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The purpose of this paper is threefold. First, an analytical model based on one-dimensional Dowell’s equation for computing ac-to-dc winding resistance ratio FR of litz wire is presented. The model takes into account proximity effect within the bundle and between bundle layers as well as the skin effect. Second, low- and medium-frequency approximation of Dowell’s equation for the litz-wire winding is derived. Third, a derivation of an analytical equation is given for the optimum strand diameter of the litz-wire winding independent on the porosity factor.

The methodology is as follows. First, the model of the litz-wire bundle is assumed to be a square shape. Than the effective number of layers in the litz wire bundle is derived. Second, the litz-wire winding is presented and an analytical equation for the winding resistance is derived. Third, analytical optimization of the strand diameter in the litz-wire winding is independent on the porosity factor performed, where the strand diameter is independent on the porosity factor. The boundary frequency between the low-frequency and the medium-frequency ranges for both solid-round-wire and litz-wire windings are derived. Hence, useful frequency range of both windings can be determined and compared.

Closed form analytical equations for the optimum strand diameter independent of the porosity factor are derived. It has been shown that the ac-to-dc winding resistance ratio of the litz-wire winding for the optimum strand diameter is equal to 1.5. Moreover, it has been shown that litz-wire winding is better than the solid-round-wire winding only in specific frequency range. At very high frequencies the litz-wire winding ac resistance becomes much greater than the solid-round-wire winding due to proximity effect between the strands in the litz-wire bundle. The accuracy of the derived equations is experimentally verified.

Derived equations takes into account the losses due to induced eddy-currents caused by the applied current. Equations does not take into account the losses caused by the fringing flux, curvature, edge and end winding effects.

This paper presents derivations of the closed-form analytical equations for the optimum bare strand diameter of the litz-wire winding independent on the porosity factor. Significant advantage of derived equations is their simplicity and easy to use for the inductor designers.

The purpose of this paper is to study the multi-objective optimization design method of high-power high-frequency magnetic-resonance air-core transformer (ACT).

First, this paper studies the interleaved winding technology, the process of modeling and simulation, the calculation method of high-frequency loss of Litz wire and the design of magnetic shielding in detail. Second, the multi-objective optimization design process of high-frequency magnetic-resonance ACT is established by parametric scanning method and orthogonal experiment method.

An ACT model of 2 kV/100 kW/81.34 kHz was designed. The efficiency, weight power density and volume power density are 99.61%, 21.6 kW/kg and 5.1 kW/kg, respectively. Finally, the multi-physical field coupling simulation method is used to calculate the port excitation voltages and currents and temperature field of ACT. The maximum temperature of the ACT is 95.5 °C, which meets the design requirements.

The above research provides guidance and basis for the optimization design of high-power high-frequency magnetic-resonance ACT.

It takes long time for estimating a copper loss in the coil winding of the motor by using the finite element method (FEM). The purpose of this paper is to calculate fast the copper loss by zooming method.

The authors adopt the “zooming method” to FEM. The authors compare the accuracy and the calculation time with zooming method and normal FEM.

The zooming method contributes to speeding up and the high accuracy of calculation. In the results, the 43-fold speed increase is achieved in the calculation of synchronous motor compared to usual FEM.

The AC copper loss calculation of 3D motor analysis can be calculated in practical computation time.

The main advantage of employment of zooming method is significantly reduction of the computation time in the loss calculation of the coil winding.

The purpose of this paper is to introduce a new method to model a stranded wire efficiently in 3D finite element simulations.

In this method, the stranded wires are numerically approximated with the Cauer ladder network (CLN) model order reduction method in 2D. This approximates the eddy current effect such as the skin and proximity effect for the whole wire. This is then projected to a mesh which does not include each strand. The 3D fields are efficiently calculated with the CLN method and are projected in the 3D geometry to be used in simulations of electrical components with a current vector potential and a homogenized conductivity at each time step.

In applications where the stranded wire geometry is known and does not change, this homogenization approach is an efficient and accurate method, which can be used with any stranded wire configuration, homogenized stranded wire mesh and any input signal dependent on time steps or frequencies.

In comparison to other methods, this method has no direct frequency dependency, which makes the method usable in the time domain for an arbitrary input signal. The CLN can also be used to interconnected stranded cables arbitrarily in electrical components.

Litz wire manufacturing using mechanical procedures presents several limitations regarding reliability and repeatability, especially when a small strand diameter is used. This paper aims to propose a power supply design for Litz wire manufacturing using a high-frequency high-performance resonant converter.

This paper proposes the design of a resonant power supply for induction heating specially designed to tackle with the challenge of heating Litz wires quickly.

The proposed converter enables the removal of the isolating coating from the Litz wire through induction heating, improving significantly the manufacturing process.

The proposed converter improves significantly the manufacturing process of Litz wire through induction heating, with economic and reliability benefits.

The purpose of this paper is to determine the broadband frequency response of the impedance matrix of wireless power transfer (WPT) systems comprising litz wire coils.

A finite-element (FE)-based method is proposed which treats the microstructure of litz wires by an auxiliary cell problem. In the macroscopic model, litz wires are represented by a block with a homogeneous, artificial material whose properties are derived from the cell problem. As the frequency characteristics of the material closely resemble a Debye relaxation, it is possible to convert the macroscopic model to polynomial form, which enables the application of model reduction techniques of moment-matching type.

FE-based model-order reduction using litz wire homogenization provides an efficient approach to the broadband analysis of WPT systems. The error of the reduced-order model (ROM) is comparable to that of the underlying original model and can be controlled by varying the ROM dimension.

Since the present model does not account for displacement currents, the operating frequency of the system must lie well below its first self-resonance frequency.

The proposed method is well-suited for the computer-aided design of WPT systems. It outperforms traditional FE analysis in computational efficiency.

The presented homogenization method employs a new formulation for the cell problem which combines the benefits of several existing approaches. Its incorporation into an order-reduction method enables the fast computation of broadband frequency sweeps.

The purpose of this paper is to compare the performance of conventional, novel E‐ and C‐core switched‐flux permanent magnet (SFPM) machines having different combinations of stator and rotor pole numbers, with particular reference to the conductor and magnet eddy current loss and iron loss.

The electromagnetic performance of the analysed machines is compared using the finite element (FE) analysis.

Both iron and conductor eddy current losses increase with the rotor pole number, while the 11‐ and 13‐rotor pole machine always exhibit lower magnet eddy current loss than those of the 10‐ and 14‐rotor pole machines, respectively. The E‐ and C‐core machines use half the number and volume of magnets and also exhibit higher efficiency than those of the conventional SFPM machine.

Investigation of the influence of stator and rotor pole combinations on the performances of conventional, novel E‐ and C‐core SFPM machines, include losses and efficiency.

The purpose of this paper is to present, a novel boost‐active clamp bridge single stage high‐frequency zero voltage soft‐switching‐pulse width modulation (ZVS‐PWM) inverter, which converts the utility frequency AC power into high‐frequency AC power with an embedded controller. This single stage high‐frequency inverter is composed of a single‐phase diode bridge rectifier, a non‐smoothing filter, a boost‐active clamp bridge type ZVS‐PWM high‐frequency inverter, and an induction‐heated load with planar type litz wire working coil assembly. Also, the paper discusses how to extend the soft‐switching operation ranges and improve power conversion efficiency.

The proposed converter is simulated and it is implemented using embedded controller.

It was found that the single stage high‐frequency induction heating (IH) inverter using boosted voltage function can eliminate the DC and low‐frequency components of the working coil current and reduce the power dissipation of the circuit components and switching devices.

The paper shows that the PWM HF inverter is preferred for IH, since it has reduced switching losses and switching stresses. The paper can be extended to PC‐based wireless control, which can be part of a distributed control system in major industrial heating systems.

This paper presents a computer‐aided design (CAD) tool for the design of isolated dc‐dc converters.

This tool, developed in Matlab environment, is based on multiobjective optimization (MO) using genetic algorithms. The Elitist Nondominated Sorting Genetic Algorithm is used to perform search and optimization whereas analytical models are used to model the power converters. The design problem requires minimizing the weight, losses and cost of the converter while ensuring the satisfaction of a number of constraints. The optimization variables are, as for them, the operating frequency, the current density, the maximum flux density, the transformer dimensions, the wire diameter, the core material, the conductor material, the converter topology (among Flyback, Forward, Push‐Pull, half‐bridge and full‐bridge topologies), the number of semiconductor devices associated in parallel, the number of cells associated in series or parallel as well as the kinds of input and output connections (serial or parallel) of these cells. Finally, the design of an auxiliary railway power supply is presented and discussed.

The results show that such tool to design dc‐dc power converters presents several advantages. In particular, it proposes to the designer a set of solutions – instead of a single one – so that he can choose a posteriori which solution best fits the application under consideration. Moreover, interesting solutions not considered a priori can be found with this tool.

To the best of the authors’ knowledge, such a CAD tool including a MO procedure taking several topologies into account has not been suggested so far.

THE Funk Gerat 10 equipment is the latest standardized type, and is installed in all the later bombers and reconnaissance machines of the Luftwaffe.