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This paper seeks to model magneto‐harmonic solid conductors in the presence of ferromagnetic materials.

The approach takes the form of a coupling between the FEM and the PEEC method.

The paper shows one how to use the FEM‐PEEC coupled method to model a problem comprising solid conductors and ferromagnetic materials and compare its results with the FEM.

The formulation allows one to treat linear material in the magneto‐harmonic assumption.

The two methods FE and PEEC are well‐known. The innovation here is coupling these methods in order to profit by the main advantages.

An analytical approach is preferred to carry out the harmonic modelling of power electronics converters because it is generally faster than time simulation chained with FFT. However, the difficulty of such an approach is to build the model and to manage the uncontrolled commutations that occur in the studied static converter, and also to deal with large equations. The purpose of this paper is to propose an aid in the frequency modelling of the drive elements, in the frequency domain, including all key parameters for sizing aim i.e. a way to optimize the EMC filter using different algorithms.

The paper aims to propose an aid to create such models, and to assure its good solving, i.e. that the correct operating mode is represented. So, the solving problem is formulated as an optimization problem under constraints, to solve this difficulty.

The difficulty is to be sure to deal with the good operating mode of the static converter when soft or uncontrolled commutations occur. So, the model is formulated as a constrained optimization problem. The paper proposes a symbolic approach, that allows to build automatically the frequency model. It is translated to be solved in Matlab.

The approach does not fit for static converters with a control implying numerous commutations per operating period. However, the approach deals with natural and soft commutations.

The modelling is based on the use of linear components and ideal switches.

The paper deals with the sizing of a flyback converter. The approach proposes to use symbolic calculation to perform sizing times, the accuracy and the number of parameters to size. So, it presents a symbolic model to size a flyback converter using optimisation techniques. Such an approach is preferred to a simulation approach thanks to the flexibility of symbolic models and their possibility to treat a great set of criteria in few seconds or minutes. The expressions of a great part of the criteria are made by an automatic symbolic process – model builders – and the others are carried out by the designer. Such a model is used in a gradient optimisation process well known for its convergence properties. From this model, a builder carries out automatically the building of a dedicated sizing tool, by automatically transforming it into an optimisation problem and by automatically giving the corresponding sizing tool with its GUI.

The aim of this paper is to model time‐harmonic problems in unbounded domains with coils of complex geometry and ferromagnetic materials.

The approach takes the form of a coupling between two integrals methods: the magnetic moment method (MMM) and the partial element equivalent circuit (PEEC) method. The modeling of conductor system is achieved thanks to PEEC method while the MMM method is considered for the magnetic material.

The paper shows how to use the MMM/PEEC coupled method to model a problem comprising conductors and ferromagnetic materials and compare its results with the FEM and the FEM/PEEC coupling.

The two methods PEEC and MMM are well‐known. The innovation here is coupling these methods in order to take advantages from both methods. Moreover, the performances of this coupling are studied in comparison with others (FEM, FEM/PEEC coupling).

The frequency simulation and optimisation of electromagnetic compatibility (EMC) filter is often computation time consuming. The purpose of this paper is to propose an approach for easy and fast modelling and optimization of power electronics structures.

The paper proposes an approach for easy and fast modelling and optimization of power electronics structures. It focuses on the EMC filter design. To achieve this task time simulation, FFT and automatic frequency modelling are combined.

An automatic frequency modelling is proposed and also gives automatically the model gradients. Therefore, the model can be used to optimize the EMC filter, but also can help in choosing its topology. Several optimization algorithms are used and compared.

The power electronics load is supposed to be a set of predefined harmonic sources, obtained by time simulation + FFT before the optimisation process.

The frequency model allows for the rapid designing and comparing of several structures or modelling hypothesis with regard to the parasitic elements and circuit imperfections.

The frequency model is automatically generated, and sizing criteria on the component (e.g. inductors, capacitor) can be added in an analytical form, for example, to deal with volume or mass criteria.

With the increasing number of onboard controlled static converters in aeronautics, methods to design lighter configurations are required. This study aims to help the designer sizing optimal electromagnetic compatibility (EMC) filters and, moreover, finding optimal voltage levels and switching frequency, which have a great impact on the design and global mass of such converters.

Analytical models for capacitors, inductors and heatsink are settled. Using frequency modeling, EMC can be studied analytically. To deal with frequency and voltages variations, models of perturbations sources are developed. Concerning the problem of surveilling thousands of harmonics to check the whole frequency range of EMC standards in optimization, a strategy that drastically reduces the number of computations and has a good convergence is proposed.

The methods settled in the paper allow to optimize a controlled static converter with its EMC filters along with finding optimal switching frequency and voltage levels. A study on a three-phase rectifier reveals the importance of the switching frequency on converter design with EMC filters. A 28 per cent mass reduction is predicted by increasing the switching frequency from 10 to 30 kHz. The designed converters are verified by simulations.

Investigating the voltage levels along with the switching frequency has not been achieved yet for static controlled converters with EMC constraints. The approach lacks experimental validations, but it is currently ongoing.

Dealing analytically with the changes of frequency or voltages in an EMC study is a new feature. The possibility to use deterministic algorithm is essential for dealing with the important number of constraints and the numerous interactions between all the parts of the problem, especially EMC.

The purpose of this paper is to deal with the design of passive filter for power electronics voltage inverters used in aircraft electrical drives (a permanent magnet synchronous machine fed by a six-phase voltage inverter with PMW control), using optimization for both sizing and sensibility analyses.

The approach is generic. An aid allows to modify easily the frequency model and so to check various study cases, and to carry out the filter optimization for different topologies or control strategies.

The approach is generic. An aid allows to modify easily the frequency model and so to check various study cases, and to carry out the filter optimization for different topologies or control strategies.

The power electronics load is supposed to be a set of predefined harmonic sources, obtained by experiment or time simulation plus fast fourier transformation before the optimization process.

The problem has numerous constraints on the components, mainly technological constraints. The volume is minimized, respecting electromagnetic standards and an electro magnetic interference filter prototype has been made.

The frequency model is automatically generated. A complex aircraft application has been studied thanks to the approach. Several sensibility analyses have been carried out. An EMC filter has been sized and an experimental prototype has been made, comforting the sizing by optimization.

This paper aims to analyze the dominant stray parameters of the DC bus bar and focus on weakening the influence of the stray parameters instead of reducing the value of the stray parameters in DC bus bar while switching. By finding the mechanisms to reduce the effects of stray parameters on switching transient, the simple and straightforward optimization methods could be given for the engineering designer.

The investigations are focused on the equivalent circuit by segmented impedance evaluation in the low-frequency band and the energy propagation by wave impedance evaluation in the high frequency band. This paper proposes an equivalent impedance calculation model to locate the dominant stray parameters in the DC bus bar and takes the energy propagation characteristics using wave impedance into consideration, which can simplify the optimization design of DC bus bar.

According to the equivalent circuit and electromagnetic field analysis, this paper proves the existence of the dominant stray parameters in DC bus bar that is widely used on high-power converters and certifies that not all the stray parameters in different areas of DC bus bar have the same effects on switching process, which can give a good guidance for the optimization design of DC bus bar.

The positions of DC-link capacitors, resulting in only part of stray parameters in DC bus bar has more impact during switching, are significant to the DC bus bar optimization design. These stray parameters named dominant stray parameters in this paper play a leading role in the switching transient process. The area of DC bus bar, which is close to IGBTs and far from DC-link capacitors, contains the dominant stray parameters in the switching transient process. Therefore, the distance between DC-link capacitors and IGBTs should be shortened as much as possible. Based on the results, the efficiency for the DC bus bar optimization design could be improved by weakening the influence of the stray parameters, such as reducing the dominant stray parameters only. Therefore, it can save the cost and time of DC bus bar optimization design.

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.

This paper aims to present how to use the difference equations for analysis of flyback converter circuit.

Switching circuits have variable structural topologies. In every switched-mode, they have different dynamics and different equations. First, the exact equivalent circuit of flyback converter, then, set of difference equations are obtained. The flyback converter has a nonlinear structure; however, the presented technique allows the circuit equations to be linear. The transient-state and steady-state analysis of flyback converter, one of popular switching circuits, are carried out by using difference-equations.

The proposed analysis method does not contain any numerical approximation and the results are in the form of exact solution. Another superiority of the method is that the desired instantaneous values can be obtained directly, the simulation does not need to be started from the beginning. Numerical results agree well with the theoretical results of flyback converter. The simulation results obtained by using the proposed method and Matlab-based results are compared.

This paper contributes a different mathematical background for analysis of switching converters to the literature.