This paper presents a theoretical review and comparisons between Vector fitting, Matrix-Pencil-Method and Loewner Matrix techniques for the fitting of frequency-domain functions. Firstly, the theoretical fundaments of each technique are briefly reviewed. Secondly, their computational performances and fitting accuracy are compared through different case studies. As for Loewner Matrix method, a novel implementation is proposed for a fair comparison with the other two techniques. Moreover, it is demonstrated that this novel implementation has some advantages over the traditional one. Finally, global remarks and recommendations are specified to take advantage of the capabilities exhibited by each technique.

This letter proposes a two-stage fitting procedure for transmission line/cable functions in which low frequency samples are exclusively considered. At the first stage, fitting is performed for a reduced band by excluding frequencies close to DC. Reducing the fitting range relieves the fitting. The second stage consists of finding a correction term for the out-of-band samples close to DC. The procedure, when used with the recently introduced frequency-dependent cable model (FDCM) approach, allows modeling transmission lines and cables with improved fitting precision at low frequencies. Overall, the new approach is called FDM (Frequency Dependent Model) with DC correction, i.e., FDM/DC. It can also be used to complement the prevailing Universal Line Model (ULM) in two ways: for reducing the integration errors due to unbalanced fitting, and for improving the precision of DC response. Two examples are provided to demonstrate the utility of the new approach.

This paper proposes a rational approximation-based approach to find positive real parameters for the extended Debye model (EDM), aimed at condition assessment of insulation systems of power transformers. The EDM can model the slow and fast polarization phenomenon, including relaxation mechanisms with different relaxation times within a composite dielectric material. In the proposed approach, the complex permittivity of the transformer’s composite insulation is approximated via rational functions, as given by the vector fitting (VF) software tool, and the EDM parameters are identified from the obtained poles/residues. To guarantee positive real parameters, i.e., a physically realizable circuit, VF is internally modified to calculate the final residues of the rational approximation via a constrained linear least-squares problem without resorting to further post-processing algorithms, as in existing methods, hence without affecting fitting accuracy. The effectiveness of the parametrized EDM is demonstrated in two ways: (a) by reconstructing frequency domain spectroscopy (FDS) curves provided via measurements in new oil-immersed power transformers and (b) by the comparison of the calculated polarization current given by EDM versus real measurements in time domain. The achieved fitting accuracy in most of the cases is above 99 percent for the reconstructed FDS curves, while the polarization current waveform is reproduced with good agreement.

This paper presents a novel methodology for the computation of rational models for electromagnetic transients simulations. The proposed methodology combines the capabilities of either the Loewner Matrix (LM) or the Matrix Pencil Method (MPM) for model-order identification with the high accuracy of the vector fitting (VF) technique. The proposed technique achieves improved performance compared with individual application of MPM, LM, and VF techniques. A unique advantage of the proposed algorithm is that the model order can be determined automatically.

This study presents a novel methodology for steady and dynamic states harmonic analysis of power systems. It employs a decomposition framework so that harmonic‐producing devices are considered as separate subsystems which are solved via the extended harmonic domain (EHD) technique. The EHD is inherently a frequency domain dependent solution method that provides dynamic harmonic indices based on operational matrices. The remaining system is modelled and resolved via commonly used harmonic analysis methods while transient stability (TS) is conducted (at fundamental frequency) to account for dynamic behaviour of generators and controllers. Interfacing of EHD and TS solutions is performed via an iterative scheme. As for steady‐state initialisation, an efficient and robust algorithm is proposed in this study. The proposed method is implemented in an existing software package and applied to IEEE 9‐bus test system. A thorough comparison of the proposed method with the PSCAD/EMTDC software tool is also presented.