Rational Modeling of Multiport Systems via a Symmetry and Passivity Preserving Mode-Revealing Transformation

Abstract

Modeling of frequency-dependent components and subnetworks is often based on a terminal description by an admittance matrix in the frequency domain. One challenge in the extraction of state-space models from such data is to prevent possible error magnification when the model is to be applied in time-domain simulations. The error magnification is a consequence of inaccurate representation of small eigenvalues of the admittance matrix. This paper resolves the problem by introducing a similarity transformation matrix which better reveals the eigenvalues of the admittance matrix. The chosen transformation preserves the passivity and symmetry of the original data, allowing the modeling to be performed by standard methods for model extraction and passivity enforcement. The approach is demonstrated for the wideband modeling of subnetworks and power transformers. The new technique is shown to accurately capture the large and small eigenvalues alike, thereby avoiding error magnifications in time-domain simulations.Index Terms-Electromagnetic transients, frequency-dependent network equivalent (FDNE) , network equivalent, pole-residue model, rational model, simulation, state-space model, vector fitting.

Modelling of non‐uniform lines using rational approximation and mode revealing transformation

“…below 10 −15 or less. This is achieved by limiting the value of the (inverse) weighting function when solving the associated least squares problem as reported in [16].…”

“…The extraction of the model (9) is made difficult by the fact that Y eq has at low frequencies a combination of very large and very small eigenvalues. To prevent the small eigenvalues to be lost in the fitting process, we make use of the MRT introduced in [16]. MRT aims at improving the observability of this small eigenvalues by choosing a suitable transformation matrix T that preserves the physical properties of symmetry, realness, stability, causality and passivity.…”

“…One difficulty encountered with the approach is that the small admittance elements associated with charging currents at low frequencies tend to be lost in the (large) short-circuit currents. We therefore introduce a mode-revealing transformation (MRT) [16] to make the small eigenvalues more observable in the admittance matrix. In order to obtain a model suitable for time-domain simulation, the transformed admittance matrix is subjected to rational function model extraction using vector fitting (VF) [17][18][19], followed by passivity removal by perturbation [20].…”

Development and Applicability of Online Passivity Enforced Wide-Band Multi-Port Equivalents For Hybrid Transient Simulation

“…FDNEs are generally formulated as frequency-dependent black-box terminal equivalents based on rational functions. In [6], FDNE is formulated using modal vector fitting (VF) method and in [7] passivity of the rational function is enforced using mode revealing algorithm. The authors in [8], used VF method to generate FDNE combined with TSA component for real-time simulation and, in [9] this method was improved by including generator coherency.…”

Βελτιωμένη Μοντελοποίηση Εξαρτώμενη Από Τη Συχνότητα Της Μεταβατικής Συμπεριφοράς Γραμμών Μεταφοράς Ηλεκτρικής Ενέργειας

“…Το κύριο μειονέκτημα αυτής της μεθόδου είναι η απαίτηση για λεπτομερή υπολογισμό του πίνακα σύνθετων αγωγιμοτήτων κόμβων στο πεδίο της συχνότητας, καθώς τα στοιχεία του στις υψηλές συχνότητες χαρακτηρίζονται από μια σειρά αιχμών και απότομης διακύμανσης [28], [44], [45], [50], [52]. Επιπρόσθετα, απαιτείται η χρησιμοποίηση ενός σημαντικού αριθμού ρητών συναρτήσεων για την ακριβή μοντελοποίηση του πίνακα σύνθετων αγωγιμοτήτων κόμβων, γεγονός που οφείλεται στους χρόνους διάδοσης των γραμμών μεταφοράς που ενυπάρχουν στα στοιχεία του πίνακα [44], [45].…”