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In this paper, an eddy-current formulation is used to determine the transmission-line parameters of a machine winding. It is shown that this formulation covers a broader frequency range than the commonly used low-frequency magnetostatic and high-frequency magnetodynamic approximations. The eddy-current formulation, however, suffers from large computation times and may lead to severe inaccuracies if the finite-element mesh does not resolve the skin depth, a modelling concern that does not exist for the traditional formulations. The three finite-element models are compared according to the accuracy of the resulting transmission-line model applied to the winding of a permanent-magnet synchronous machine.
In this paper, differential conductivity and reluctivity matrices
are constructed for formulations discretised by the finite
integration technique and linearised by the Newton method. It turns
out that these matrices are nondiagonal and unsymmetric, even in the
case that orthogonal grids are used. A diagonal approximation of the
differential matrices leads to an approximate Newton method where
cross-magnetisation effects are no longer considered, except in the
update between the successive nonlinear iteration steps. The approximate method does not guarantee second order convergence but outperforms the true Newton method when only a moderate accuracy is required.
Steady-state operation modes of three-phase induction machines can
be efficiently simulated by 2D nonlinear time-harmonic finite-element models, although only induced currents with respect to the fundamental air-gap field are correctly taken into account.
This technique does not generalise to single-phase induction
machines. An approach based on multiple rotor models and a spectral
decomposition of the air-gap field enables to consider higher
harmonic air-gap field contributions. In a capacitor-motor model,
the first, third and fifth forward and backward rotating components
give raise to different frequencies in the rotor which result in
different eddy-current effects. The torque dip due to the third
harmonic is accurately simulated.
The presence of materials with a relative large difference in permeability has a harmful influence on the convergence of Krylov subspace iterative solvers. Some slow converging
components are not cured by preconditioning and correspond to eigenvectors reflecting the domains
with relatively low permeable material. Approximations for those eigenvectors are determined using
physical knowledge of the problem. The iterative solution process is split up in a small problem
counting for the separated eigenmodes and a full-size problem out of which the slow converging
modes are removed. This deflated preconditioned solver is faster converging compared to more
common approaches, such as the incomplete Cholesky conjugate gradient method.
An electrodynamic field is coupled to a magnetic equivalent circuit. The electrodynamic
problem is formulated by the electric vector potential and discretised by finite elements. The
magnetic lumped parameter model is described in terms of unknown fluxes and magnetomotive
forces. The coupled system matrix has a mixed and hybrid nature. In this presentation, the method is
applied to simulate eddy current distributions in laminated material and losses in a dielectric heater.
A generalized tree theory is presented in order to deal with all possible connections of solid
and stranded conductors in an electric circuit coupled with a magnetic
finite element model. A
generalized Signal Flow Graph is used to determine the unknown currents and voltages necessary to
describe the circuit behaviour in a symmetric way. The method is applied to an example. The aim of this
paper is to state a general network theory able to deal with all possible connections of voltage and current
sources, impedances, solid and stranded conductors leading to a symmetric and compact coupling matrix
without zero diagonals.
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