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Article
Publication date: 4 September 2017

Jennifer Susanne Dutiné, Markus Clemens and Sebastian Schöps

Discretizing the magnetic vector potential formulation of eddy current problems in space results in an infinitely stiff differential algebraic equation system that is…

Abstract

Purpose

Discretizing the magnetic vector potential formulation of eddy current problems in space results in an infinitely stiff differential algebraic equation system that is integrated in time using implicit time integration methods. Applying a generalized Schur complement to the differential algebraic equation system yields an ordinary differential equation (ODE) system. This ODE system can be integrated in time using explicit time integration schemes by which the solution of high-dimensional nonlinear algebraic systems of equations is avoided. The purpose of this paper is to further investigate the explicit time integration of eddy current problems.

Design/methodology/approach

The resulting magnetoquasistatic Schur complement ODE system is integrated in time using the explicit Euler method taking into account the Courant–Friedrich–Levy (CFL) stability criterion. The maximum stable CFL time step can be rather small for magnetoquasistatic field problems owing to its proportionality to the smallest edge length in the mesh. Ferromagnetic materials require updating the reluctivity matrix in nonlinear material in every time step. Because of the small time-step size, it is proposed to only selectively update the reluctivity matrix, keeping it constant for as many time steps as possible.

Findings

Numerical simulations of the TEAM 10 benchmark problem show that the proposed selective update strategy decreases computation time while maintaining good accuracy for different dynamics of the source current excitation.

Originality/value

The explicit time integration of the Schur complement vector potential formulation of the eddy current problem is accelerated by updating the reluctivity matrix selectively. A strategy for this is proposed and investigated.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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Article
Publication date: 6 May 2020

Christoph Jörgens and Markus Clemens

In high-voltage direct current (HVDC) cable systems, space charges accumulate because of the constant applied voltage and the nonlinear electric conductivity of the…

Abstract

Purpose

In high-voltage direct current (HVDC) cable systems, space charges accumulate because of the constant applied voltage and the nonlinear electric conductivity of the insulating material. The change in the charge distribution results in a slowly time-varying electric field. Space charges accumulate within the insulation bulk and at interfaces. With an operation time of several years of HVDC systems, typically the stationary electric field is of interest. The purpose of this study is to investigate the influence of interfaces on the stationary electric field stress and space charge density.

Design/methodology/approach

An analytic description of the stationary electric field inside cable insulation is developed and numerical simulations of a cable joint geometry are applied, considering spatial variations of the conductivity in the vicinity of the electrodes and interfaces.

Findings

With increasing conductivity values toward the electrodes, the resulting field stress decreases, whereas a decreasing conductivity results in an increasing electric field. The increased electric field may cause partial discharge, resulting in accelerated aging of the insulation material. Thus, interfaces and surfaces are characterized as critical areas for the reliability of HVDC cable systems.

Research limitations/implications

This study is restricted to stationary electric field and temperature distributions. The electric field variations during a polarity reversal or a time-varying temperature may result in an increased electric conductivity and electric field at interfaces and surfaces.

Originality/value

An analytical description of the electric field, considering surface effects, is developed. The used conductivity model is applicable for cable and cable-joint insulations, where homo- and hetero-charge effects are simulated. These simulations compare well against measurements.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 20 August 2018

Christoph Jörgens and Markus Clemens

In high voltage direct current (HVDC), power cables heat is generated inside the conductor and the insulation during operation. A higher amount of the generated heat in…

Abstract

Purpose

In high voltage direct current (HVDC), power cables heat is generated inside the conductor and the insulation during operation. A higher amount of the generated heat in comparison to the dissipated one, results in a possible thermal breakdown. The accumulation of space charges inside the insulation results in an electric field that contributes to the geometric electric field, which comes from the applied voltage. The total electric field decreases in the vicinity of the conductor, while it increases near the sheath, causing a possible change of the breakdown voltage.

Design/methodology/approach

Here, the thermal breakdown is studied, also incorporating the presence of space charges. For a developed electro-thermal HVDC cable model, at different temperatures, the breakdown voltage is computed through numerical simulations.

Findings

The simulation results show a dependence of the breakdown voltage on the temperature at the location of the sheath. The results also show only limited influence of the space charges on the breakdown voltage.

Research limitations/implications

The study is restricted to one-dimensional problems, using radial symmetry of the cable, and does not include any aging or long-term effect of space charges. Such aging effect can locally increase the electric field, resulting in a reduced breakdown voltage.

Originality/value

A comparison of the breakdown voltage with and without space charges is novel. The chosen approach allows for the first time to assess the influence of space charges and field inversion on the thermal breakdown.

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: 21 April 2020

Sebastian Böhmelt, Nils Kielian, Michael Hagel, Marcus Stiemer, Marvin-Lucas Henkel and Markus Clemens

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS…

Abstract

Purpose

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed.

Design/methodology/approach

The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid.

Findings

The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method.

Originality/value

The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 25 July 2019

Fotios Kasolis and Markus Clemens

This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order…

Abstract

Purpose

This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order reduction for transient strongly nonlinear electro-quasistatic (EQS) field problems.

Design/methodology/approach

The paper provides convincing empirical insights to support the proposed domain decomposition algorithm, a numerical investigation of the performance of the algorithm for different snapshots and model order reduction experiments.

Findings

The proposed method successfully decomposes the computational domain, while the resulting reduced models are highly accurate. Further, the algorithm is computationally efficient and robust, while it can be embedded in black-box model reduction implementations.

Originality/value

This paper fulfills the demand to effectively perform model order reduction for transient strongly nonlinear EQS field problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 June 2001

Markus Clemens, Markus Wilke and Thomas Weiland

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects…

Abstract

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects of moving conductors with simple geometries by different approaches. A new regularization of the formulation using discrete grad‐div augmentation of the curlcurl formulation is presented and tested. To improve the implicit time integration process, several schemes for an error controlled variable time step selection are presented and for the repetitive solution of the arising large sparse systems of equations a sparse direct solver is compared to iterative methods such as a preconditioned conjugate gradient method and a new algebraic multigrid solver, which is aware of the curlcurl nullspace.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 20 no. 2
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 December 2004

Galina Benderskaya, Herbert De Gersem, Thomas Weiland and Markus Clemens

The coupling between a 3D modified magnetic vector potential formulation discretized by the finite integration technique and an electrical circuit that includes solid and…

Abstract

The coupling between a 3D modified magnetic vector potential formulation discretized by the finite integration technique and an electrical circuit that includes solid and stranded conductors is presented. This paper describes classical time integration methods and the implicit Runge‐Kutta methods, the latter being an appropriate alternative to the first ones to solve effectively index 1 differential‐algebraic equations arising from combined simulation of electromagnetic fields and electrical circuits.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 January 2006

Galina Benderskaya, Herbert De Gersem, Thomas Weiland and Markus Clemens

To provide a numerical technique for the quick and simple determination of the switching time instants for field‐circuit coupled problems with switching elements.

Abstract

Purpose

To provide a numerical technique for the quick and simple determination of the switching time instants for field‐circuit coupled problems with switching elements.

Design/methodology/approach

3D magnetic vector potential formulation coupled to an electrical circuit with switching elements, for example, diodes, is presented. The change of the state of the switching elements is implemented as a modification of the model topology.

Findings

Since every step of the singly diagonally implicit Runge‐Kutta methods delivers not only the solution of this time step but also its stage derivatives, they can be efficiently employed to construct a dense‐output‐based interpolation polynomial, with their roots approximating the switching time instants.

Originality/value

This paper presents a computationally cheap interpolation approach for quick and accurate determination of switching time instances for field‐circuit coupled problems with switching elements. The proposed technique can be successfully incorporated into software packages designed to model coupled problems of different nature, where sudden changes of quality may take place.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 25 no. 1
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 15 November 2011

Markus Clemens, Sebastian Scho¨ps, Herbert De Gersem and Andreas Bartel

The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically…

Abstract

Purpose

The space discretization of eddy‐current problems in the magnetic vector potential formulation leads to a system of differential‐algebraic equations. They are typically time discretized by an implicit method. This requires the solution of large linear systems in the Newton iterations. The authors seek to speed up this procedure. In most relevant applications, several materials are non‐conducting and behave linearly, e.g. air and insulation materials. The corresponding matrix system parts remain constant but are repeatedly solved during Newton iterations and time‐stepping routines. The paper aims to exploit invariant matrix parts to accelerate the system solution.

Design/methodology/approach

Following the principle “reduce, reuse, recycle”, the paper proposes a Schur complement method to precompute a factorization of the linear parts. In 3D models this decomposition requires a regularization in non‐conductive regions. Therefore, the grad‐div regularization is revisited and tailored such that it takes anisotropies into account.

Findings

The reduced problem exhibits a decreased effective condition number. Thus, fewer preconditioned conjugate gradient iterations are necessary. Numerical examples show a decrease of the overall simulation time, if the step size is small enough. 3D simulations with large time step sizes might not benefit from this approach, because the better condition does not compensate for the computational costs of the direct solvers used for the Schur complement. The combination of the Schur approach with other more sophisticated preconditioners or multigrid solvers is subject to current research.

Originality/value

The Schur complement method is adapted for the eddy‐current problem. Therefore, a new partitioning approach into linear/non‐linear and static/dynamic domains is proposed. Furthermore, a new variant of the grad‐div gauging is introduced that allows for anisotropies and enables the Schur complement method in 3D.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 6
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 December 2004

Herbert De Gersem, Markus Wilke, Markus Clemens and Thomas Weiland

Certain sophisticated boundary conditions offer powerful modelling features for many electrotechnical models. Their application, however, wipes out the particular…

Abstract

Certain sophisticated boundary conditions offer powerful modelling features for many electrotechnical models. Their application, however, wipes out the particular structure of the system matrices which occurs when structured grids are applied. In this paper, this effect is prevented by considering the unconstrained system together with additional constraint equations or by projecting the algebraic system using an oblique or orthogonal projector. The numerical tests indicate that the efficiency of sparse iterative solvers can be preserved even in the presence of complicated boundary relations. The described projections are also advantageous for formulations derived for unstructured grids.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 23 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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