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The purpose of this paper is to develop a reluctance‐resistance network (RRN) formulation for determining the induced current distributions in a 3D space of multiply connected conducting systems.

The proposed RRN method has been applied to solve Problem No. 7 of the International TEAM Workshops. The induced currents in the conductive plate with an asymmetrically situated “hole” have been analysed. The RRN equations have been formed by means of the finite element method using the magnetic vector potential A and the electric vector potentials T and T₀. The block relaxation method combined with the Cholesky decomposition procedure has been applied to solve the resultant RRN equations.

Comparison with results published in literature has demonstrated high accuracy of the proposed RRN computational scheme while offering significant savings in computing times.

A novel formulation of the RRN approach has been proposed and demonstrated to be computationally efficient.

The purpose of this paper is to find effective methods of loop analysis of multi‐branch and multi‐node non‐linear circuits using a singular formulation.

The classical loop analysis and the loop analysis using a singular formulation have been compared. The non‐linear systems of equations have been considered and iterative procedures of solving non‐linear equations have been applied. Special attention has been paid to the Newton‐Raphson method combined with successive over relaxation and incomplete Cholesky conjugate gradient methods. The convergence of the methods has been discussed.

It has been shown that in the case of the loop analysis of non‐linear circuits it is not necessary to form fundamental loops. The system of loop equations with a singular coefficient matrix can be successfully solved iteratively. Using a singular formulation one of the infinitely many solutions can be found quicker than the only one resulting from a classical method with a non‐singular coefficient matrix. Therefore, in the case of the analysis of multi‐branch and multi‐node non‐linear circuits using iterative methods, it is beneficial to introduce superfluous loops. This results in more economical computation and faster convergence.

The presented methods of solving multi‐branch and multi‐node non‐linear circuits using a singular formulation are universal and may be successfully applied both in circuit analysis and the FE analysis using edge elements for non‐linear problems with a large number of unknowns.

The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.

The proposed algorithms are related to the analysis of electrical machines using the methods of equivalent magnetic networks. The presented permeance and reluctance networks are formulated using FE methods. Attention is paid to the algorithms of electromagnetic torque calculation for 3D models. The virtual work principle is applied. The principle is adapted to the discrete network models. The network representations of Maxwell's stress formula are given.

The proposed method of electromagnetic torque calculation can be successfully applied in the 3D calculations of rotating electrical machines. It can be used for scalar and vector potential formulations. The obtained results and their comparison with the measurements show that the method is sufficiently accurate.

The presented formulas of electromagnetic torque calculation are universal and can be successfully applied in the FE analysis of electrical machines using nodal and edge elements.

The aim of this paper is to develop network models of an electromagnetic field containing both eddy and displacement currents. The proposed network models provide good physical insight, help understanding of complicated electromagnetic phenomena and aid explanation of methods of analysis of electromagnetic systems.

The models consist of magnetic and electric networks coupled via sources. The analogy between the finite element method and the loop and nodal formulations of electric circuits is emphasised. The models include networks containing branches associated with element edges (edge networks) or facets (facet networks).

Methods of determining mmf sources of magnetic networks from loop and branch currents in electric circuits, as well as emf sources in electric networks on the basis of the rate of change of loop and branch fluxes in electric networks, have been carefully considered. The models are general and allow creation of networks of electromagnetic systems containing non‐homogenous materials and multiply‐connected conducting regions.

The presented analogies between the finite element formulation and the equivalent network models not only facilitate understanding of the methods of field analysis but also help to formulate efficient computational algorithms.

The purpose of this paper is to investigate application possibilities of soft magnetic composites (SMC) in the design of high speed permanent motors for home appliances.

The design of high speed permanent magnet motor (HSPM) with core made of SMC has been proposed. The governing information about SMC has been presented. The possible advantages and disadvantages of applying magnetic powder materials in the design of electrical machines have been studied. To solve the partial differential equations describing magnetic vector distribution in considered HSPM, the edge element method (EEM) has been applied. The formulas of permanent magnet and winding descriptions, and electromagnetic torque calculations have been presented and studied. To verify accuracy of methodology and functionality of the elaborated software, a prototype of the considered motor has been built and the experimental setup for testing torque and electromotive force has been elaborated. The comparison between measured and simulated motor characteristics have been presented and discussed.

Comparison between measured and simulated motor characteristics proves the model accuracy. The obtained results show that the designed HSPM motor has sinusoidal electromotive force waveforms, low cogging torque value and the sinusoidal torque versus rotor angle characteristics. Moreover, it has been indicated that the application of SMC materials can reduce power losses in the high speed motors.

The paper describes the development of the numerical method and software for analysis of HSPM with core made of powder materials.

The purpose of this paper is to analyse the stray losses in the windings of permanent magnet synchronous machines (PMSM).

The 2D field model, based on the edge element method (EEM) and

-V formulation, has been developed and utilized for the determination and analysis of stray losses in the PMSM with concentrated windings made of strip conductors. The influence of the supply frequency as well as the slot opening width on the losses caused by eddy currents has been examined. The different arrangements of the conductors in the tape wound coils have been studied. The obtained results have been compared to the reference case when the eddy current effect is neglected.

The usefulness of the proposed methodology of the stray losses evaluation has been tested on the case study problem. It has been observed that the stray losses in the windings of the considered machine can be reduced by choosing the proper value of the slot opening. The dependence of the stray losses on the frequency of the supply currents has been examined. The obtained results show that with the increase of frequency the stray losses caused by the eddy currents in the strip conductors increase.

The proposed 2D field numerical model makes it possible to analyse the stray losses in the tape wound concentrated windings of the PMSM motor. The presented model can be utilized for the optimization of the magnetic circuit of the machine with the aim of minimizing eddy current losses.

The end‐turn leakage inductances of the armature winding of the permanent magnet motor have been calculated. In order to describe the magnetic field distribution the edge element method using vector magnetic potential has been applied. First, the formulae that describe the total self‐inductance and total mutual conductance for phase windings are presented. Three‐dimensional and two‐dimensional formulations are considered. The end‐turn leakage inductances have been obtained by comparing the results of these formulations. The symmetrical components transformation has been applied, and the self inductances and mutual inductances have been transformed into the zero‐sequence and positive‐sequence inductances. The calculations have been performed for different dimensions of the coil‐end region. The influence of the position of the boundary surfaces on the results has been investigated.

This paper aims to elaborate the method and algorithm for the analysis of the influence of temperature on back electromotive force (BEMF) waveforms in a line start permanent magnet synchronous motor (LSPMSM).

The paper presents a finite element analysis of temperature influence on BEMF and back electromotive coefficient in a LSPMSM. In this paper, a two-dimensional field model of coupled electromagnetic and thermal phenomena in the LSPMSM was presented. The influence of temperature on magnetic properties of the permanent magnets as well as on electric and thermal properties of the materials has been taken into account. Simulation results have been compared to measurements. The selected results have been presented and discussed.

The simulations results are compared with measurements to confirm the adequacy of this approach to the analysis of coupled electromagnetic-thermal problems.

The paper offers appropriate author’s software for the transient and steady-state analysis of coupled electromagnetic and thermal problems in LSPMS motor.

The purpose of this paper is to show that constructing magnetic equivalent circuits (MECs) for simulating accelerator magnets is possible by defining a three-port magnetic element for modelling the T-shape field distribution, where the flux leaves the yoke and enters the aperture.

A linear three-port magnetic element is extracted from an analytical field solution and can be represented by a number of two-port elements. Its nonlinear counterpart is obtained as a combination of the corresponding nonlinear two-port elements. An improved nonlinear three-port element is developed on the basis of an embedded nonlinear one-dimensional finite element model.

The T-shaped field distribution comes together with a complicated interplay between the saturation of the ferromagnetic yoke parts and flux leaking to the aperture. This is more accurately modelled by the improved nonlinear three-port magnetic element.

MECs have a limited validity range, especially for configurations where a high saturation level and fringing flux effects coexist.

The results of the paper appeal to be careful with applying nonlinear MECs for simulating bending magnets.

A new nonlinear three-port magnetic element for ferromagnetic yoke parts with T-shaped flux distribution has been developed.

The electromagnetic torque oscillations caused by saturation harmonics in a squirrel cage machine are analysed. Special attention is paid to the most important saturation harmonic of alternating field that has three times as many poles as fundamental harmonic and three times its frequency. The operations of the machine as a motor and as a self‐excited generator have been investigated. The 2D finite element time‐stepping method has been applied to the analysis of a particular machine performance. The finite element equations are coupled with circuits equations which describe the winding connections. The skew of the rotor slots is taken into account.