Analysis of time-varying power system loads via Chebyshev polynomials

This paper presents a frequency domain based methodology using Chebyshev polynomials of the first kind, the methodology can be used to make an analysis of time-varying linear systems in the transient state. The method takes advantages of the operational properties available to most orthogonal series expression, i.e. integration, differentiation, product and coefficient matrices. 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. A high order time-varying system is presented and it is analyzed via the proposed methodology.