A Reduction Algorithm for Fractional Order Transmission Line Modeling with Skin Effect

In this paper, we deduce a fractional-order model based on skin effect for frequency dependent transmission line model. The voltages and currents at any location in transmission line can be calculated by the proposed fractional partial differential equations. Then the fractional ordinary differential equation can obtained from the transmission line fractional partial differential equations through the discrete space and the fractional order differential item of approximation to replace. In practical, there are tens of thousands of turns in transformer winding, and the order of parameter matrix is very large, so we define a new plane based on the Laplace transformation and propose a model order reduction (MOR) method for the fractional order system. And combine with the new distributed distance points, the voltages and currents can be calculated.