Rational approximation of frequency domain responses in the S and Z planes

In time domain analysis, approximated rational functions are used to model components or parts of a power system whose characteristic is known in the frequency domain. Over the years, many techniques have been proposed to fit the frequency response to rational functions to ensure accurate computational models for transient studies. In this work, a comparison of different approaches is made. Linear and nonlinear fitting routines are applied to the synthesis of lumped and distributed parameter circuits. The fittings are performed in S and Z-domains. The following methods have been considered: Golub´s algorithm, singular value decomposition (SVD), vector fitting, Levenberg-Marquardt´s method and a full-Newton implementation developed by the authors. The presented techniques may be applied on modelling transmission lines and transformers, and to the development of frequency-dependent network equivalents.