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Article
Publication date: 2 May 2017

Marek Golebiowski

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…

257

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Practical implications

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 July 2017

Jerzy Golebiowski and Marek Zareba

The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire.

55

Abstract

Purpose

The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire.

Design/methodology/approach

The effect of the air boundary layer was modelled by means of changing the total heat transfer coefficient on the external perimeter of the wire. This leads to an elliptical boundary problem with Hankel’s condition dependent on the angular coordinate. The eigenfunctions of the problem were determined analytically. On the other hand, the unknown coefficients of eigenfunctions and the constants were calculated numerically by solving a respective system of algebraic equations. The steady state current rating was determined with an iterative method.

Findings

By means of the presented method, the thermal field distribution deprived of axial symmetry in the double insulated wire was determined. The obtained results have good physical interpretation and were verified with the finite element method (by means of NISA v. 16 software). The determined values of the steady-state current rating were compared with those calculated by means of the equivalent heat transfer coefficient method and the International Electrotechnical Commission (IEC) standard.

Research limitations/implications

The method is applied to analyse scalar fields in layered cylindrical structures. This could be expanded to the case of a wire of any number of insulation layers. What is more, one could also consider heat sources without axial symmetry and located within the external area.

Originality/value

The analytical method of determining a thermal field deprived of axial symmetry in heterogeneous cylindrical system (the wire composed of three different materials) was developed.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 28 March 2019

Jerzy Gołębiowski and Marek Zaręba

The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

80

Abstract

Purpose

The purpose of this paper is to analyse the dynamics of a thermal field generated in a tubular bus with rated current by using two models of electrical resistivity of copper.

Design/methodology/approach

The boundary-initial problem of the modified heat equation was formulated for the tubular bus. Analytical solutions were obtained by means of Green’s functions as the kernels of the integral operator inverse to the corresponding differential operator. The results were presented graphically and verified using the finite element method. The calculations were made by considering the example of the Storm Power Components tubular bus (USA).

Findings

Analytical field models were used to determine time- and space-variable heating curves, time constants and steady-state current ratings.

Research limitations/implications

This paper is related to the structure of a hollow cylinder. Other bus sections can be taken into account by using the coordinate systems of different curvilinear orthogonal symmetry.

Originality/value

Using the analytical method, the influence of the variable (temperature dependent) electrical resistivity on some important parameters and characteristics of the tubular bus was investigated. The system was considered as an element with distributed parameters.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 6 March 2009

Jerzy Gołębiowski and Marek Zaręba

The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

189

Abstract

Purpose

The purpose of this paper is to present a method of solving a thermal conduction equation in three‐zone axially‐symmetrical systems.

Design/methodology/approach

In the method developed, the field functions are determined in the analytical way by the superposition of states and separation of variables method. The coefficients of the field functions and eigenvalues of the boundary‐initial problem are computed by the numerical method. The coefficients are the solution to the corresponding sets of equations. These sets are the result of scalar products of non‐orthogonal functions at the respective zones of the cable. The eigenvalues are determined by an algorithm, which uses the field properties and elements of the golden cut method.

Findings

The method made it possible to develop a mathematical model of the dynamics of the thermal field in a polymer DC cable. This model has good physical interpretation. The paper also presents the field distributions determined in an analytical form. Some arguments of the expressions derived are however computed numerically. The results obtained by the paper's method and by the finite elements methods were compared. The relative differences are less than 6 per cent.

Research limitations/implications

The method concerns axially‐symmetrical three‐zone systems under nominal conditions.

Practical implications

By means of the method important parameters of DC lines can be determined (e.g. spatial‐temporal heat‐up curves, admissible sustained currents, time constants).

Originality/value

An analytical‐numerical method of analysis of the thermal field in a three‐zone axially‐symmetrical system was developed. Its original element is the algorithm of determination of eigenvalues of the boundary‐initial problem and coefficients of non‐orthogonal field functions.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 10 August 2022

Nadia Albis Salas, Isabel Alvarez and John Cantwell

This paper explains the mechanisms underlying the generation of two-way knowledge spillovers through the interaction of subsidiaries with differentiated local responsibilities and…

239

Abstract

Purpose

This paper explains the mechanisms underlying the generation of two-way knowledge spillovers through the interaction of subsidiaries with differentiated local responsibilities and domestic firms.

Design/methodology/approach

The study is based on firm-level panel data from a census of Colombian manufacturing firms for the period 2003–2012. The estimation procedure involves two stages. In the first one, total factor productivity (TFP) of foreign and domestic firms is estimated. In a second step, we estimate conventional spillovers (from foreign-owned to local firms) and reverse spillovers (from local to foreign-owned firms) separately, using a random effect approach.

Findings

This study’s findings reveal that only locally creative subsidiaries enjoy positive and significant two-way knowledge spillover effects. The connectivity of subsidiaries to local and international networks is reinforced by reciprocal relationships among actors that enhance bidirectional knowledge flows, these being favored by the dynamics of clustering effects.

Originality/value

The paper contributes with new empirical evidence about the mechanism explaining how the technological heterogeneity of subsidiaries plays a determinant role in the generation of both knowledge flows from foreign to domestic firms and to the reverse, all integrated into the same framework.

Details

International Journal of Emerging Markets, vol. 19 no. 4
Type: Research Article
ISSN: 1746-8809

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