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This paper aims to work out a method for calculating losses in induction motor steel taking into account its saturation.

The theory of electric machines is applied during the analysis of induction motor equivalent circuits. The theory of Fourier series is used to determine the harmonic components of voltage, current and power. Instantaneous power theory and trigonometric transformations are used to solve algebraic and differential equations and their systems. The methods of approximation and interpolation are applied to obtain analytical expressions from the experimental data. Experimental research was carried out to verify the reliability of theoretical provisions and research results.

A method for assessing an induction machine steel as a function of the generalized electromotive force has been proposed. It allows taking into account higher harmonics of the current, which are caused by the presence of nonlinearity of an induction motor magnetic circuit.

The obtained results can be used in calculating the energy characteristics and operating modes of an induction motor, as well as in the construction of control systems.

A method for determining the losses in the stator steel of an induction motor, using a generalized electromotive force, has been proposed for the first time. It enables taking into account the currents flowing both in the stator circuit and in the rotor circuit.

Analytical determination of harmonic components of current in electric circuits containing semiconductor converters with the use of a small parameter method (SPM) in frequency domain. The paper aims to discuss these issues.

A SPM realized in frequency domain was used in the analytical analysis of electric circuits with semiconductor converters. An automated method of formation of orthogonal harmonic components of electrical values on the basis of discrete convolution algorithm was used to provide the possibility of realization of calculation in frequency domain. A nonlinear characteristic of a semiconductor converter was presented by the method of numerical approximation. A numerical structured simulation method was applied to determination of the reference values of current in the analyzed circuit. Laws of theoretical electrical engineering were used for formation of the equations of voltage balance in the circuit with a nonlinear element.

It is shown that application of a SPM with its realization in frequency domain enables significant simplification of the process of the analysis of electric circuits with semiconductor converters in an analytical form and facilitation of calculation automation. Analytical and numerical calculation of a circuit with a diode under active-inductive load demonstrated efficiency and sufficient accuracy of the proposed method. It is shown that increase of the order of approximating polynomial and of the number of the analyzed harmonics provides the improvement of the accuracy of numerical calculations.

The results of the work can be used in calculation of electrotechnical devices containing semiconductor appliances and electric devices with nonlinear characteristics. Moreover, the obtained results enable studying the processes of compensation of current higher harmonics in electric networks with a nonlinear load containing semiconductor converters.

For the first time it was proposed to apply a SPM with its realization in frequency domain to the analysis of nonlinear electric circuits. The significance of the paper consists in the fact that the offered method makes it possible to carry out both circuit analytical and numerical analysis with the possibility of its automation.

To analyze the Jiles and Atherton hysteresis model used for hysteresis losses estimation in soft magnetic composite (SMC) material.

The Jiles and Atherton hysteresis model parameters are optimized with genetic algorithms (GAs) according to measured symmetric hysteresis loop of soft magnetic composite material. To overcome the uncertainty, finding the best‐optimized parameters in a wide predefined searching area is done with the proposed new approach. These parameters are then used to calculate the hysteresis losses for the modeled hysteresis. The asymmetric hysteresis loops are also investigated.

The classical GAs are good optimization methods when a pre‐defined possible set of solutions is known. If no assumption on solutions is present and a wide searching area range for parameter estimation is selected then the use of the new approach with nested GAs gives good results for symmetric hysteresis loops and further for the estimation of hysteresis losses.

The use of the Jiles and Atherton hysteresis model for asymmetric hysteresis must be explored further. Only one set of optimized Jiles and Atherton hysteresis model parameters used for estimation of hysteresis losses gives good results for only symmetric hysteresis loops. These parameters have limitations for asymmetric hysteresis loops.

Nested GAs are a useful method for optimization when a wide searching area is used.

The originality of the paper is in the establishment of nested GAs and their application in Jiles and Atherton hysteresis model parameters optimization. Also, original is the use of the Jiles and Atherton hysteresis model for hysteresis loop description of soft‐magnetic composite material.

The purpose of this paper is to derive the geometry‐based equations for inductances which are used in circuit theory analysis of synchronous reluctance motor (SRM). Transient and steady state performance analyze of SRM by using the 2D time‐stepping finite‐element method (FEM).

The analytical approach is used to obtain the equations which describe geometry dependent magnetizing inductances of SRM. Transient and steady state performance of the SRM is analyzed by using the 2D time‐stepping FEM. The external electric circuit connected with the finite‐element model of the SRM geometry allows the study of almost any of the electric and magnetic properties of the machine. Presented SRM model is also connected to the external mechanical loads (friction, rotor inertia and load torque). The use of different materials for the magnetic‐pole part of the rotor and for flux barriers was analyzed. The flux barriers in the first SRM rotor were filled with a pure massive electrically conductive ferromagnetic with a proper B‐H curve, whereas the rotor magnetic segments were made of non‐conductive electric steel described with its B‐H curve. The conductive barriers with their end rings form a squirrel cage and allow SRM to start on‐line. The flux barriers of the second SRM rotor were made of aluminum but between the second and third flux barrier a massive electrically‐conductive ferromagnetic was inserted which during starting‐up acted as a part of the squirrel cage. All of the flux barriers of the third SRM rotor were made of electrically‐conductive aluminum with iron parts axially laminated. The finite‐element SRM models coupled with an electric circuit is also used to evaluate the motor performance at various asynchronous speeds.

Analytical geometry‐dependant equations for the d‐ and q‐axis SRM inductances are derived. On the basis of the proposed 2D time‐stepping finite‐element analysis, the start‐up performance for the SRM rotor design using different materials is established. The torque distribution as a function of time at any of the observed asynchronous speeds is not smooth and uniform. It consists of the stator‐to‐rotor tooth pulsating torque, and the synchronous and asynchronous component.

The main disadvantage of analytical geometry‐dependant equations for the d‐ and q‐axis SRM inductances is the linearization of any of the ferromagnetic parts.

On the basis of the proposed 2D time‐stepping finite‐element analysis, the start‐up performance, asynchronous run and synchronous torque characteristics for the SRM rotor design using different materials are established.

The value of the paper is the closed view about happenings in rotor flux barriers of SRM, mostly regarding the time distribution of induced currents in the rotor flux barriers. On the base of 2D time‐stepping FEM, the use of different materials for the magnetic‐pole part of the rotor and for flux barriers was analyzed.

The purpose of this paper is the investigation of eddy currents induced in the axial‐flux permanent‐magnet machine housing by the leakage flux and the introduction of permanent magnets in the steady‐state AC finite‐element analysis and coupling their effects with the transient thermal analysis.

The proposed approach is based on the finite‐element method as well as on using the basic analytical equations. The approach was first applied in the magneto transient analyses. Because of the different physical transient‐time constants, the steady‐state AC analysis coupled with transient thermal should be used.

The permanent magnets in the steady‐state AC analysis coupled with the transient thermal analysis can be simulated by coils with an imposed current of a frequency depending on the number of pole pairs and rotation speed. Using any of the electrically conductive materials for the axial‐flux inner slotless stator permanent‐magnet machine housing should be avoided.

The leakage flux induced by permanent magnets and spreading into the axial‐flux permanent‐machine housing is first defined by using the magneto‐transient finite‐element analysis and further used in the steady‐state AC analysis coupled with the transient thermal analyses, all in 3D. Based on the results of these analyses, the temperature distribution in entire machine is calculated and compared with the measurement results.

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.