The study of inrush current phenomenon using operational matrices

The paper presents a new methodology for calculating magnetizing inrush currents. Similarly to the seminal work of Rajakovic and Semlyen, all the calculations are conducted in the frequency domain, hence, circumventing the many problems encountered when time domain simulations are used to solve this problem. Unlike the work of Rajakovic and Semlyen [1], where a pre-determined sequence of steady-state “images” are obtained for a sufficiently long number of cycles to capture the complete picture of the inrush phenomenon, our method produces the full solution, with no loss of fidelity, of the overall inrush phenomenon. The solution is achieved by resorting to operational matrices and it is fully equivalent to that produced by time domain simulations but carried out entirely in the frequency domain. In principle, any orthogonal series expansion could be used with this method but in this paper Hartley series have been selected. The usefulness of the methodology is illustrated with simple but practical circuits. Comparisons against time domain simulations are given.