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The paper presents a method of creating electrical equivalent diagrams of magnetic circuits. The method is based on bond‐graph techniques, using flux derivative as flow variable. Couplings between magnetic and electric part of the system are represented by gyrators. Simple models of magnetic branches, including non‐linear effects due to saturation, hysteresis and eddy currents, are presented. These models can be easily combined into magnetic circuit models, which can be transformed into dual electric equivalent circuit. Various equivalent circuits of transformers are discussed. The proposed models are simple and particularly useful for system‐level simulation of power electronic and motion control systems with magnetic elements. These models can be easily developed if needed. Theoretical considerations are illustrated by examples of digital simulation and experimental results.

The purpose of this paper is to develop the method of taking the eddy current losses in the laminated magnetic circuits into account during implicit transient calculations. The nonlinear magnetization characteristic of iron and the hysteresis losses can also be considered in the simulations done with the developed method.

The paper presents complex equivalent magnetic permeability derived from the presumed angular frequency in a laminated magnetic circuit. On this basis, the synthesis of a magnetic permeability as a function of the Laplace variable “s” is presented. After transformation of the variable “s” to a variable “z” of the Z transformation, it is possible to conduct discrete time calculation of transient states of magnetic circuits including the eddy current losses. An iterative process is developed to take the saturation of the magnetic circuit in these calculations into account. As regards hysteresis losses, the scalar model of magnetic hysteresis by Juhani Tellinen was implemented. The new method is validated by calculations of a two-coil transformer.

It is important to take into account the losses in sheet metal directly in the implicit transient calculations. This possibility is provided by the presented method based on the synthesis of the equivalent magnetic permeability μ^(s). The presented method was proved to be correct and efficient. The calculated sheet metal losses were compared with the results presented in literature. Good conformance of results was attained.

The method enables calculation of eddy current and hysteresis losses in laminated magnetic circuits during calculations of transient states. It does not need, unlike the previous methods, previously provided information (“a priori”) about the content of higher harmonics in waveforms. The method takes into account mutual dependence of transient waveforms of currents in the analysed system and losses of laminated magnetic circuit, expressed by eddy currents and hysteresis losses. Its implementation comes down to using in calculations a filter of the IIR type and corresponds to its calculation complexity. The author plans to use the presented method in the finite elements method transient calculations.

A new approach is a synthesis of the equivalent magnetic permeability in Laplace domain, which creates an equivalent RC circuit for permeability. Analytic equations for parameters of this equivalent circuit are original. A method for considering nonlinear magnetization characteristic and hysteresis losses was presented. In calculations of transient states of systems with magnetic circuits, one can use the developed equivalent circuit of magnetic permeability in a form of the IIR filter. Operator magnetic permeability includes fractional derivative of Laplace’s variable “vs”. Therefore, the equivalent IIR filter includes “history” of the processes that take place in the laminated magnetic circuit to the current, calculated time moment. This “history” in terms of its content is limited only by the degree of the applied IIR filter. It enables to calculate “step by step”, without previous (“a priori”) knowledge about harmonic components of the whole waveforms. It was necessary in the previously used methods, when determining parameters of magnetic permeability. The method proposed in the paper allows for calculations with taking into account direct dependence of an electric part of the system on its magnetic part.

The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.

In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.

The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.

Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to propose a method to estimate the magnetic saturation and end effect of linear switched reluctance machines (LSRMs) with fully pitched winding configuration used in the wave energy conversion.

The magnetic saturation and strong coupling make it very difficult to derive a comprehensive mathematical model for the behavior of the LSRMs. Meanwhile, the various end effects could not be comprehensively considered in the two‐dimensional model which is widely studied. Therefore, the magnetic equivalent circuit model including the three‐dimensional (3‐D) effects is presented in this paper and 3‐D finite element analysis (FEA) is used to validate the mathematical model.

The results from 3‐D FEA are in good agreement with the numerical simulation, which validates the accuracy of the magnetic equivalent circuit modeling method.

This technique helps one to know the influence exerted by the magnet saturation and end effect of LSRMs and provides a powerful computer‐aided analysis tool. Meanwhile, this modeling method supplies accurate values for the following study of reliable control algorithm.

The paper presents a magnetic equivalent method to estimate the magnetic saturation and end effect of LSRMs with fully pitched winding configuration used in the wave energy conversion.

A general approach to the formation of magnetic equivalent circuit describing the magnetic process inside the electric machines is proposed. This formation is based on tooth contour method. Coupling with external and internal electric circuits of electric machines is emphasized as well as mechanical coupling with load. The resulting model allows the simulation of electromechanical converter, but with the number of element being fewer by several orders compared to traditional finite element models. Non‐linearity such as saturation or electronic switch is taken into account. General equations for the magnetic fields and electric circuits of electrical machines are written using a common basis – the nodal potential method. The whole process is illustrated on the simulation of a claw poles alternator compared with measurements.

This paper aims to present an accurate magnetic equivalent circuit for modeling the cylindrical electromagnet so that by analyzing it, the magnetic flux density in different parts of the electromagnet, as well as its lifting force, can be calculated.

The structure of the electromagnet is divided into parts that can be modeled by lumped element parameters. Mathematical equations for calculating these elements are presented and proved. The axial symmetry of the cylindrical electromagnet made it possible to use planar circuits for its modeling. To increase the accuracy of the proposed equivalent circuit, attention has been paid to the leakage flux as well as the nonlinear behavior of the ferromagnetic core. Also, the curvature of the magnetic flux path is considered in the calculation of the corner permeances of the core.

The magnetic flux density in different parts of the electromagnet was calculated using nodal analysis of the circuit and compared to the results of the finite element method. Also, a test bed was established to measure the lifting force of the electromagnet. Comparing the results shows a difference of less than 3% which indicate the good accuracy of the proposed circuit. In addition, due to the curvature of the flux path, there is a no-flux region in the center of the disk, the extent of which depends on the thickness of the disk and the diameter of the middle leg.

Magnetic equivalent circuit is a new contribution to analyze the cylindrical electromagnet and calculate its lifting force with good accuracy. The circuit lumped elements can be quickly calculated using mathematical equations and software such as MATLAB according to the actual path of the magnetic flux. Compared to other methods, the proposed circuit analyzes the electromagnet in a shorter period of time. This is the most important advantage of the proposed circuit model.

This paper aims to study the relationship between leakage flux coefficient and the coreless axial magnetic field permanent magnet synchronous generator (AFPMSG) size and obtain the expressions of leakage flux coefficient.

In this paper, a magnetic circuit model of coreless AFPMSG is proposed. Four kinds of leakage permeances of permanent magnet (PM) are considered, and the expression of no-load leakage flux coefficient is obtained. Solving the integral region of leakage permeances by generator size, which improves the accuracy of the solution.

Finite element method and magnetic circuit method are used to obtain the no-load leakage flux coefficient and its variation trend charts with the change of pole arc coefficient, air gap length and PM thickness. The average errors of the two methods are 2.835%, 0.84% and 1.347%, respectively. At the same time, the results of single-phase electromotive force obtained by magnetic circuit method, three dimensional finite element method and prototype experiments are 19.36 V, 18.82 V and 19.09 V, respectively. The results show that the magnetic circuit method is correct in calculating the no-load leakage flux coefficient.

The special structure of the coreless AFPMSG is considered in the presented equivalent magnetic circuit and equations, and the equations in this paper can be applied for leakage flux evaluating purposes and initial parameter selection of the coreless AFPMSG.

The purpose of this paper is to create a reliable nonlinear magnetic equivalent circuit (NMEC) of the hybrid magnetic bearing (HMB). Commonly used magnetic equivalent circuits of HMB omit a saturation effect of the magnetic material as well as the leakage and fringing flux. It results in imprecise modelling of the magnetic field distribution. On the other hand, only 3D finite element analysis (FEA) can be used to precisely simulate the magnetic field in this type of the magnetic bearing. The proposed NMEC incorporates the saturation effect of the magnetic material, as well as the leakage and fringing flux.

The magnetic equivalent circuit of presented HMB is proposed to obtain a reliable model that ensures short calculation time. Developed NMEC incorporates the phenomena as the saturation effect, as well as the leakage and fringing flux. The reluctance of the air gap that includes the fringing flux was calculated using 3D FEA. Kirchhoffs’ laws were used to create a set of nonlinear equations that were iteratively solved by Broyden’s method.

Incorporating into NMEC of the HMB a saturation effect of the magnetic material, as well as the leakage and fringing flux, resulted in the accurate model that was in good agreement with 3 D finite element model and the real object. The developed NMEC offers the calculation time in the range of miliseconds, therefore can be successfully used in the engineering design instead of the FEM.

Presented NMEC can be considered as a fundamental model that can be successfully used for accurate and fast simulation of the HMB. Proposed NMEC includes considerable factors that decide about the model accuracy such as the saturation effect of the ferromagnetic material and the leakage and fringing flux. The developed NMEC can be used in the optimization procedures and for simulations of dynamic responses.

This paper aims to propose an efficient model for analysis of power electronic circuits with integrated magnetic components.

The inductance modeling technique is used as the traditional method for analyzing magnetic components. This model is simple and enough to generate for individual components, that is, an inductor and a transformer. However, it becomes difficult to realize this model for the integrated magnetic structures. This paper shows an appropriate model for individual magnetic components as well as integrated magnetic components and its application to magnetically coupled DC–DC converters. Gyrator–capacitor (G–C) modeling offers a unified, reasonable way of understanding the magnetic components commonly met with in power electronics and the other disciplines.

G–C model allows any electrical and magnetic circuit to be simultaneously simulated with circuit simulators. In this regard, this paper gives a complete simulation model and analysis as an illustrative example. There is no limitation of this paper or future works. The proposed G–C model can be applied to all power electronic circuits having integrated magnetic components.

In the proposed model, the magnetic circuit is converted to a pure electric circuit with capacitors and controlled sources; every winding is replaced with a pair of current controlled voltage sources, namely, a gyrator.