An Efficient Harmonic Method for Solving Nonlinear Time-Periodic Eddy-Current Problems

Ciric, I.R.; Hantila, Florea I.

doi:10.1109/tmag.2006.890952

Cited by 42 publications

(29 citation statements)

References 4 publications

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“…The modified dynamic overrelaxation, also proposed and illustrated in this paper for 2D structures, is expected to be highly efficient for the field solution in 3D structures as well. This modified technique is applied to determine very efficiently a good approximation of the fundamental harmonic and, then, the addition of successive higher harmonics is dealt with by employing the previously developed iterative technique (Ciric and Hantila, 2007). For strongly nonlinear media, where the contributions of the fundamental and the third harmonics are comparable, the dynamic overrelaxation procedure can be initiated for both these harmonics, but the number of equal segments within the interval considered for the fundamental of the magnetic induction should be reduced to allow for a number of segments within the interval for the third harmonic.…”

Section: Discussionmentioning

confidence: 99%

“…COMPEL 30,6 B. Periodic regime with eddy currents The integral equation employed to obtain the eddy currents at each odd harmonic n of angular frequency nv is (Ciric and Hantila, 2007):…”

Section: A Periodic Regime Without Eddy Currentsmentioning

confidence: 99%

“…The relative error for the fundamental is evaluated as: DM ðnÞ n M ðnÞ k k n and it is shown in Figure 3 versus the computation time for the four cases mentioned above. In each of them, the rate of convergence is presented for the old PFPM procedure (Ciric and Hantila, 2007) with overrelaxation and for the proposed modified 3 -modified technique without overrelaxation; 4 -old PFPM procedure (Ciric and Hantila, 2007) with overrelaxation Convergence acceleration technique without and with overrelaxation, using a constant overrelaxation factor of u ¼ 1.95, as well as for the modified technique with dynamic overrelaxation. In the case of a strong saturation, the old iterative technique cannot be used to decrease the relative error below certain values (for example, below 1.4 £ 10 2 4 for a current I 0 ¼ 1,500 A (Figure 3(c) and (d))).…”

Section: Convergence Accelerationmentioning

confidence: 99%

“…Harmonic content of the magnetic induction at the point P in Figure 1, for the four cases in Figure 3 Case Notes: 1 -Modified technique with dynamic overrelaxation; 4 -old PFPM procedure (Ciric and Hantila, 2007) with overrelaxation Table II.…”

Section: Convergence Accelerationmentioning

confidence: 99%

See 3 more Smart Citations

Convergence acceleration in the polarization method for nonlinear periodic fields

Ciric

Hantila

Maricaru

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -The purpose of this paper is to present three novel techniques aimed at increasing the efficiency of the polarization fixed point method for the solution of nonlinear periodic field problems. Design/methodology/approach -Firstly, the characteristic B-M resulting from the constitutive relation B-H is replaced by a relation between the components of the harmonics of the vectors B and M. Secondly, a dynamic overrelaxation method is implemented for the convergence acceleration of the iterative process involved. Thirdly, a modified dynamic overrelaxation method is proposed, where only the relation B-M between the magnitudes of the field vectors is used. Findings -By approximating the actual characteristic B-M by the relation between the components of the harmonics of the vectors B and M, the amount of computation required for the field analysis is substantially reduced. The rate of convergence of the iterative process is increased by implementing the proposed dynamic overrelaxation technique, with the convergence being further accelerated by applying the modified dynamic overrelaxation presented. The memory space is also well reduced with respect to existent methods and accurate results for nonlinear fields in a real world structure are obtained utilizing a normal size processor notebook in a time of about one-half of one minute when no induced currents are considered and of about one minute when eddy currents induced in solid ferromagnetic parts are also fully analyzed. Originality/value -The originality of the novel techniques presented in the paper consists in the drastic approximations proposed for the material characteristics of the nonlinear ferromagnetic media in the analysis of periodic electromagnetic fields. These techniques are highly efficient and yield accurate numerical results.

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Section: Discussionmentioning

confidence: 99%

“…COMPEL 30,6 B. Periodic regime with eddy currents The integral equation employed to obtain the eddy currents at each odd harmonic n of angular frequency nv is (Ciric and Hantila, 2007):…”

Section: A Periodic Regime Without Eddy Currentsmentioning

confidence: 99%

Section: Convergence Accelerationmentioning

confidence: 99%

Section: Convergence Accelerationmentioning

confidence: 99%

See 2 more Smart Citations

Convergence acceleration in the polarization method for nonlinear periodic fields

Ciric

Hantila

Maricaru

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…Variables in electromagnetic field under steady-state excitations can be approximated by triangular series. Harmonicbalanced theory is used in the finite-element method and the integral equation method to calculate nonlinear magnetic field [4], [5]. The electromagnetic field can be solved directly in harmonic domain, without long computational time.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Analysis of Nonlinear Magnetic Field Under Sinusoidal and DC-Biased Magnetizations by the Fixed-Point Method

Zhao

Cheng³

et al. 2015

IEEE Trans. Magn.

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The laminated core is tested under sinusoidal and dc-biased magnetizations. The measured data are manipulated by the proposed modified iterative method to obtain dc-biasing hysteresis loops accurately. The hysteresis model, based on a consuming function, is used to simulate the hysteresis effects of the iron core under different magnetizations. The fixed-point technique is combined with the harmonic-balanced method to compute exciting currents and magnetic fields simultaneously by considering the hysteresis effects. The global convergent strategies are presented to guarantee the convergence of harmonic solutions. The hysteretic characteristics and iron loss of the laminated core are analyzed on the basis of harmonic solutions of the magnetic field.Index Terms-DC bias, fixed-point reluctivity, harmonic-balanced method, hysteresis effect, laminated core.

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Advanced Numerical Approach using HBFEM

Lu¹,

Zhao²,

Yamada³

2016

Harmonic Balance Finite Element Method

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An Efficient Harmonic Method for Solving Nonlinear Time-Periodic Eddy-Current Problems

Cited by 42 publications

References 4 publications

Convergence acceleration in the polarization method for nonlinear periodic fields

Convergence acceleration in the polarization method for nonlinear periodic fields

Harmonic Analysis of Nonlinear Magnetic Field Under Sinusoidal and DC-Biased Magnetizations by the Fixed-Point Method

Advanced Numerical Approach using HBFEM

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