An optimal vector fitting method for estimating frequency-dependent network equivalents in power systems

Vector fitting (VF) algorithms have become popular and powerful tools for estimating models formed by rational basis function (RBF) expansions. In this paper, we first translate the well-known continuous time-domain VF method (cTD-VF) to a discrete time-domain framework. We denote this new domain VF method by dTD-VF. Differently from the cTD-VF, the dTD-VF formulation does not rely on a numerical approximation of convolution integrals and, as a result, it can be easily implemented with a variety of RBF sets. The second part of this paper shows that the proposed dTD-VF can also be transformed into a novel instrumental variable (IV)-dTD-VF technique, which is shown to have a guaranteed optimal solution at convergence. Moreover, this important optimality property does not depend on the nature of the noise that corrupts the data (for instance, if it is white or colored). Two case studies highlight the advantages of using the proposed methods. One of these examples consists of modeling the admittance characteristics of a power system implemented as a frequency-dependent network equivalent (FDNE).