Studying State Convergence of Input-to-State Stable Systems with Applications to Power System Analysis

Antonio T. Alexandridis
Additional contact information
Antonio T. Alexandridis: Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece

Energies, 2019, vol. 13, issue 1, 1-24

Abstract: In stability studies, the response of a system enforced by external, known or unknown, inputs is of great importance. Although such an analysis is quite easy for linear systems, it becomes a cumbersome task when nonlinearities exist in the system model. Nevertheless, most of the real-world systems are externally enforced nonlinear systems with nonzero equilibriums. Representative examples in this category include power systems, where studies on stability and convergence to equilibrium constitute crucial objectives. Driven by this need, the aim of the present work is twofold: First, to substantially complete the theoretical infrastructure by establishing globally valid sufficient conditions for externally enforced nonlinear systems that converge to nonzero equilibriums and, second, to deploy an efficient method easily applicable on practical problems as it is analyzed in detail on a typical power system example. To that end, in the theoretical first part of the paper, a rigorous nonlinear analysis is developed. Particularly, starting from the well-established nonlinear systems theory based on Lyapunov techniques and on the input-to-state stability (ISS) notion, it is proven after a systematic and lengthy analysis that ISS can also guarantee convergence to nonzero equilibrium. Two theorems and two corollaries are established to provide the sufficient conditions. As shown in the paper, the main stability and convergence objectives for externally enforced systems are fulfilled if simple exponential or asymptotic converging conditions can be proven for the unforced system. Then, global or local convergence is established, respectively, while for the latter case, a novel method based on a distance-like measure for determining the region of attraction (RoA) is proposed. The theoretical results are examined on classic power system generation nonlinear models. The power system examples are suitably selected in order to effectively demonstrate the proposed method as a stability analysis tool and to validate all the particular steps, especially that of evaluating the RoA. The examined system results clearly verify the theoretical part, indicating a rather wide range of applications in power systems.

Keywords: stability; nonlinear systems; power system analysis; convergence to equilibrium (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/13/1/92/pdf (application/pdf)
https://www.mdpi.com/1996-1073/13/1/92/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:13:y:2019:i:1:p:92-:d:301283

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().