Modeling of Dynamical Objects with Hypercomplex Numbers for Railway Non Traction Consumers with Renewable Energy Sources

The paper deals with development of mathematical backgrounds for modeling and simulation of dynamical object with hypercomplex terms. These backgrounds” usage allows reducing order of model and representing inner object links in compact form. For linear dynamical object., this form produces extended matrix form., which are described by using block-matrices of object parameters. Both compact and extended forms can be used for further studying of the object dynamic and static. For nonlinear object we offer to find piecewise linear approximations for upper and lower boundaries of nonlinear functions and rewrite object equations in linear-like interval form. The considered example of nonlinear modeling shows reducing model order more than twice.