-slot SPMVMs with different slot/pole combinations, gear ratios, slot openings, and magnet thickness to evaluate the impacts of motor parameters on high-power-factor and high-torque-density designs. Finally, an SPMVM with the characteristics of high torque density and power factor is fabricated to verify the analytical model at the power rating of 0.8 kW and the speed of 500 r/min. The experimental results show that the prototype exhibits a high power factor of 0.9 and high torque density 22.5 Nm/L. [ABSTRACT FROM AUTHOR]

Variable reluctance resolvers (VRRs) have been widely used for rotor position detection in harsh working conditions. However, conventional installation of VRRs inevitably occupies the axial space of machine systems, and may weaken the reliability of rotor position detection encountering shock and vibration. In this article, a novel VRR structure with inner stator is investigated, which is radially integrated inside a permanent magnet synchronous machine (PMSM) to construct compact machine topology. The hybrid machine topology is first discussed, and detailed electromagnetic design is carried out. Improved analytical analysis on air gap flux density distribution and inductance evaluation of the integrated VRR is derived based on modified winding function approach, and testified by finite element analysis. A prototype is manufactured from an existing 2.2 kW PMSM, and experiments are conducted to validate the effectiveness of proposed machine topology. [ABSTRACT FROM AUTHOR]

Surface-mounted permanent magnet (SPM) machines with skewed slots as vehicle drives are widely used. Due to skewed slots, electromagnetic characteristics are modulated by the skew effect. To analyze the skew effect, Maxwell’s equations-based 3-D analytical model is proposed. Based on differences in 3-D air-gap flux density distribution, the mechanism by which the skew effect modulates cogging torque, flux linkage, and back electromotive force (EMF) is investigated. The effectiveness of the theory about the skew effect is verified by both the finite element method (FEM) and the experimental result. [ABSTRACT FROM AUTHOR]

This article proposes a hybrid evaluation method of electromagnetic force and vibration for electrical machines considering high-frequency current harmonics caused by the inverter. First, the permeance and armature magnetomotive force (MMF) is calculated based on the virtual MMF and the slot matrix. Then, the air-gap flux density and electromagnetic force construction process under arbitrary current is thoroughly studied. The vibration transfer function is obtained by utilizing the modal analysis and the modal test. Finally, the vibration can be calculated according to the modal superposition method. By applying this method to an interior permanent magnet machine, it can significantly reduce the computation efforts compared with the multiphysics procedure due to the extensive use of the finite-element method. In addition, the accuracy of this method is validated by conducting an experimental study. [ABSTRACT FROM AUTHOR]

The mechanism of torque ripple generation by time and space harmonic magnetic fields in permanent magnet synchronous motors is investigated to obtain advanced motor designs. The general expression between the torque ripples and harmonic air-gap flux densities in the motor is derived by using Maxwell stress tensor. Both the numerical and experimental verifications of this expression are carried out. By using this expression, the difference of the torque ripple generation between the surface and interior permanent magnet synchronous motors are discussed. Based on these investigations, the shape of the rotor surface of an interior permanent magnet motor is optimized. It is clarified that specific harmonic components of thetorque ripples in interior permanent magnet synchronous motors can be reduced to be nearly zero by optimizing the rotor surface shape. [ABSTRACT FROM AUTHOR]

To address the contradiction between dynamic performance and robustness of the enhanced linear active disturbance rejection control (ELADRC) method, a fuzzy-ELADRC method for a bearingless induction motor (BIM) is proposed. First, based on the air-gap flux oriented control, the first-order and second-order ELADRC are designed for the torque system and the suspension system of the BIM, respectively. Second, a fuzzy controller is introduced to adjust the controller bandwidth and observer bandwidth of ELADRC online. The fuzzy rules are established by analyzing the influence of ELADRC with different bandwidths on the BIM system, and adaptive initial bandwidth is adopted to improve the variable speed performance of the BIM. Finally, the simulation and experimental comparisons of the PID control method, the ELADRC method, and the fuzzy-ELADRC method are carried out. The results show that the proposed method not only realizes the rapid and stable suspension of the rotor, but also effectively improves the starting performance, variable speed performance, and antidisturbance performance of the BIM system. [ABSTRACT FROM AUTHOR]

This article presents a novel system to connect a three-phase doubly fed induction generator (DFIG) to a dc-microgrid. The proposed topology is based on two three-phase half-controlled converters connected in series with the generator stator windings, in an open-end winding configuration. The converters operating principles, pulsewidth modulation, power and air-gap flux controls, and zero-sequence current minimization strategies are discussed. The proposed system is compared with conventional systems in terms of current harmonic distortions, torque ripple, and semiconductor losses. Simulations and experiments were also performed, showing steady-state and transient results for the DFIG generating 500 W. Finally, it was verified that the proposed system can operate with lower power losses and maintain low-distorted voltages and currents over the DFIG stator windings. [ABSTRACT FROM AUTHOR]

Due to the high power density, short axial size, and wide permanent magnet (PM) flux linkage regulation range, an axial-flux PM memory machine (AFPMMM) with hybrid Halbach array is investigated in this article. To solve the problem of magnetic density variation of Halbach array composed of different types of PMs in asymmetric bilateral air-gap structure, the analytical method for calculating the air-gap flux density of AFPMMM is presented through mathematical analysis, which uses cylindrical coordinate system instead of Cartesian coordinate system and is solved by equivalent method, separated variable method, and boundary conditions. The magnetic field generated by the Halbach array is divided into three directions: radial, circumferential, and axial. The analytical model is compared with the finite element method (FEM) simulation results to verify its effectiveness. In addition, an approximate piecewise linear hysteresis model with parallelogram return line is established based on the analytical expression of magnetic field. By applying different pulse currents to change the residual flux density of PM, the flux regulation characteristics of the motor are studied, and it is found that the air-gap flux density of the motor can be smoothly adjusted by continuously changing the pulse current, which plays a positive role in solving the problem of online magnetic regulation of the motor. [ABSTRACT FROM AUTHOR]

This article presents an accurate analytical model (AM) for synchronous reluctance machine (SynRM) that incorporates the effect of stator slots on the air gap flux density and torque waveforms. From the formulation of magnetic potential in the air gap for both the stator and rotor, the flux density is obtained, considering the first harmonic of the flux density and the electric loading, the average torque is calculated using the Lorentz’s force. The ripple torque is obtained from the energy stored in magnetic circuit. The method is developed for a rotor with one flux barrier per pole and then extended to a larger number of barriers. To validate the results obtained by the AM proposed finite element analysis have been carried out. Several comparisons have been derived considering different rotor positions as well as different harmonic orders, and the pros and cons of the method are highlighted. The model performs fast and can predict results with high accuracy, and can be adopted to speed up the preliminary design and optimizations of this type of motors, with respect to finite element. In addition, from the analytical expressions it is possible to obtain all the correlations between electrical, magnetic, and geometrical characteristics of the machine, with the advantage of enabling a faster machine design. [ABSTRACT FROM AUTHOR]

In this paper, the boundary discretization method is used to improve the traditional subdomain model. The improved model can be used to calculate the magnetic field distribution in the region containing non-orthogonal boundary, avoiding the influence of the simplified stator slot or permanent magnet shape on the results in calculating the motor magnetic field using the traditional subdomain model. In addition, the improved subdomain model can also be used to calculate the air-gap flux density when the rotor is eccentric, instead of segmenting the air-gap to an equivalent state without eccentricity. The calculation object of this paper is a surface-mount permanent magnet motor with a rectangular stator slot. The air-gap flux density under no-load and load conditions is calculated, respectively. Since the improved subdomain model does not need to simplify the stator slot shape, the magnetic potential in the stator slot is also calculated. Finally, the air-gap flux density under rotor eccentricity is calculated, and the influence of the calculating parameters on the results of the improved subdomain model is discussed. All the calculated results are compared with those obtained by the finite element method, which verifies the accuracy of the improved calculation model. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear analysis model for predicting the performance of eddy current recoil brakes (ECRB) is proposed by combining the magnetic equivalent circuit (MEC) model and the subdomain model. The subdomain model introduces the equivalent region to improve the inherent shortcomings of the equivalent current sheet (ECS) method. The outer tube is divided into a magnetic saturated region and an unsaturated region in the subdomain model to simulate the magnetic saturation of the outer tube during recoil. The MEC model is applied to calculate the air gap magnetic flux density and the relative permeability of the equivalent region. Leakage flux and magnetic saturation are considered in the MEC model. The eddy current resistance of ECRB is calculated by the subdomain model. The model is verified by the finite element model, and it is able to predict the performance of ECRB with different structural parameters. In addition, the prototype of the ECRB was manufactured. A test was carried out on a 155 mm artillery to verify the accuracy of the proposed nonlinear analysis model. [ABSTRACT FROM AUTHOR]

The peripheral magnetic field of the motor may cause magnetic field interference to the surrounding sensors, which would reduce the accuracy of sensors and affect the safety and concealment of vessel. This article explored the environmental magnetic field distribution law of a permanent magnet (PM) motor with two-pole parallel magnetization. A no-cogging magnetic field model was obtained by solving Maxwell equations, and the relationship between the air gap flux density and the environment flux density was built considering the motor cogging effect. In addition, a mathematical model of connections between the back electromotive force (EMF) and the environmental flux density was built, and the correctness of the model was verified by COMSOL. It is concluded that the circumferential and radial components of the environmental magnetic field are distributed sinusoidally, and the magnetic flux density modulus remains constant on the equidistant circumferential line, but attenuates squarely with the distance from the motor. It provides ideas for magnetic field analysis in the peripheral environment of other types of motors, sensors, and other anti-motor electromagnetic interference, magnetic field compensation for geomagnetic measurement, and motor fault diagnosis. [ABSTRACT FROM AUTHOR]

A new partitioned stator field modulation machine (PSFMM) with H-shape permanent magnet (HPM) excitation (HPM-PSFMM) is proposed, which is evolved from the conventional flux-switching machine (FSM) and flux-reversal machine (FRM). The proposed HPM-PSFMM combines the merits of high reliability and good heat dissipation characteristic. In addition, it exhibits high torque production with low torque ripple. Based on the theory of electrical machine operation, the FSM and FRM can be transformed into PSFMM with interior permanent magnet (IPM) and surface-mounted PM (SPM) excitation by changing the position of PM excitation, respectively. It benefits to improve space utilization and increase slot area for a large number of armature windings. For reducing the flux leakage and enhancing the flux density in air gaps, the IPM and SPM excitation are combined into HPM excitation. The iron-pole rotor between the inner and outer stators acts the role of modulator to modulate the magnetic field excited by HPM excitation to couple with the armature reaction for converting electromechanical energy. The evolution process, operating principle, and key design parameters of the proposed HPM-PSFMM are presented. Finally, using the finite element analysis (FEA), it can be proven that the proposed HPM-PSFMM has the merits of high torque production, low flux leakage, low total harmonic distortion (THD), and low torque ripple when compared to other stator-PM machines, which is a desirable choice for high stability applications. [ABSTRACT FROM AUTHOR]

The magnetic field distribution in the air gap is of great importance in the design of rotary machines. In this article, an efficient analytical method is presented, which is capable of plotting the air-gap flux density waveform of induction machines (IMs) less time-consuming than the finite element method (FEM) does. The proposed method, based on the product of the current linkage waveform and the permeance waveform, utilizes the calculations of the steady-state equivalent circuit to ensure the accuracy and an equivalent air-gap reluctance model to take into account both the slot opening effect and the rotor movement. The method is tested on a general IM with different load cases and different design parameters, and the results are compared to the FEM calculations. It can be concluded that the proposed analytical method is an efficient option in the motor design to investigate the influence of the parameters on the flux density distribution. [ABSTRACT FROM AUTHOR]

This article proposes a new hybrid-excited partitioned stator flux modulated machine with a dual-permanent magnet (HE-PSFMDPMM). The HE-PSFMDPMM employs consequent-pole (CP) permanent magnets (PMs) on the inner stator and Halbach array CP PMs on the rotor, which can yield abundant air-gap flux density working harmonics to increase the torque capability. Meanwhile, the field windings are housed in the inner stator to achieve flux weakening. The topology, working principle, and design optimization of HE-PSFMDPMM are investigated, respectively. The electromagnetic performances of HE-PSFMDPMM are analyzed and compared with that of a contrast model with conventional CP PMs on the rotor. The results indicate that by using dual-PM excitation, HE-PSFMDPMM can provide large flux linkage, high torque production with low torque ripple, and high efficiency. Meanwhile, a good flux weakening capability is obtained with the aid of direct current (dc) excitation. Moreover, compared with the contrast model, the proposed HE-PSFMDPMM with Halbach array CP PMs on the rotor can offer the merits of lower cogging torque and torque ripple, higher power factor, and better flux weakening capability. [ABSTRACT FROM AUTHOR]

This article proposes a novel axial field switched flux memory machine (AF-SFMM) which is analyzed by a combined analytical method. Compared with conventional axial field (AF) permanent magnet (PM) machines having magnets in the rotor side, the AF-SFMM benefits from good heat dissipation, high rotor robustness, and improved power density. Meanwhile, because of the utilization of low coercive force PM materials, the proposed machine can flexibly regulate air-gap flux. This analytical method is characterized by the combination of a quasi-3-D (quasi-3D) finite element method, a magnetomotive force–permeance-based method, and a virtual linear hysteresis model of low coercive force PM. In addition, compared with conventional time-consuming 3-D finite element analysis (FEA), the proposed method can improve the computational efficiency significantly with satisfactory accuracy. This makes the proposed combined analytical method suitable for preliminary sizing determination of AF-SFMM. Meanwhile, the effectiveness of the proposed analytical method is validated by FEA results. [ABSTRACT FROM AUTHOR]

This study investigated an efficient procedure for developing an accurate behavioral model of a cage induction motor (IM) based on the multiport Cauer ladder network (CLN). The CLN method was applied to a cage IM with semi-closed rotor slots as a model order reduction (MOR) technique, and a method for selecting the appropriate space harmonics (SHs) included in the air-gap flux density, which is necessary for a multiport CLN method for induction machines, was discussed. Then, the developed approach was applied to the transient analysis of the cage IM coupled with a control system, and its effectiveness in terms of computational accuracy and cost was investigated. [ABSTRACT FROM AUTHOR]

A new type of hybrid magnet dual stator field modulation machine with different split ratios of stators (DSR-HMDSFMM) is proposed in this article, which has the merit of high torque density. The split teeth of stator sever as modulators to modulate air gap flux density based on the magnetic gearing effect for high torque production. The total split tooth number of inner stator is equal to that of outer stator because the pole pair numbers of armature reaction and permanent magnet (PM) excitation on rotor are equal. Furtherly, the inner and outer stators with different split ratios and same split tooth number are employed to increase torque production because armature windings with high winding factor and high turn number can be used. In addition, the employment of hybrid magnet excitation can increase space utilization and enhance the air gap flux density with low harmonic distortion. Therefore, the proposed DSR-HMDSFMM can achieve high torque production with the same volume and PM usage. In order to find the optimal split ratio match of stators, several DSR-HMDSFMMs with different combinations of split ratios are proposed and calculated. The configuration and operating principle are illustrated, together with electromagnetic performances of the proposed machines analyzed using finite element analysis (FEA). The FEA-predicted results show that the proposed HMDSFMM exhibits high air-gap flux density with low harmonic distortion and high torque density, which is promising for the direct-drive applications. [ABSTRACT FROM AUTHOR]

In recent years, Vernier permanent magnet machines (VPMs) have gained much interest in academia. However, due to the large leakage flux, the power factor of Vernier machines is too low to be applied in real industry. In this article, a novel split-tooth, concentrated-winding Vernier machine using ferrite magnets is proposed for high-torque, low-speed direct-drive applications in home appliance industry. It uses consequent-pole magnets in the rotor, as well as additional assisted magnets in the stator teeth, in order to reduce the leakage flux and boost the torque density. A systematic way of reducing the torque ripple from 40% to 4% is proposed by carefully choosing the right combination of stator/rotor pole-pair numbers. A comprehensive design optimization is conducted to achieve the optimal performance. Finally, the ac loading is carefully reduced to meet the torque, saturation, power factor and space requirements. The test results of a prototyped machine show that the proposed design can achieve 34% more torque and 20% less loss with a reasonable power factor of 0.63, compared with an optimized PM synchronous machine under the same volume. It is found that the significant torque boost is attributed to the multiple working harmonics of the air-gap flux density. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach to determine the air-gap magnetic field and the winding inductance in the brushless doubly-fed reluctance machine (BDFRM) with flux barriers. By dividing one flux guide layer into several segments, a calculus method based on magnetic circuit analysis is developed and specific analytical expression of the air-gap flux density is rigorously derived. Then, the included angle between fundamental components with the same pole pairs is also discussed. Based on the air-gap flux density distribution, the inductance expressions between different windings are also presented. Three kinds of finite element analysis models are established and studied. As a result, the accuracy of the analytical model can be verified by simulations and experimental data from an existing BDFRM prototype. [ABSTRACT FROM AUTHOR]

A comparative study of new partitioned stator hybrid excitation axial flux switching permanent magnet (HEAFSPM) motors with different partitioned excitation stator topologies for in-wheel traction applications is presented in this paper. The realization approaches of the partitioned stator HEAFSPM motor are discussed, and the motor topology with windings and permanent magnets (PMs) separately setting on different stators is selected in view of the advantageous structure for thermal management. On this basis, two partitioned excitation stator topologies including C-type tooth core and T-type tooth core stator configuration are proposed, and the air-gap flux modulation and flux regulation principle of the motors are analyzed. In addition, the design method of the partitioned stator HEAFSPM motor considering the effect of hybrid excitation sources is provided, and the two motors with different tooth cores are designed respectively. Meanwhile, for a fair comparison, the multiple objectives optimization method coupled with the sensitivity analysis is employed to optimize the two motors. The electromagnetic performances, anti-demagnetization capability, and flux regulation performance of the two motors are all investigated in detail. Finally, two prototype motors are fabricated and tested. Both the theoretical analysis and experimental results verify the effectiveness and reasonability of the motor. [ABSTRACT FROM AUTHOR]

This paper proposed a hybrid subdomain model (HSM) for calculating the magnetic field distribution of interior permanent-magnet (IPM) machine accounting for slotting effect, rotor saliency, and iron nonlinearity. In the constant permeability region, i.e., slots, slot-opening, and air-gap, three subdomains are introduced to represent their magnetic field. By applying the subdomains interface conditions and nonlinear boundary conditions, the analytical air-gap field solution can be obtained based on the governing Laplace and Poisson equation. For the iron region, the magnetic reluctance network (MRN) is proposed to account for rotor saliency iron and nonlinearity. The magnetic voltage source is introduced to represent the permanent-magnet (PM) while the air-gap flux source is used to replace the air-gap reluctance network, which is the key to guarantee the computational efficiency and high accuracy. The electromagnetic performances of both flat-shaped and V-shaped IPM machines are investigated to show the advantages of different IPM machine topologies analytically. The HSM predictions for both IPM machines are validated by finite-element (FE) analysis and experimental results. [ABSTRACT FROM AUTHOR]

Spoke structure can increase the torque density of coaxial magnetic gear (CMG). However, the outer rotor can produce a large number of magnetic leakages. To improve the utility of PMs, a novel magnetic gear was proposed in this paper. The structure of the auxiliary flux modulator is a slotted iron yoke, and the slot angle is same as the stationary ring. Among, the permanent magnets (PMs) of inner rotor are adopted uneven block structure to improve air gap flux density. At the same time, the stationary ring adopts high-temperature superconducting (HTS) bulks, replacing the epoxy resin. In addition, Genetic algorithm (GA) is applied to calculate the optimal parameters of the proposed CMG. Finally, the air gap flux density and output torque of the magnetic gear a compared by the finite element method. The results show that the output torque of the proposed magnetic gear is effectively improved. [ABSTRACT FROM AUTHOR]

This article presents a magnetic–pneumatic levitation system for gravity offload system of large deployable mechanisms, which combines the attractive force of magnetic stage and thrust force of air-bearing and is characterized by inner stability. The article focuses on the design of the hybrid magnetic stage. The equivalent magnetic circuit network method is used to analyze the electromagnetic (EM)-permanent hybrid magnetic field, the distribution of magnetic flux density of the air gap is solved, and then the magnetic force is obtained. To improve the design efficiency, the two-step design is adopted. First, the air gap is determined by sweeping the reluctance ratio to reduce the influence of parameter deviation of cast iron on the magnetic force. Then, the other parameters of the hybrid magnetic stage are optimized based on the multi-objective particle swarm optimization (MOPSO) algorithm. Through the comparison between the results of finite-element simulation and prototype experiments, the accuracy of the model is verified, and the expected design goal is achieved. [ABSTRACT FROM AUTHOR]

Asynchronous operation of a turbo generator after the loss of field caused by the excitation fault can avoid large-scale blackout and, therefore, improve the reliability of the power systems. In order to consume the magnetic energy stored in the field winding as soon as possible, a field discharge resistor (FDR) is often connected to the field winding after the excitation fault, but it may affect the asynchronous operating ability of the turbo generator and result in the overvoltage of the field winding. In order to study the influence of the FDR on the asynchronous operating ability of turbo generator, a field-circuit coupled time-stepping finite-element model is established, and the experimental validation is performed on a model machine. For a 300-MW turbo generator, the electromagnetic characteristics, such as torque pulsation, air-gap radial flux density, and flux density distribution, are calculated and compared under different FDRs. The variation of the asynchronous operating ability along with the increase of the value of the FDR is revealed. Under the consideration of the withstanding voltage of field winding, the suitable value of the FDR that can improve the asynchronous operating ability is obtained. The results could provide a theoretical basis for improving the asynchronous operating ability of the turbo generator. [ABSTRACT FROM AUTHOR]

Some induction motors present saliencies that periodically modify the air-gap flux following a sinusoidal shape. Consequently, these modulations are reflected in the transient leakage inductance. Therefore, transient leakage inductance can be expressed as a constant term or offset, which comes from the symmetrical machine, plus all motor saliency sinusoids, modulated by the mentioned saliencies. Since saliencies are linked to the rotor position or flux, calculation of transient leakage inductance enables encoderless vector control. A way to calculate transient leakage inductance is to excite the machine with voltage steps and estimate the resulting phase current slopes since they are inversely proportional to phase transient inductance. For creating a vector, only the three current slopes resulting from a single active state are sufficient. The vector sum of the three current slopes leads to the so-called saliency-offset vector, which is a vector composed of an offset, which is created due to the contribution of the transient inductance offset, plus several saliency phasors, superposed to the offset. To access saliencies, it is critical to accurately identify the offset of the saliency-offset vector, especially in induction motors since offset is much bigger than saliencies. This article presents an advanced signal processing scheme that identifies the offset in the saliency-offset vector, assuming offset amplitude differsdepending on the voltage step applied. Using a feedforward scheme, the offset is eliminated, leading to a saliency vector where rotor slotting can be extracted from. A novel excitation is proposed to reduce additional current distortions coming from the one-active excitation. [ABSTRACT FROM AUTHOR]

This article proposes a swirling actuator that uses the electromagnetic radial force and mechanical gears to generate rotational torque. The proposed actuator generates a rotating radial force between an inner stator and a swirler. The gears on the swirler and outer rotor convert the circular motion of the swirler to low-speed rotor rotation. Thus, the proposed actuator is aimed at low-speed high-torque applications. In this study, the air-gap radial flux density and electromagnetic radial force are investigated analytically and verified through finite-element analysis. The static radial force and output torque are measured in a prototype of the actuator. The system efficiency and the gear efficiency are evaluated. A peak torque density of 27 Nm/L with a small volume of 0.16 L is realized in the prototype. [ABSTRACT FROM AUTHOR]

Torque ripple reduction for permanent magnet assisted reluctance (PMAREL) machine has always been concerned by designers. In order to seek the internal factors of torque ripple for PMAREL, this article proposes an effective torque calculation model considering air-gap field time-space harmonics using finite element method (FEM) combined with two-dimensional fast Fourier transform (2D-FFT). It can be used to investigate the contribution of air-gap field time-space harmonics to average torque and torque ripple, and precisely extract the characteristic components of the air-gap field time-space harmonics that contribute to the torque. Besides, the details of time-space harmonic order, movement form, magnitude and initial phase will be obtained from the characteristic components. Hence, the time-space harmonics of air-gap field that mainly contribute to the torque ripple can be found through this model and suppressed by adjusting the angles of the flux-barrier ends for making torque smooth. According to the optimized design, a 36-slot 4-pole PMAREL is manufactured and tested. Both finite element analysis and experimental results confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The consequent permanent magnet (CPM) pole rotor and harmonic utilization permanent magnet (HUPM) rotor are promising candidates for electric machines with less rare earth materials. Therefore, this article focuses on the analysis and comparison of these rotor types in terms of air-gap flux density characteristics, magnet utilization, and torque density. In the first part, an analytical approach is used to investigate the magneto motive force (MMF) distribution of the rotor and air-gap flux density characteristics. In the second part, finite-element methods (FEMs) are used to compare both rotor topologies with a conventional interior permanent magnet (PM) and spoke PM rotor. The results show that CPM and HUPM rotors can reduce the volume of PMs compared with the conventional configurations. However, with the HUPM rotor, a higher torque density and magnet utilization ratio can be achieved at the same time. [ABSTRACT FROM AUTHOR]

Due to the unchangeable air-gap flux density, the voltage output by permanent magnet synchronous generator (PMSG) will have a variation when the load changes. In order to reduce the voltage variation when PMSGs provide power for the rectifier load in diesel railway vehicles, an optimal method is presented to design a 9-phase PMSG. This optimal method not only ensures the open-circuit voltage of the generator equals the rated voltage of the load, but also it guarantees the PMSG has a low voltage change rate at the same time. In this paper, the saliency ratio range and the relationship between resistance of load and the induction of d-axis are derived according to the two-axis theory, when the PMSG has the negative or zero voltage change rate. Then based on the result of the derivation, by adding the I-shaped permanent magnet (PM) to the d-axis magnetic circuit of V-shaped interior PM rotor, a V-I-shaped PMSG is formed. After that, the Kriging method and the finite-element method (FEM) are used to establish a multi-objective function model. By calculating the minimum value of the multi-objective function, the construct dimension of the I-shaped PM is obtained. After the optimal design results are verified by the FEM, a 520 kVA 9-phase PMSG is manufactured to validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Fast and accurate modeling of large turbogenerators is of great importance for optimal design and commercial value. Therefore, a 2-D nonlinear magnetic equivalent circuit (MEC) model considering saturation and rotor motion is proposed in this article. When the node-based MEC adopts relaxation iteration for nonlinear calculation, it is not easy to converge by using traditional interpolation function and piecewise fitting of the core B–H or $u_{r} (B)$ curve. The main contribution of this article is to find that using continuous fitting function is of great significance for the convergence of nonlinear iteration. At the same time, a simple and effective MEC of air gap is also provided. The flux density of air gap and stator tooth obtained by the proposed method is in good agreement with results of the finite element. No-load characteristics were also verified by the finite element and experiment. The calculation time of a cycle takes about 700 s by the finite element, and however, MEC only takes about 2 s. [ABSTRACT FROM AUTHOR]

Offshore wind turbines are the key enabling technology to increase the green energy penetration in the electricity market. Increasing the power generation per tower and reducing the levelized cost of energy are the two significant problems faced by wind turbine manufacturers. Traditional turbine manufacturers use rare-earth permanent magnets (PMs) to increase the air-gap flux density and maximize the machine outer diameter (OD) to increase the torque output. Since the air-gap flux density achievable with available PM is limited, increasing the power output of a traditional generator invariably leads to a significant increase in the volume and mass on top of the turbine tower and associated manufacturing, transportation, and installation costs. Superconducting (SC) wind turbine generators offer 5 to 10 times the air-gap flux density of a PM generator, and a corresponding increase in specific power and power density. Previous MW scale SC wind turbines designs used heavy back iron in the design, iron saturation limits the achievable air-gap flux density in the designs and resulted in bulky generators and moderate efficiency. In this article, a hybrid design approach is proposed to reach an ultrahigh field (5 to 10 times of PM air-gap flux density) and high efficiency (>98%) SC wind turbine for offshore wind turbine. An additional stray field limitation is introduced for safety concerns and shielding techniques are explored. Electromagnetic, mechanical, and cooling designs are provided to support the feasibility of proposed SC wind turbines. A nacelle integration inside a commercially available 6 MW wind turbine is shown to demonstrate the size comparison of the proposed generator. [ABSTRACT FROM AUTHOR]

In this article, a novel spoke-type permanent magnet (PM) machine with two types of PM materials is proposed to reduce the cost. In order to improve torque density and reduce torque ripple, the multi-objective optimization combined finite element method (FEM) and genetic algorithm (GA) are used. In addition, the electromagnetic performances of the novel spoke-type PM machine, including no-load air-gap flux density, electromagnetic torque, torque ripple, efficiency, and cost are compared with the conventional spoke-type PM machine. It is demonstrated that the novel spoke-type PM machine obtains a 1.5% lower torque ripple and 36% lower cost, and the torque density is 4.3% lower than the conventional spoke-type PM machine. Meanwhile, the novel spoke-type PM machine has lower core loss and higher efficiency. Finally, a 40 kW spoke-type PM machine is manufactured to verify the analyzing method. Experimental results demonstrate that the proposed machine exhibits high torque density and low cost in the application of electric vehicles (EVs). [ABSTRACT FROM AUTHOR]

This article proposes a rotor design method suitable for double-layer interior permanent magnet synchronous motor (DIPMSM), which can reduce electromagnetic torque ripple and at the same time reduce the electromagnetic noise of the motor. In previous studies, the inverse cosine function (ICF) was used to modify the rotor shape for making the air-gap flux density distribution sinusoidal under no-load conditions, which can reduce the torque ripple. However, conventional ICF can only be used in a single-layer interior rotor structure. Consequently, this article proposes a piecewise inverse cosine function (PICF) based on ICF, which can be applied to DIPMSM. To verify the improvement of the proposed method in the electromagnetic and noise aspects of the motor, the electromagnetic model and a noise prediction model of the 36-slot/8-pole motor are established by the finite element method. The PICF model is compared with the prototype in the aspects of electromagnetic performance and noise. The torque ripple is reduced by 54.16%, from ±2.4 to ±1.1 N m, and the electromagnetic noise is reduced by about 4.9 dB. Finally, the accuracy of the noise prediction model is verified by the noise test of the prototype. [ABSTRACT FROM AUTHOR]

Electromagnetic performance of high-speed permanent magnet synchronous machines (PMSMs) is studied for electro-hydrostatic actuator (EHA) applications in this article. The electromotive force (EMF) of different magnet pole-arc to pole-pitch ratios is studied. The no-load air-gap density, cogging torque, average torque, torque ripple, core loss, and rotor eddy current losses are investigated by closed slots design. The rotor eddy current losses of different magnetic retaining sleeve materials such as stainless steel, titanium alloy, and carbon fiber are calculated by finite-element analysis (FEA). The results show that, compared with the opening slot structure, the torque ripple and the rotor eddy current losses of closed slot structure are extremely reduced due to the fact that the 11th and 13th harmonics of air-gap flux density are significantly reduced and the slotting effect are effectively weakened. Increase the closed slot height not only reduce the average torque and increase the core loss but also the torque ripple and the rotor eddy current losses reduction effect is slight. A high-speed PMSM with closed slots design is prototyped to verify the analysis. [ABSTRACT FROM AUTHOR]

In general, an air gap plays an important function in the magnetic core. It will enhance the stability of the inductance value of a reactor, increase the power density of the inductor, and optimize the properties of a high-frequency transformer. Hence, it is of great significance to study the influence of the air gap on the properties of magnetic cores. Based on a novel designed tester, the dynamic magnetic properties of the C-type amorphous (AMCC025) core and nanocrystalline (F3CC0125) core with different lengths of the air gaps are measured and analyzed when the cores are excited at different frequencies. In addition, the modified Steinmetz empirical formula which takes the fringing magnetic flux near the air gap into account is proposed. The calculated magnetic properties obtained from the modified formula show great agreement with the measured results. The average prediction error of the modified model is confined in 10%. Both the calculated and experimental results indicate that the influence of the fringing magnetic flux could be ignored when the length of the air gap is less than 5% length of the equivalent magnetic circuit. In particular, the frequency-dependent losses decrease to a minimum value and then increase with the increase in flux density accordingly. The modified loss model and results would be beneficial to the design of high-frequency inductors and transformer cores. [ABSTRACT FROM AUTHOR]

In this article, based on a 6-stator coil/17 rotor-tooth (6/17) conventional concentrated-winding multitooth flux-switching permanent magnet (C-MFSPM) machine, a novel full-pitch multitooth flux-switching permanent magnet (FP-MFSPM) machine is proposed by changing winding configurations. Then the electromagnetic performance of six FP-MFSPM topologies sharing the same 6-stator coil but with different rotor teeth combinations, namely, 6/13, 6/15, 6/17, 6/19, 6/21, and 6/23, is compared by using finite-element analysis (FEA). The results show that 6/17 and 6/19 are the optimal stator coil/rotor tooth combinations for FP-MFSPM machines, which exhibit better electromagnetic performance such as more enormous torque and smaller torque ripple. Thereafter, the existing C-MFSPM and the proposed FP-MFSPM machines with 6/17 and 6/19 structures are quantitatively compared in terms of no-load back electromotive force (back EMF), air-gap flux density, cogging torque, electromagnetic torque, torque ripple, and so on. The FEA-predicted results validate that the proposed FP-MFSPM machines have more sinusoidal back EMF, larger torque output, and smaller torque ripple, which are superior to the C-MFSPM topologies. [ABSTRACT FROM AUTHOR]

This article proposes a new maximum torque per ampere (MTPA) control strategy for an induction motor (IM) controlled by the scalar (v/f) method. In scalar control, constant air-gap flux control is generally adopted for IM drives to provide the same torque capability in all operating ranges. However, this control method results in poor motor efficiency due to excessive stator current at light loads. This work proposes a new MTPA control method to minimize the stator current amplitude based on reactive power without measuring the rotor mechanical speed, resulting in improved system efficiency at light loads. In addition, this method proposes an online machine parameter compensation method. Thus, this proposed method is robust to parameter variations. Simulation and experimental results are provided to verify the performance of this MTPA control strategy. [ABSTRACT FROM AUTHOR]

Performance prediction of induction machines (IMs) is highly dependent on the accuracy of the material characteristics and geometry of the machine during the modeling stage. To reduce the complexity of an IM model, normally the slotting effects are neglected. Likewise, the permeability of the stator and rotor cores are assumed to be infinite leading to an ideal set of partial differential equations (PDEs) for homogenous and isotropic materials. In this paper, the permeability of the stator and rotor cores are assumed not to be infinite and the slotting effects are taken into consideration to propose a more accurate and realistic model of an IM to reduce the discrepancies between the performance expectations and actual results. Fourier-based (FB) magnetic field approach is used to fulfill this aim via anisotropic layer theory (ALT) enabling the proposed model to include distortion of magnetic flux in the slotted regions. Air-gap flux density, core losses, efficiency and torque of an IM are predicted via the FB model and are validated through the finite element analysis (FEA) and experimental studies. [ABSTRACT FROM AUTHOR]

Accurate and computationally-efficient models of induction machines (IMs) are essential for many simulation programs and analysis of power systems transients. Conventionally, when modeling magnetic saturation in the classical qd0 models, only the fundamental component of magnetizing flux is considered. To represent the saturation air-gap flux harmonics, fairly complicated phase-domain and/or implicit models have been proposed in the prior literature. In this paper, a new explicit two-axis IM model is developed to include the air-gap harmonics caused by magnetic saturation. The new model is validated by experimental measurements and simulations in various steady state and transient scenarios and is shown to provide accurate results while being simple to implement. [ABSTRACT FROM AUTHOR]

In this paper, superposition methods including the superposition of a single stator tooth and the superposition of a single rotor tooth, are proposed to predict the open-circuit performances of flux-reversal permanent magnet (FRPM) machines. By the proposed superposition methods, the electromagnetic performances, such as air-gap flux density, electromotive force, cogging torque, and unbalanced magnetic pull (UMP) are investigated and verified by 2D finite element analysis (FEA). Further, according to the superposition methods, cogging torque reduction techniques can be acquired from both stator side and rotor side. In addition, the influence of stator-slot/rotor-pole-pairs (slot/pole) combination on UMP is also studied, and consequently, a reasonable slot/pole combination rule is suggested to avoid UMP. Then, an improved configuration for UMP reduction is also investigated and verified by FEA. Finally, the prototype machines are manufactured and tested to further verify the theoretical analysis and FEA predictions. [ABSTRACT FROM AUTHOR]

For a marine electrical machine, its high power density and large electromagnetic (EM) load tend to bring high saturation to the magnetic circuit. When the non-linearity of ferromagnetic material is not taken into consideration, large errors will appear in the calculation of air-gap flux density and EM force wave. Considering the radial and tangential EM force waves that cause the stator core to vibrate and deform are the primary sources of EM vibration of a non-salient pole synchronous generator (NSPSG), this paper introduces a semi-analytical method of calculating the radial and tangential EM force waves, with the non-linearity of ferromagnetic material taken into account. The method includes the distributed magnetic circuit method (DMCM), the separation variable method (SVM) and the complex variable conformal transformation method (CVCTM). First of all, the radial air-gap flux density is obtained by using the DMCM to calculate the no-load magnetic circuit of the NSPSG and dealing with the non-linearity of ferromagnetic material by B-H curve. Then, the tangential air-gap flux density is calculated by the SVM and the complex relative air-gap permeance is calculated by the CVCTM to determine the effect of slotting. Finally, the radial and tangential EM force waves are obtained by Maxwell stress tensor method. The proposed semi-analytical method is verified through measuring vibration acceleration of the NSPSG. [ABSTRACT FROM AUTHOR]

This paper proposes a monolayer Halbach array based permanent magnet spherical motor (PMSpM) using cubic permanent magnets (PM). The research aims to provide a fast computing model to calculate the magnetic field for this PMSpM, which helps for future PMSpM optimization and control study. Three thickness equivalence principles are provided and compared for cubic PMs. The magnetic scalar potential is introduced, and the spherical harmonics expansion is implemented for rotor magnetic field analysis. Engineering revision is used to reduce the Legendre function deviation in polar angle direction. Torques and forces are deduced using the Lorentz force law, and relatively simple models of this PMSpM for both magnetic fields and torques are acquired. In addition, a prototype motor has been developed, and the analytic results of air-gap flux density and torque are compared with their finite element simulation and experimental results, which are proved consistent. It is concluded that the fundamental component of the spherical harmonics can be used to present the magnetic field model, which uses fewer integrals than the Biot-Savart law based solution, and the modeling results of the magnetic field flux density, forces and torques are in line with the expectations. The analytic models are proved correct. [ABSTRACT FROM AUTHOR]

This article investigates the influence of stator slot number on electromagnetic performance of two-pole high speed permanent magnet (HSPM) slotted motors with toroidal (TO) windings. Four two-pole slotted motors with different slot numbers, i.e., 3, 6, 9, and 12, are globally optimised for maximum torque, and their electromagnetic performance are compared, including winding factor, air-gap flux density, back electromotive force, cogging torque, electromagnetic torque, winding inductances, unbalanced magnetic force (UMF), and various loss components. It shows that the six-slot/two-pole HSPM motor with TO windings is eminently suitable for high speed application due to no UMF and easy to realise a modular structure. In addition, TO and tooth-coil windings are compared in the three-slot/two-pole motors, and the results confirm that TO windings are not suitable for use in the three-slot/two-pole HSPM slotted motor due to large airgap field harmonics. Finally, a six-slot/two-pole prototype motor is manufactured and tested to validate the finite element predictions. [ABSTRACT FROM AUTHOR]

The overall driving cycle efficiency of conventional permanent magnet synchronous machines (PMSMs) for electric vehicle tractions in a wide speed range is constrained due to the large field weakening current and high iron loss in high speed. The series hybrid permanent magnet variable flux machines (HPM-VFMs) which employ both low coercive force (LCF) magnets and high coercive force magnets are proposed to obtain high torque density and flexible air-gap flux density simultaneously. The key of HPM-VFMs design is the accuracy of hysteresis model of LCF magnets and operating principle analysis. This article contributes to clarify operating principle based on hysteresis model of AlNiCo magnets and propose a novel design consideration to reduce magnetizing and demagnetizing current. Based on the theoretical analysis, this article proposes a novel series HPM-VFM, in which the NdFeB and AlNiCo magnets are arranged separately. Furthermore, flux paths are designed to achieve appropriate interaction between two kinds of magnets. The proposed machine has features of wide magnetization state (MS) variation range, low magnetizing and demagnetizing current, and low risk of unintentional demagnetization. By manipulating the MS of the proposed machine, the losses of a wide speed range operation could be reduced. The comparison of efficiency maps and the worldwide-harmonized light vehicles test cycle driving cycle losses between the proposed machine and a conventional interior PMSM proves that the proposed machine achieves higher efficiency for electric vehicle. [ABSTRACT FROM AUTHOR]