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Purpose: When rotor and stator teeth are close, the connecting air gap flux tube's cross-sectional area exceeds the tooth overlap area. This flux fringing effect is disregarded in the air gap permeance calculation of single-slice magnetic equivalent circuits (MECs) of electric motors with skewed rotors. This paper aims to extend an air gap permeance calculation method incorporating flux fringing for unskewed rotors to skewed and radially eccentric rotors. Design/methodology/approach: Assuming axial independence, the unskewed air gap permeance is rotated according to the skew and integrated along the axial dimension, resulting in a first method. The integral is approximated analytically, resulting in a second method. Results are compared to a commonly used reference method and validated using a non-linear finite element method (FEM) simulation. Findings: The proposed methods provide better alignment with the FEM validation compared to the reference method for skewed rotors and common rotor eccentricity, i.e. below 50% of the air gap length. The analytical method is shown to be competitive with the reference method regarding computational time cost. Originality/value: Two novel air gap permeance methods are proposed for single-slice MECs with skewed rotors. Their characteristics are discussed and validated. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this paper is to introduce an accurate asymmetric fault index for the diagnosis of the faulty linear permanent magnet Vernier machine (LPMVM). Design/methodology/approach: Three-dimensional finite element method is applied to model the LPMVM. The geometrical and physical properties of the machine, the effect of stator and translator teeth, magnetic saturation of core and nonuniform air gap due to asymmetric fault are taken into account in the simulation. The air gap asymmetric fault is proposed. This analytical method estimates the air gap flux density of an LPMVM. Findings: This paper presents an analytical method to predict the performance of a healthy and faulty LPMVM. The introduced index is based on the frequency patterns of the stator current. Besides, the robustness of the index in different loads and fault severity is addressed. Originality/value: Introducing index for air gap asymmetry fault diagnosis of LPMVM. [ABSTRACT FROM AUTHOR]

Purpose: Calculating the stator end-winding leakage inductance, taking into account the rotor, is difficult due to the irregular shape of the end-winding. The end-winding leakage may distribute at the end of the active part and the fringing flux of the air gap. The fringing flux belongs to the main flux but goes into the end-winding region. Then, not all the magnetic flux occurring in the end region is the end-winding leakage flux. The purpose of this paper was to find a method to accurately separate the leakage from the total flux, taking into account the rotor. Design/methodology/approach: In this paper, two methods based on energy calculation are presented. Both methods require the assumption that the machine is symmetrical. The first method depends on the total leakage inductance and the machine's active region length. The second method is based on the energy stored in the end region of the machine. In this case, removing the energy produced by the fringing flux of the air gap is necessary. The model should have a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. Findings: The method presented in the paper does not require rotor removal. The values of the end-winding leakage inductance computed based on the proposed method were compared with values computed using the method with the removed rotor. The computations show that the proposed method is closest to the results from the method presented in the literature. Results obtained in the first method present that rotor influence on the value of end-winding leakage inductance exists. The model of the stator end-winding described in the paper is general. Therefore, the proposed methods are suitable for calculating the end-winding leakage inductance of other electric machines. Originality/value: The method presented in the paper considers the rotor in end-winding leakage inductance calculation. It is not necessary to remove the rotor as in the similar method presented in the literature. The authors elaborated a parametric model with a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. The authors also elaborated their 3D model of the machine winding for calculations in Opera 3D. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to unveil the generation mechanism of the thrust force in a tubular flux-switching permanent magnet (PM) linear (TFSPML) machine; the operation principle of the TFSPML machine is analyzed. Design/methodology/approach: First, the air-gap flux density harmonic characteristics excited by PMs and armature windings are investigated and summarized based on a simple magnetomotive force (MMF)-permeance model. Then, the air-gap field modulation theory is applied in analyzing the air-gap flux density harmonics that contribute to the electromagnetic force. In addition, a simple method for separating the end force of the TFSPML machine is proposed, which is a significant foundation for the comprehensive analysis of this type of machine. As a result, the operation principle of the TFSPML machine is thoroughly revealed. Findings: The analysis shows that the average electromagnetic force is mainly contributed by the air-gap dominant harmonics, and the thrust force ripple is mainly caused by the end force. Originality/value: In this paper, the operation principle of the TFSPML machine is analyzed from the perspective of air-gap field modulation. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to propose an analytical model with consideration of the permeability of soft-magnetic materials, which can predict the magnetic field distribution more accurately and facilitate the initial design and parameter optimization of the machine. Design/methodology/approach: This paper proposes an analytical model of stator yokeless radial flux dual rotor permanent magnet synchronous machine (SYRFDR-PMSM) with the consideration of magnetic saturation of soft-magnetic material. The analytical model of SYRFDR-PMSM is divided into seven regions along the radial direction according to the different excitation source and magnetic medium, and the iron permeability in each region is considered based on the Maxwell–Fourier method and Cauchy's product theorem. The magnetic vector potential of each region is obtained by the Laplace's or Poisson's equation, and the magnetic field solution is determined using the boundary conditions of adjacent regions. Findings: The inner and outer air-gap flux density, flux linkage, output torque, etc., of SYRFDR-PMSM are predicted by analytical model, resulting in good agreement with that of finite element model. Additionally, the SYRFDR-PMSM prototype is manufactured and the correctness of analytical model is further verified by experiments on no-load back electromotive force and current–torque curve. Reasonable design of the slot opening width and pole arc coefficient can improve the average output torque and reduce output torque ripple. Research limitations/implications: The analytical model proposed in this paper assumes that the permeability of soft-magnetic material is a fixed value. However, the actual iron's permeability varies nonlinearly; thus, the prediction results of the analytical model will have some deviations from the actual machine. Originality/value: The main contribution of this paper is to propose an accurate magnetic field analytical model of SYRFDR-PMSM. It takes into account the permeability of soft-magnetic material and slot opening, which can quickly and accurately predict the electromagnetic performance of SYRFDR-PMSM. It can provide assistance for the initial design and optimization of SYRFDR-PMSM. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate a novel rotor design model to improve the technical performance of a superconducting synchronous generator. Design/methodology/approach: Superconducting synchronous generators with a modular rotating cryostat for a single coil of the superconducting winding instead of an old-style single cryostat in which all rotor components are cold are briefly discussed. Subsequently, a new method of cryostat arrangement in the magnetic system of a rotor is considered. Different options were compared for the cryostat placement. The advantages of the novel rotor design model are noted. Findings: In the novel rotor design model, the leakage coefficient of the excitation winding decreases, and the air gap magnetic flux increases, which will save on a superconductor material. Research limitations/implications: For the purposes of this investigation, a finite element study of flux distribution in the cross section of a superconducting synchronous generator with a 10 MW rating at 10 rpm was conducted, and the magnetic fluxes and air gap flux densities were obtained for different modes. For direct-drive superconducting synchronous generators with distributed winding and different pole numbers, the calculations of magnetic fluxes were carried out by calculating the magnetic conductivities. Originality/value: A new method of the cryostat arrangement in the magnetic system of a rotor has been classified as an invention and was protected by a patent. This paper is directly applicable to the field of superconducting synchronous generators. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to develop a new and fast three-dimensional (3D) analytical model to study a synchronous axial magnetic coupling with rectangular shaped magnets. This model takes into account edge and curvature 3D effects. Design/methodology/approach: This paper firstly introduces a 3D analytical model for an axial coupler with sector shaped permanent magnet (PM) based on magnetic scalar potential formulation in cylindrical coordinates. The magnetic field in PM, air gap and iron disks is computed by solving Laplace's and Poisson's partial differential equation. This solution is then used to compute the field in rectangular shaped magnets. To do so, the adopted approach consists to divide the rectangular magnet into sector radial slices each of which the 3D model allows the determination of the magnetic field distribution. The results obtained by the proposed 3D analytical model are validated through 3D finite element computations. Furthermore, a prototype axial magnetic coupler has been constructed so air gap flux density and static torque measurements are compared to the analytical predictions. Findings: The results obtained by the analytical model show the effectiveness of the proposed geometry transformation approach. The developed model takes into account all the 3D effects without needing any correction factor. Research limitations/implications: The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process. Practical implications: The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process. Originality/value: A new and fast 3D analytical model, to improve the computation of the electromagnetic torque developed by a synchronous magnetic coupler with rectangular shaped magnets, has been developed. The proposed approach is really effective as it leads to consistent results when compared to 3D finite element method ones without any need for correction factor. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to establish a piecewise Maxwell stress analytical model of bearingless switched reluctance motor (BSRM) for the full rotor angular positions. The proposed model varies from the existing models, which are only applicable to the partial-overlapping positions of stator and rotor poles. By extending the applicable rotor angular positions, this model provides a basic analytical model for the multi-phase excitation control of BSRM. Design/methodology/approach: The full rotor angular positions are classified into the partial-overlapping positions and the non-overlapping positions. At first, two different air gap subdividing methods are proposed, respectively, for the two-position ranges. Then, different integration paths are selected accordingly. Furthermore, two approximate methods are presented to calculate the average flux density of each air gap subdivision. Finally, considering the mutual coupling between the two perpendicular radial suspension forces, a piecewise Maxwell stress analytical model is derived for the full rotor angular positions of BSRM. Findings: A piecewise Maxwell stress analytical model of BSRM is built for the full rotor angular positions, and applicable to the multi-phase excitation mode of BSRM. For the partial-overlapping positions and the non-overlapping positions, two sets of air gap subdividing methods, integration paths and approximate calculation methods of air gap flux densities are proposed, respectively. The accuracy and reliability of the proposed model are verified by the finite element method. Originality/value: The piecewise Maxwell stress analytical model of BSRM for the full rotor angular positions is proposed for the first time. The novel air gap subdividing methods, integration paths, approximate calculation methods of air gap flux densities and the coupling between the two radial suspension forces are adopted to improve the modeling accuracy. As the applicable range of rotor angular position is extended, this model overcomes the limitation of the existing models only for single-phase excitation mode and contributes to the accurate control of BSRM multi-phase excitation mode. [ABSTRACT FROM AUTHOR]

Purpose: To improve the power density and generation efficiency of the tubular permanent magnetic linear generators (TPMLGs) under realistic sea-stator condition, a TPMLG with 120° phase belt toroidal windings (120°-TPMLG) for wave energy conversion is proposed in this paper. Design/methodology/approach: First, the structure of the 120°-TPMLG is introduced and its operation principle is analyzed. Second, the design process of the 120°-TPMLG is described. Meanwhile, the finite-element models of the 120°-TPMLG and the TPMLG with traditional fractional pitch windings (T-TPMLG) are established based on the similar overall dimensions. Then, the electromagnetic characteristics of the 120°-TPMLG are analyzed, such as air gap flux density, back electromotive force and load voltage. Finally, a comparative analysis of the magnetic flux density, flux linkage, load and no-load performance of the two generators are conducted. Findings: The result shows that the 120°-TPMLG has higher power density and generation efficiency than the T-TPMLG. Originality/value: This paper proposes a TPMLG with 120° phase belt toroidal windings (120°-TPMLG) to improve the power density and generation efficiency. [ABSTRACT FROM AUTHOR]

Purpose: In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem. Design/methodology/approach: Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed. Findings: In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained. Research limitations/implications: The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM. Originality/value: The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap. Design/methodology/approach: The superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP. Findings: The radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results. Originality/value: This paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to improve the finite element modelling of transformers subjected to DC excitation, by including core joint details.Design/methodology/approach Geomagnetically induced currents (GICs) or leakage DC can cause part-cycle, half wave saturation of a power transformer’s core. Practical measurements and finite element matrix (FEM) simulation were carried out using three laboratory-scale, untanked single-phase four limb transformers resembling real power transformers in terms of the core steel and parallel winding assemblies. “Equivalent air gaps” at the joints, based on AC measurements, were applied to the FEM models for simultaneous AC and DC excitation.Findings Measurements confirm that introducing equivalent air gaps at the joints improves the FEM simulation of transformers carrying DC.Research limitations/implications The FEM simulations based on the laboratory transformers are exemplary, showing the difference between modelling core joints as solid or including equivalent air gaps. They show that, for more representative results, laboratory transformers used for research should have mitred core joints (like power transformers).Originality/value This research shows why joint details are important in FEM models for analysing transformer core saturation in the presence of DC/GICs. Extending this, other core structures of power transformers with mitred joints should improve the understanding of the leakage flux during half-wave saturation. [ABSTRACT FROM AUTHOR]

Purpose Consideration of leakage fluxes in the preliminary design stage of a machine is important for accurate determination of machine dimensions and prediction of performance characteristics. This paper aims to obtain some equations for calculating the average air gap flux density, the flux density within the magnet and the air gap leakage flux factor.Design/methodology/approach A detailed magnetic equivalent circuit (MEC) is presented for a TORUS-type non-slotted axial flux permanent magnet (TORUS-NS AFPM) machine. In this MEC, the leakage flux occurring between two adjacent magnets and the leakage fluxes taking place between the magnet and rotor iron at the interpolar, inner and outer edges of the magnets are considered. According to the proposed MEC and by using flux division law, some equations are extracted. A three-dimensional finite element method (FEM) is used to evaluate the proposed analytical equations. The study machine is a 3.7 kW and 1,400 rpm TORUS-NS AFPM machine.Findings The air gap leakage flux factor, the average air gap flux density and the flux density within the magnet are calculated using the proposed equations and FEM. All the results of FEM confirm the excellent accuracy of the proposed analytical method.Originality/value The new equations presented in this paper can be applied for leakage flux evaluating purposes. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to introduce an asymmetric structure of the magnetic equivalent circuit (MEC) for analysis of the linear induction machine (LIM) with an internal short circuit fault.Design/methodology/approach By applying a proper MEC to the LIM, a generalized relation for the inductance matrix of the machine can be directly determined. To evaluate the proposed model, the stator currents and the air-gap flux with the proposed technique are given and compared to the simulation and experimental results in the healthy and fault conditions.Findings The LIM is an axial flux machine with a wide range of applications in high-performance drives. Due to a well-tried effect of the first tooth and the last one (the end effect), the performance level of the LIM decreases. Also, the analysis of the linear machines in fault conditions illustrates more complexity compared to the rotary induction machine. However, the MEC is very simple, describing the behavior of the asymmetric electromechanical devices using the magnetic reluctance or the permeance of flux paths.Originality/value Using the proposed model, there would be some decrease in the complications of the LIM analysis in the asymmetrical conditions. Moreover, analyzing some of the characteristics of the LIM, such as turn-fault condition, it can be calculated with high accuracy. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to propose an analytical model for the calculation of forces ripples in bearingless permanent magnet motor.Design/methodology/approach The model is based on a spectral modeling of the forces based on a spectral analysis of the air-gap flux density.Findings The proposed methodology allows the prediction of the ripples of the levitation according the design of the machine and the topology of the winding. It can be used in the design procedure of bearingless motor in order to avoid mechanical resonance of the rotor shaft.Research limitations/implications This model cannot be used for high saturated machines.Originality/value The main originality of this paper consists in the evaluation of the field harmonics according to their sources and the contribution of the different harmonics to the force ripples. This can help the designer to focus on reducing or eliminating only the harmonics of flux density which create the force ripples. [ABSTRACT FROM AUTHOR]