Analysis of switching loads in networks using operational matrices

This letter presents an approach for rapid calculation of the steady state of time-varying electric networks based on the use of orthogonal series expansions. The method takes advantage of the operational properties available to most orthogonal series expansions, i.e., integration, differentiation, product, and coefficients matrices. An important feature of this approach is that an analytical expression for the steady state is provided. The approach may be seen as an extension of phasor analysis commonly used for the analysis of linear time invariant electric networks to periodic networks.