Application of Extrapolation Capability of Vector Fitting for Out-of-Band Dominant Modal Synthesis of Voltage-Source Converters

Conventional state-space-based stability assessment method of voltage-source converters (VSCs) can be hindered by the black-box feature. Black box-based state-space model identification method using the terminal admittance/impedance frequency responses has thus been drawing increasing research attentions recently. However, the estimation of out-of-band modes commonly suffers from narrow bandwidth of frequency responses. This article presents, for the first time, the potential identification of several critical out-of-band modes of an artificially created rational function and a grid-connected VSC. This identification is achieved through their band-limited frequency responses using the vector fitting (VF) algorithm. On its basis, a sensitivity index of a partial fraction term is derived to explain the out-of-band modal identification behavior of the VF. The effects of the pole, residue, and fitting frequency interval width on the sensitivity index are further investigated and demonstrated. The numerical analysis shows that, with the help of the proposed sensitivity index, the extrapolation behavior of the VF can be explained, and several invisible out-of-band modes can further be identified or synthesized from a band-limited frequency response. This extrapolation feature may strengthen the curve fitting capability of the VF, i.e., compared to the VSC's band-limited frequency responses, more modal information can be obtained and further used for eigenvalue-based stability analysis.