Fourier-series approach to model order reduction and controller interaction analysis of large-scale power system models

• Published in: IET generation, transmission & distribution transmission & distribution, 2018-03, Vol.12 (6), p.1247-1255
• Main Authors: Rergis, Carlos Morales, Betancourt, Ramón Jiménez, Espejo, Emilio Barocio, Messina, Arturo Román
• Format: Article
• Language: English
• Subjects: approximate Hankel‐based interaction measures; approximation theory; conformal mapping; conformal mapping principle; control system synthesis; controller design; controller interaction analysis; discrete equivalent; discrete system representation; discrete time systems; discrete‐time transfer function; Fourier series; Fourier series approach; large‐scale dynamical system; large‐scale power system model; linear systems; linearised system model; model order reduction; power system control; reduced order systems; reduced‐order model; Research Article; ROM; transfer functions; unstable dynamic systems analysis
• ISSN: 1751-8687; 1751-8695; 1751-8695
• DOI: 10.1049/iet-gtd.2017.0465

In this study, a comprehensive approach for model order reduction based on a Fourier series of a discrete system representation is proposed. The developed method represents an alternative to model reduction of large-scale dynamical systems and can be used for the analysis of unstable dynamic systems and the study of interactions among power system controls. Drawing on the principle of conformal mapping, the linearised system model is first transformed into its discrete equivalent. Then, the Fourier series of the discrete-time transfer function is used to obtain a reduced-order model (ROM). Using this model, approximate Hankel-based interaction measures are proposed to efficiently analyse large, unstable linear system representations and determine pairs of input outputs to design controller. The high degree of applicability and accuracy offered by the method, and its ability to extract ROMs from stable and unstable systems is demonstrated on three test systems.