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The purpose of this paper is to compare parameters and properties of optimal structures of a line-start permanent magnet synchronous motor (LSPMSM) for the cage winding of a different rotor bar shape.

The mathematical model of the considered motor includes the equation of the electromagnetic field, the electric circuit equations and equation of mechanical equilibrium. The numerical implementation is based on finite element method (FEM) and step-by-step algorithm. To improve the particle swarm optimization (PSO) algorithm convergence, the velocity equation in the classical PSO method is supplemented by an additional term. This term represents the location of the center of mass of the swarm. The modified particle swarm algorithm (PSO-MC) has been used in the optimization calculations.

The LSPMSM with drop type bars has better performance and synchronization parameters than motors with circular bars. It is also proved that the used modification of the classical PSO procedure ensures faster convergence for solving the problem of optimization LSPMSM. This modification is particularly useful when the field model of phenomena is used.

The authors noticed that to obtain the maximum power factor and efficiency of the LSPMSM, the designer should take into account dimensions and the placement of the magnets in the designing process. In the authors’ opinion, the equivalent circuit models can be used only at the preliminary stage of the designing of line-start permanent magnet motors.

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 purpose of this paper is to elaborate the method and algorithm for the analysis of electromagnetic and thermal transients in a squirrel cage induction motor.

The paper presents the special software for transient finite element (FE) analysis of coupled electromagnetic‐thermal problems in a squirrel cage induction motor. The software has been prepared and is successfully applied in the design of special squirrel cage motors, e.g. the motors working in cryogenic conditions. A time‐stepping FE method and transients analysis of an induction motor has been applied. The nonlinearity of the magnetic circuit, the movement of the rotor and the skewed slots have been taken into account. The results of computations have been compared with measurements.

The method presented and the elaborated specialised software for FE analysis of electromagnetic and thermal transients are used to determine the dynamic performance of the squirrel‐cage induction motor. The results of simulations compared with measurements confirm the adequacy of this approach to the analysis of coupled electromagnetic‐thermal problems.

3D effects have only been taken into account by quasi‐3D techniques (e.g. the multi‐slice for the skewed rotor slots).

The software developed can be useful in the analysis and design of squirrel cage motor, especially motors working in cryogenic conditions.

The paper offers appropriate software for transient analysis of coupled electromagnetic and thermal problems in squirrel cage motors with skewed slots.

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.

This paper seeks to develop 3D finite element methods for the electromagnetic field calculation in electrical machines and to present the discrete methods of winding description.

The 3D finite element models of electrical machine windings are considered. Attention is paid to the windings with stranded conductors. The finite element equations are considered as the equations of magnetic networks. The formulation of matrix that transforms winding currents into the field sources is discussed. This matrix is also used in the calculations of flux linkages. In the proposed method, the winding loops are replaced by a set of plane loops. The field sources are defined by the numbers of these loops around the element edges and loops associated with element facets.

The presented description is the 3D finite element representation of MMF description used in the classical models of electrical machines. The advantage of the proposed approach is that the source description can be successfully applied in the FE method using single scalar potential. In addition, the presented approach guarantees a good convergence of ICCG procedure of solving edge element equations for ungauged formulation using magnetic vector potential.

The applied analogies between the finite element formulation and the equivalent magnetic network models help to formulate an efficient method of field source description. The developed method allows one to apply single magnetic scalar potential in the 3D finite element analysis of electrical machines.