Analysis of Transient Response of Magnetic Flux in Nonlinear Magnetic Circuit

Abstract

In this paper, we first introduce some new two-dimensional theoretical equations for the transient response of the magnetic flux in a fundamental nonlinear magnetic circuit which can be applied to that containing the interpole in a dc machine. Then we develop a numerical method for solving those theoretical nonlinear equations, in which a difference analogue is used, derived from both the non-uniform grid system for space and the Crank-Nicolson method for the time derivative. Next, the transient response of the flux and distribution of the magnetic field intensity and flux density in the interpole are investigated in a case where the step exciting current is supplied to the interpole winding. As a result, it is clearly seen that the magnetic saturation occurs because of a strong magnetic field intensity in the skin of the interpole. This is caused by an eddy current induced in the interpole, and the saturation has a large influence on the flux response. Hence, the flux response is too fast in the numerical calculation results by the conventional linear theory in which the saturation is not considered. Also, it is noted that the transient response is influenced very much by the conductivity of the pole as well as the lengths and cross-sectional areas of the pole and pole gap. Furthermore, we calculate the flux response in a case where a full-wave rectified magnetomotive-force is applied to the interpole winding, whereby it is clarified that the wave form of the flux response is distorted largely by the saturation.