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This paper presents a nonlinear analytical model of a multi-V-shape interior permanent magnet (IPM) motor with nonoverlapping concentrated winding. The model relies on Ampere's theorem and the flux conservation law in order to compute the flux density in the different parts of the motor. This article proposes a saturated analytical model of the stator and the rotor. The analytical model is used to calculate the average torque, the power factor, and the voltage of the motor. It is five times faster than the 2-D finite element analysis (FEA). The results are compared with 2-D FEA simulations and experimentally validated using a prototype motor. [ABSTRACT FROM PUBLISHER]

To study the clamping device in reluctance force launcher, the Maxwell stress tensor method is extended to contact force calculations. It is generally believed that the Maxwell stress tensor method is only suitable for objects surrounded by air or vacuum. However, in this article, the Maxwell stress tensor applicable to ferromagnetic materials is re-derived, and the classical Maxwell stress tensor is successfully reproduced. Its integral region is determined as the outer surface of the interface between the object and the outside world, which means that the Maxwell stress tensor method can be used for contact force calculations. Subsequently, the Maxwell stress tensor method was used for force studies in the clamping device. The needed clamping force of the clamping device is calculated. The reducing effect of ferromagnetic materials on the clamping force and the effect on the acceleration force of the projectile are analyzed. Finally, based on the determined integral region, the reason why the integral result of Maxwell stress tensor method is related to the integral path is successfully explained, which provides another theoretical basis for the contact force calculation method in this article. [ABSTRACT FROM AUTHOR]

A finite-element formulation based on the use of magnetic scalar potential is proposed. It allows to describe circuit-coupled electromagnetic formulation using magnetic scalar potential in presence of multiply connected solid conductors (with holes), treated by surface impedance condition. This formulation offers powerful solutions at a low cost. An example of application is given. [ABSTRACT FROM AUTHOR]

Evaluates several equivalences and approximations that lead to usable approximations of copper losses in a transformer intended to a flyback converter. Equivalent permeability; Field approximation for continuous core; Analytical estimation of proximity losses; Evaluation of air-gap-related losses; Extension to a flyback transformer.

The commentor takes issue with various points made in the original article by P.R. Bhattacharjee (ibid., vol.32, no.2, pp.24,26, April 2013). In particular she feels that the most fundamental flaw in Bhattacharjee's scheme is that defining 'current' in a direction perpendicular to the flow of charge becasue this redefinition breaks the symmetry of the Maxwell equations. She feels Bhattacharjee's article does nothing to clear up any confusion and offers no new insight. Rather, the author confuses lumped and vectorial models of electromagnetics, real vectors, and psuedovectors and only muddies the waters. In replying Bhattacharjee notes that the work described in the original article had been an extension of the previous article "Discovering the Vectorial Nature of Electric Current," which appeared in the vol. 3, 2012 issue of the International Journal of Physical and Mathematical Sciences (IJPMS), a peer-reviewed journal published by the International Centre of Cultural Inventory (icoci.org). It was clearly stated in the earlier 2012 published paper in IJPMS that the said work deals with a debatable issue and what has been reported in it is exclusively related to the feeling of the author with respect to the long-running misleading concept about electric current. It has also been mentioned in that paper that the said study reflects a discovery of the real truth, which has been overlooked so far and, as such, deserves special attention. The author feels the newly introduced vectorial portrayal of electric current is very much clear, leaving no room for confusion and has rationality with the convention used in regard to the direction of unit positive normal in defining vector area in vector calculus. Also, such a direction for the vectorial current follows from the well-known Ampere's theorem of equivalent magnetic shell [ABSTRACT FROM PUBLISHER]

A new resistance bridge has been built at the Laboratoire national de métrologie et d’essais (LNE) to improve the ohm realization in the Système International (SI) of units from the quantum Hall effect. We describe the instrument, the performance of which relies on two synchronized and noise-filtered current sources, an accurate and stable current divider, and a cryogenic current comparator (CCC) having a low noise of $\mathrm {80~pA.t/Hz^{1/2}}$. The uncertainty budget for the measurement of the 100- $\Omega /(R_{\textrm {K}}/2)$ resistance ratio, where $R_{\textrm {K}}$ is the von Klitzing constant, amounts to a few parts in $10^{10}$ only. [ABSTRACT FROM AUTHOR]

A hybrid field model (HFM) based on the combination of magnetic equivalent circuit (MEC) and exact conformal mapping (ECM) is developed to calculate the open-circuit field of interior permanent-magnet (IPM) motor. In the proposed HFM, the IPM and iron saturations are transformed into equivalent current on the rotor surface and stator bore. ECM can calculate the air-gap field analytically using the equivalent current. Once the air-gap field is obtained, the MEC in the iron region can be solved and gives the new value of equivalent current, which forms a calculation loop. Hence, iterative solving process is required to determine the equivalent current and iron permeability in the rotor and stator. In order to verify the proposed model, both finite-element (FE) analysis and experiment are performed on IPM motors with V-type rotor and conventional “-” type rotor. Their results demonstrate the high accuracy of HFM. [ABSTRACT FROM AUTHOR]

In this paper, a multiphysics model is proposed for a multi-V-shape interior permanent magnet motor with concentrated winding. This paper develops a nonlinear magnetic model that computes the flux density in the motor. The analytical model includes several novel aspects: it takes into account the local saturation near the iron bridges, it proposes a method for modeling the concentrated tooth winding, and it calculates the slot tangential leakage flux and includes it in the flux linkage calculation. The magnetic model is coupled with an electrical model that computes the power factor and the voltage at the motor terminals. A loss model is developed in order to calculate the copper and the iron losses. They are used as inputs to a nodal thermal model that introduces a thermal circuit for concentrated end-winding and computes the temperature of the motor. A mechanical model is developed. It evaluates the mechanical constraints encountered by the structure. The models are verified using finite element computations and numerical calculations performed with dedicated software. Besides, the coupled analytical model is experimentally validated using a prototype motor. Finally, two multiphysics bi-objective optimizations are carried out in order to design the motor for high-torque and low-speed application. [ABSTRACT FROM AUTHOR]

Rogowski coil is used as a current transducer in complex electromagnetic environment, whose anti-interference property bears on the accuracy of the current measurement. Based on the ordinal straight-coupled foils of the current PCB Rogowski coil, this paper proposes a newly designed PCB Rogowski coil with symmetrical double-printed imprints and returning turn to gain better precision and performance. The mutual inductance between the coil and the primary conductor is chosen as the sensitivity parameter to contrastively analyze the anti-interference property of three coils, including the ordinary straight-coupled coil, the symmetrically printed coil with or without returning turn. The calculation and measurement of mutual inductance have been made under different disturbed conditions, such as the eccentricity from axis of the primary conductor and the influence of external parallel and perpendicular currents. The results indicate that the newly designed PCB Rogowski coil with symmetric imprints and returning turn is good in compatibility, strong in anti-interference property, and also accurate and steady in mutual inductance. Therefore, it is suitably applied as the sensing head of current measurement in the complex stray electromagnetic fields. [ABSTRACT FROM PUBLISHER]

A new analytical computation of magnetic flux distribution and eddy currents is proposed in this paper. Equations are set down for a plate subjected to a time-varying flux excitation. This method consists of using Neumann's boundary conditions in the flux-density diffusion equation to consider the instantaneous variations of the imposed flux waveform. The diffusion equation is solved by separation of variables and Duhamel's theorem. Different cases of imposed magnetic flux are studied: sinusoidal flux, flux ramp, and arbitrary time-varying flux. This new analytical method is a complement of the classical approach (with Dirichlet's boundary conditions) where induction at boundary needs to be corrected to fit the instantaneous total flux. In this paper, a distinctive method allows to compute the instantaneous distributions and corresponding losses directly from the experimental flux measurements on electromagnetic devices. The analytical expressions of magnetic flux density and eddy current distributions are explicitly given. The comparison between analytical and finite-element simulation results shows the validity of the new analytical method. [ABSTRACT FROM PUBLISHER]

This paper presents an analytical methodology based on subdomain field model to calculate eddy current loss in vertical conductor windings (VCWs) of surface mounted, radial flux, permanent magnet (PM) machines considering the current penetration effect. The proposed model can be used with any slot–pole combination including fractional slot machines having VCW. Initially, the model solves the two-dimensional problem based on the Laplace's and Poisson's equations using the separation of variables technique for each of the subdomains: PM, airgap, slot opening, and slot. Then, based on that obtained solution, the eddy current reaction field in the slot is calculated by solving complex Helmholtz's equation. The validity and accuracy of the model is verified using finite-element (FE) analysis. The limitations of analytical method are discussed. [ABSTRACT FROM AUTHOR]

Based on the Stieltjes integral, this paper investigates the characteristics of the torque area of surface permanent magnet motors with sinusoidal magnetization used in hard disk drives. Then, a simple torque calculation algorithm is proposed and verified through comparison with the finite element analysis. Meanwhile, an improved motor having the sintered NdFeB with sinusoidal magnetization and smaller airgap length is recommended. [ABSTRACT FROM PUBLISHER]

Some high-torque electric machines, such as low-speed wind generators, may be very difficult to test on load because of the large and expensive mechanical equipment required to load them (motors) or to drive them (generators). In this paper, a full-load regenerative testing methodology is described which does not require any rotating equipment to be coupled to the machine where the rated active power flows in a closed loop between the machine and a suitably connected dual-stage converter. The successful application of this methodology to a 780-kW 14-r/min wind generator prototype is addressed as a study case. Relevant experimental results are reported in a companion paper. [ABSTRACT FROM AUTHOR]

The paper proposes an improved analytical model, valid for a wide frequency range, of interlaminar short-circuits on the edges of the sheets of high power transformers working at 50–60 Hz. This model is able to determine the current flowing in the microscopic interlaminar contacts formed by burrs, in order to estimate the maximum power dissipated in such hot spots. With this theoretical approach, it is also possible to get an interpretation of impedance measurements on a test coil wound around the core, in order to define a new index able to characterize the part of the shearing burrs in the manufacturing factor of large transformer cores. This new index will help the transformer manufacturers to improve their processes. [ABSTRACT FROM PUBLISHER]

By visualizing the torque as an area enclosed by locus of magnet operating points in B\-H plane, several surface mounted permanent magnet (SPM) motors with different pole/slot combinations for hard disk drive (HDD) spindle motors are analyzed to clarify their geometrical characteristics of the maximum torque area. Then, a simple and fast calculation algorithm of predicting the maximum torque is proposed based on the torque geometrical interpretation and its validity is verified through comparison with FEA results. In addition, optimum pole/slot combinations for modern HDD spindle motors are recommended from the view points of reducing vibration resource caused by cogging torque and increasing speed control accuracy. [ABSTRACT FROM AUTHOR]

High-speed electric drive design is concerned with paying particular attention to thermal and mechanical design of the machine. Therefore, this paper proposes a multiphysic modeling of an interior permanent-magnet synchronous machine (IPMSM) dedicated to high speed, including magnetic, electric, thermal, and mechanical aspects. The proposed analytical models are verified using finite-element (FE) computations. These models are then subjected to a multiobjective optimization—based on genetic algorithm—to design an IPMSM for a high-speed compressor application that develops 30 kW at 20 000 r/min. The design is formulated as a constrained optimization problem consisting of maximizing the machine efficiency while minimizing its weight. The result of this process is a Pareto front between efficiency and weight of the machine allowing the designer to make a posteriori choice. A particular optimal machine is chosen and its performances are validated with FE analysis. This study carries out an optimal multiphysic and multiobjective design approach that allows rationalization of the design process in a realistic computation time thanks to the analytical models involved. [ABSTRACT FROM AUTHOR]

A robust numerical method based on 2-D mixed finite-elements-finite volumes (FE-FV) allows the solution of diffusion problems in superconducting (SC) materials. The proposed approach handles the strong nonlinearity of the E(J) constitutive power law of high-temperature superconductors (HTS). The method is tested for a SC cylinder submitted to a sinusoidal transport current or to a transverse sinusoidal external field. The current density distributions as well as the AC losses are computed. Comparisons to a FE analyses that use the magnetic field as state variable show the validity of the proposed approach. It can be seen that the proposed method is very stable even for large n-values for which the FE method does not converge. [ABSTRACT FROM AUTHOR]

The complementary energy bounds of dual formulations on dual meshes for eddy current problems are investigated. Based on the algebraic discretization of Maxwell equations on the dual meshes using different working variables, two sets of dual formulations, both for the finite-element method (FEM) and the finite integral technique (FIT), can be derived. A rational comparison between these formulations and the circuit networks is performed. The complementary bounds of magnetic energy and power losses are studied through an example. The study shows that the energy bounds are due to the numerical discretization of the Hodge operators on dual meshes. The dependency of the upper and lower energy bounds on the field excitation is also illustrated. The relation of the numerical bounds of the global circuit elements to the dual mesh discretization is given. [ABSTRACT FROM AUTHOR]

As a consequence of the increase of power needs in low-voltage applications, wiring several windings in parallel to sustain large currents has become common. This choice may have a serious impact on the transformer reliability. In practice, due to additional currents that we call "circulation currents," highly localized extra losses occur. Although hot points resulting from these currents can destroy the component, the related losses are generally not taken into account by analytical approaches. In planar transformers, windings are made of printed circuit board layers, and circulation currents lead to severe unbalance of current sharing between parallel layers. This paper presents an analytical method enabling the evaluation of the currents in every layer using only a circuit simulation software such as Pspice or PSIM. For a designer, this method is very intuitive and fast compared with the use of finite element method simulations. Several extensions of the modeling method used here are also presented. [ABSTRACT FROM AUTHOR]

This paper analyzes the efficiencies of the new coupling between finite-element methods (FEMs) and the partial element equivalent circuit method (PEEC), which are computation time and memory space. To show its performance, a common mode filter is modeled by the coupling and the results are then compared with those of a FEM analysis. The comparison shows that the coupling is very efficient to model electromagnetic systems comprising magnetic materials and systems of complex thin conductors. [ABSTRACT FROM AUTHOR]

The contribution of powerful numerical calculation methods in the design procedure of electrical actuators is usually restricted to the analysis of structures with known geometric dimensions. This paper describes a computer-aided design tool with a multiphysics design methodology starting from datasheet specifications. It is operational from the first design phases due to the association of analytical and numerical approaches that are performed by the coupling of two software tools. The analytical study associates a coupled electromagnetic-thermal model with a gradient optimization algorithm and provides a quick first solution. This solution is then optimized, according to other criteria, by a further numerical study that is based on a finite-element model that is linked to a simplex algorithm. The vibratory behavior of the obtained solution is finally studied using modal analysis. This methodology is applied to design a permanent-magnet synchronous machine. [ABSTRACT FROM AUTHOR]

When the total current going through a transformer window is equal to zero, only a negligible part of the magnetic energy reaches its core. This is shown by finite-element-method simulations carried out on several two-winding transformers having different shapes. Moreover, induction and energy-density values obtained by 3-D simulations and by 2-D approximations are very close to each other. These two key observations justify the use of formulas that give the induction created by straight rectangular cross-sectional wires, as used in the partial-element-equivalent-circuit method, to compute the window field and, thus, to value the leakage inductances. To refine this approach, weak magnetic-core effects are accounted for by introducing the magnetic images of currents that flow in the windings. A comparison between the calculated values and measured ones is provided. [ABSTRACT FROM AUTHOR]

The magnetic field profile on the surface of Bi-2223/Ag tapes has been dynamically measured across the width of the samples. The experimental technique uses a flail-probe array with 7 sensors connected to a multiple channel lock-in amplifier especially programmed for fast and synchronous data acquisition measurements. The speed of the system is high enough to measure real-time profiles with 7 probes and 50 Hz sine current through the sample. A numerical method to estimate the current distribution inside the tapes using the measured field profile data is proposed. The inverse problem has been solved using certain assumptions on the current distribution in the superconductor. Validation of the results has been done by comparison with finite element method simulations. [ABSTRACT FROM AUTHOR]

This paper presents a framework which implements the common software functionalities. By using this framework, software designers focus on their activity on developing efficient data structures and algorithms. The logic programming introduced in this framework is an efficient technology for Object Constraint Language expressions. Errors made by the user when modeling a device are detected and prevented by the modeling guide. [ABSTRACT FROM AUTHOR]

Presents the theory and the validation of a finite-element formulation to realize the coupling between electric circuits and multiply connected magnetic circuits, using a magnetic scalar potential as state variable. Computation with a multiply connected domain; Description of the current transformer.

Focuses on a study which examined the formulation of electric current vector potential t-Ω for eddy-current problems in multiply connected regions. Advantage of the formulation; Details of formulation; Explanation of discrete space of vector potential in cutting domain; Information on consistent formulation for multiply connected regions; Discussion on how cuts can be automatically generated.

Presents information on a study which proposed a finite element method for modeling the imposed currents in several long conductors. Characteristic of superconducting materials; Formulation and numerical solution; Results and discussions; Conclusions.

Provides information on a study which examined several three-dimensional eddy current formulations derived from dual system of Maxwell equations. Dual formulations of eddy current problems; Comparison of field and potential formulations; Conclusions.

Focuses on a study which examined the application of several second order nodal and edge elements in a potential formulation to solve three-dimensional eddy current problems. Second order edge elements; Eddy current formulation; Comparison of results; Conclusions.