## JMI2011B-7 Fast analysis method of time-periodic nonlinear fields (pp.131-140)

Author(s)： Kenji Miyata

J. Math-for-Ind. **3B** (2011) 131-140.

- File： JMI2011B-7.pdf (2028KB)

Abstract

A fast analysis method is proposed to obtain time-periodic nonlinear fields in the presence of extremely slow decay fields. First, the analysis variables are time-averaged to reduce effects of the harmonic wave components, and next, second order time-derivatives of the time-averaged values are used to correct the variables toward the time-periodic steady-state field. The time width in time-averaging operation can be set much shorter than one half period, and so the variables can be corrected in early stage of time evolution. The presented method was validated in two-variable simultaneous equations as a simple problem and a magnetic field simulation by the finite element method as a multivariable problem. Furthermore, harmonic TDC and a serial usage of (harmonic) TDC and TP-EEC are proposed for the case that higher order time-harmonic waves are included in the corrected objectives. In addition, the conventional simplified three-phase AC TP-EEC method is expanded to a general form for the three-phase AC system.

Keyword(s). time-periodic, steady-state, correction, transient field