Magnetic Force Analysis in a Gapped-Core Reactor Model Under Harmonic Magnetizations by Efficient Frequency-Domain Decomposition.

摘要

As key electrical devices, large reactors and converter transformers play an important role in the operation of ultra high voltage direct current (UHVDC) transmission [1]. Meanwhile, the existence of rich harmonics in the exciting current or driving voltage leads to distorted flux densities in the saturated iron core. Consequently the magnetic force due to the leakage flux not only exhibits special spectrum in the frequency domain but also threatens the normal operation of electrical devices e.g. vibration and deformation of windings [2-3]. Therefore it is important to investigate the influence of magnetic force on iron core and windings when electrical devices such as reactors work under harmonic magnetizations. The time-stepping method starting from arbitrary initial value is usually used for the computation of time-periodic nonlinear problems. However, the main drawback is that many periods are required to be stepped through for steady state solution, especially when a much larger time constant exists in the nonlinear system to be analyzed. Numerical methods in time domain and frequency domain have been presented and developed to solve the steady state nonlinear magnetic field efficiently [4-5] by combining the fixed point technique with the finite element method. In this paper, the harmonic-balance system of equations is established first by approximating all time-periodic variables by complex series. Thereupon, decomposition of the system of equations is achieved according to diagonal dominant characteristic of the reluctivity matrix so that harmonic solutions can be decoupled and computed separately and in parallel. This method is used to compute the magnetic force in a gapped-core model under harmonic magnetizations based on the harmonic solutions of magnetic field.