Polynomial Fitting of Operating Point Dependency in Small-Signal State-Space Models for Power Electronic Converters

This paper presents an approach for representing nonlinear operating point dependencies in small-signal state-space modelling of power electronic converters. The intended application is for unifying a set of small-signal models identified from black-box simulation models or physical measurements into a single operating point dependent model. The approach is based on a polynomial fitting of the operating point dependency of the matrix elements in a state-space modal representation. The fitted expressions for the matrix elements provide a single model that can be utilized for small-signal analysis in a wide range of operating conditions and prevents the need for investigation of individual models at each operation point. Two different cases are discussed for evaluating the applicability of the presented approach, including a grid-forming converter with a Virtual Synchronous Machine (VSM)-based control and a conventional grid-following converter with dc-link voltage control. The results show that a quadratic fitting of the matrix elements can provide acceptable model accuracy in most cases.