Harmonic Domain Dynamic Transfer Function of a Nonliner Time-Periodic Network

This paper presents a new concept called harmonic domain dynamic transfer function (HDDTF), which characterizes the dynamics of a nonlinear time-periodic network as seen from a port (or multiple ports) in terms of the frequency response of harmonic perturbations superimposed on its underlying periodic steady state. It pertains to the transient behavior superimposed on the steady state. The HDDTF is a transfer-function matrix H(s) relating the vectors of harmonic domain input and output endowed with s-domain properties. Because the network can contain saturable (nonlinear) elements and periodically-switching (time-periodic) power electronics components, the HDDTF may be used for the analysis of power quality problems. It may also serve for the identification of a reduced-order dynamic equivalent of a nonlinear time-periodic network to be used in time-domain transient simulations. The HDDTF is obtained by linearization about the periodic steady state of the nonlinear state equations describing a given network. Following the derivation of the HDDTF, a modal analysis to characterize the HDDTF by its diagonalization is presented. Two test systems are used to produce numerical examples.