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Article
Publication date: 2 May 2017

Rene Plasser, Gergely Koczka and Oszkár Bíró

A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic

Abstract

Purpose

A transformer model is used as a benchmark for testing various methods to solve 3D nonlinear periodic eddy current problems. This paper aims to set up a nonlinear magnetic circuit problem to assess the solving procedure of the nonlinear equation system for determining the influence of various special techniques on the convergence of nonlinear iterations and hence the computational time.

Design/methodology/approach

Using the T,ϕ-ϕ formulation and the harmonic balance fixed-point approach, two techniques are investigated: the so-called “separate method” and the “combined method” for solving the equation system. When using the finite element method (FEM), the elapsed time for solving a problem is dominated by the conjugate gradient (CG) iteration process. The motivation for treating the equations of the voltage excitations separately from the rest of the equation system is to achieve a better-conditioned matrix system to determine the field quantities and hence a faster convergence of the CG process.

Findings

In fact, both methods are suitable for nonlinear computation, and for comparing the final results, the methods are equally good. Applying the combined method, the number of iterations to be executed to achieve a meaningful result is considerably less than using the separated method.

Originality/value

To facilitate a quick analysis, a simplified magnetic circuit model of the 3D problem was generated to assess how the different ways of solutions will affect the full 3D solving process. This investigation of a simple magnetic circuit problem to evaluate the benefits of computational methods provides the basis for considering this formulation in a 3D-FEM code for further investigation.

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: 24 June 2019

Dawid Wajnert and Bronislaw Tomczuk

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 38 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 6 November 2017

Lei Li and Lin Li

This paper aims to present a novel energy-efficient saturated open-core fault current limiter (FCL) with special permanent magnet (PM) modules.

Abstract

Purpose

This paper aims to present a novel energy-efficient saturated open-core fault current limiter (FCL) with special permanent magnet (PM) modules.

Design/methodology/approach

The special PM modules are used to drive the cores of FCL into a saturated state from different directions in the normal operation condition, reducing the DC current of the saturated open-core FCL. An equivalent magnetic circuit model of the saturated open-core FCL with PM modules is built to calculate the magnetic flux density in the cores of FCL. By applying the modified nodal approach on the circuit, the nonlinear equations of the magnetic circuit can be achieved. The Newton – Raphson method is used to solve the nonlinear equations. The model shows good accuracy verified by finite element simulation and a physical experiment.

Findings

Compared with the original saturated open-core FCL structure with PMs, the novel saturated open-core FCL structure can save 84% DC power. The physical experiment results show that the saturated open-core FCL has a good performance on limiting the fault current.

Originality/value

A novel saturated open-core FCL structure with PM modules is proposed in this paper. A physical model of the saturated open-core FCL structure with PM modules is manufactured and tested. About 84% DC power can be reduced by using the PM modules in this saturated open-core FCL, and it can save most of the cost of the saturated open-core FCL.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 21 August 2018

Yingying Wang and Jiansheng Yuan

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 April 1995

Adam Warzecha

Electrical machines with nonlinear magnetic circuits are usually modelled by coupling magnetic and electric equations using software for magnetic field investigation…

Abstract

Electrical machines with nonlinear magnetic circuits are usually modelled by coupling magnetic and electric equations using software for magnetic field investigation. These hybrid methods are practically effective only for steady states, due to their time‐consuming calculations. The separation of both sets of equations will be possible if the unique relationships between linked fluxes and all armature currents become determined. It needs, of course, the neglect of the eddy‐currents in the machine rotor. Generally, they are defined as the partial derivatives of coenergy:

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 14 no. 4
Type: Research Article
ISSN: 0332-1649

Abstract

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 10 July 2021

Tadeusz Sobczyk, Michał Radzik and Jarosław Tulicki

This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models.

Abstract

Purpose

This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models.

Design/methodology/approach

Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only.

Findings

An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain.

Research limitations/implications

Reduction of software and hardware requirements for determining steady-states of electromagnetic.

Practical implications

A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form.

Originality/value

Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.

Details

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

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Article
Publication date: 1 October 2006

Frederik M.L.L. De Belie, Jan A.A. Melkebeek, Lieven Vandevelde, Kristof R. Geldhof and René K. Boel

To provide a discrete‐time nonlinear model for surface permanent‐magnet synchronous machines (SPMSMs) in order to discuss the stability of such machines.

Abstract

Purpose

To provide a discrete‐time nonlinear model for surface permanent‐magnet synchronous machines (SPMSMs) in order to discuss the stability of such machines.

Design/methodology/approach

Through differencing the co‐energy, obtained from a finite element method, the main flux path can be described by a complex reluctance. Furthermore, for a SPMSM, an equivalent circuit is presented that includes the eddy‐current losses and the voltage drops across stator resistance and leakage inductance. The model is transformed to a discrete‐time state‐space model by using a forward rectangular rule. By using a root locus technique, the stability of the new model is discussed.

Findings

From the calculated root locus it is concluded that the stability of a SPMSM is only guaranteed for certain values of the open loop gain. Moreover, by using the forward rectangular rule, it is concluded that a well‐considered time step has to be chosen.

Research limitations/implications

The model considers the fundamental space harmonic components only. Moreover, the saturation of the leakage flux path is neglected.

Practical implications

As the model is formulated in discrete time, it can be used in modern drives where a digital controller is used.

Originality/value

This paper presents an equivalent electrical circuit for SPMSMs that takes into account the saturation of the magnetizing flux paths as well as the magnetic interaction between the two orthogonal magnetic axes.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 2 January 2018

Mohammadreza Baghayipour, Ahmad Darabi and Ali Dastfan

This paper aims to propose an analytical model for the harmonic content no-load magnetic fields and Back electric motive force (EMF) in double-sided TORUS-type non-slotted…

Abstract

Purpose

This paper aims to propose an analytical model for the harmonic content no-load magnetic fields and Back electric motive force (EMF) in double-sided TORUS-type non-slotted axial flux permanent magnet (TORUS-NS AFPM) machines with surface-mounted magnets considering the winding distribution and iron saturation effects.

Design/methodology/approach

First, a procedure to calculate the winding distribution with a rectangular cross-section is proposed. The magnetic field distribution and magnetic motive force (MMF) drop due to saturation in iron cores are then exactly extracted in a 2-D analytical model. The consequent influence on air-gap magnetic field and Back EMF are also calculated using a new iterative algorithm. The results are compared with those of the conventional analytical model without saturation, 2-D finite element analysis (FEA) and an experiment on a fabricated prototype machine.

Findings

Unlike the conventional method, the new method yields the no-load magnetic field distributions in air-gap and iron cores and Back EMF very exactly such that the results well match to those of the FEA and experiment.

Originality/value

Unlike the conventional winding factor, the winding distribution is considered here along the both axial and circumferential directions, which improves the accuracy level of results for non-slotted structures with relatively large air-gaps. The magnetic field distribution and MMF drop-in iron parts are also calculated as the basis for exact recalculation of air-gap magnetic field and Back EMF. Because of small computational burden beside superior accuracy, the proposed model can be treated as an accurate and fast substitute for FEA to be used during the design procedure or for predicting the other performance characteristics of TORUS-NS AFPM machines.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 3 July 2017

Amin Nosrati and Jalal Nazarzadeh

The purpose of this paper is to introduce an asymmetric structure of the magnetic equivalent circuit (MEC) for analysis of the linear induction machine (LIM) with an…

Abstract

Purpose

The purpose of this paper is to introduce an asymmetric structure of the magnetic equivalent circuit (MEC) for analysis of the linear induction machine (LIM) with an internal short circuit fault.

Design/methodology/approach

By applying a proper MEC to the LIM, a generalized relation for the inductance matrix of the machine can be directly determined. To evaluate the proposed model, the stator currents and the air-gap flux with the proposed technique are given and compared to the simulation and experimental results in the healthy and fault conditions.

Findings

The LIM is an axial flux machine with a wide range of applications in high-performance drives. Due to a well-tried effect of the first tooth and the last one (the end effect), the performance level of the LIM decreases. Also, the analysis of the linear machines in fault conditions illustrates more complexity compared to the rotary induction machine. However, the MEC is very simple, describing the behavior of the asymmetric electromechanical devices using the magnetic reluctance or the permeance of flux paths.

Originality/value

Using the proposed model, there would be some decrease in the complications of the LIM analysis in the asymmetrical conditions. Moreover, analyzing some of the characteristics of the LIM, such as turn-fault condition, it can be calculated with high accuracy.

Details

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

Keywords

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