Abstract
A new method to optimally determine the fixed-point reluctivity is presented to ensure the stable and fast convergence of harmonic solutions. Nonlinear system matrix is linearized by using the fixed-point technique, and harmonic solutions can be decoupled by the diagonal reluctivity matrix. The 1-D and 2-D non-linear eddy current problems under DC-biased magnetization are computed by the proposed method. The computational performance of the new algorithm proves the validity and efficiency of the new algorithm. The corresponding decomposed method is proposed to solve the nonlinear differential equation, in which harmonic solutions of magnetic field and exciting current are decoupled in harmonic domain.
Highlights
Non-linear eddy current problems can be solved by the time-stepping method [1] or the harmonic-balanced method [2]
A relationship between magnetic field intensity H and the magnetic induction B is represented by introducing the fixed-point reluctivity νFP[3]
A relationship between magnetic field intensity H and magnetic flux density B is represented by introducing the fixed-point reluctivity νFP [8], H
Summary
Non-linear eddy current problems can be solved by the time-stepping method [1] or the harmonic-balanced method [2]. The time-stepping method requires many periods to approach the accurate steady-state solution, while the harmonic-balanced method computes the magnetic field directly in the frequency domain. Owing to the nonlinearity of magnetic material in electromagnetic devices, there often are high-order harmonics in the exciting current and magnetic field Electrical devices such as power transformers and reactors may work abnormally due to the magnetic storm and the transmission of high voltage direct current [7]. In this paper an efficient algorithm to determine the fixed-point reluctivity νFP is proposed It is aimed at efficiently computing the non-linear eddy current problem under DC-biased magnetization. The corresponding decomposed algorithm is presented to solve the nonlinear differential equation sequentially or concurrently, which decreases the memory cost of harmonic-balanced computation of large scale problems
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