Rational Approximation of Nonlinear Systems Via NL-VF

Abstract

This paper presents an alternative vector fitting (VF)-based approach to generate a rational model of nonlinear system behaviors. The proposed approach, named here as nonlinear VF (NL-VF), has its fundament in the previously proposed time-domain VF (TD-VF). TD-VF generates rational models using TD input/output responses and numerical convolution. Unlike TD-VF, NL-VF utilizes input/output vectors in the frequency domain (FD) to produce a rational approximation of the corresponding transfer function/matrix. The input/output FD vectors are obtained in this paper by a numerical Laplace transform (NLT) algorithm. Alternatively, input/output TD vectors available from any solution algorithm can be transformed to FD via NLT and used in the NL-VF approach. Computational efficiency and accuracy of the NL-VF are compared with the TD-VF technique for the single-phase case. It is demonstrated that NL-VF gives more accurate results than TD-VF, in particular when the data is calculated from a time-window, which does not capture the system slow dynamics. Also, unlike TD-VF, NL-VF can handle in a natural way FD weighting, thus exhibiting error control. The proposed approach is applied in this paper to 1) a boost converter circuit, and 2) a network involving simultaneously a three-phase grid-tied photovoltaic (PV) system and a nonlinear reactor load.