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

Author

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  • Antonio T. Alexandridis

    (Department of Electrical and Computer Engineering, University of Patras, 26504 Patras, Greece)

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.

Suggested Citation

  • Antonio T. Alexandridis, 2019. "Studying State Convergence of Input-to-State Stable Systems with Applications to Power System Analysis," Energies, MDPI, vol. 13(1), pages 1-24, December.
  • Handle: RePEc:gam:jeners:v:13:y:2019:i:1:p:92-:d:301283
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    References listed on IDEAS

    as
    1. Dongliang Zhang & Xiaoming Yuan, 2017. "Optimization of Active Current for Large-Scale Wind Turbines Integrated into Weak Grids for Power System Transient Stability Improvement," Energies, MDPI, vol. 10(8), pages 1-18, July.
    2. Boyu Qin & Haixiang Gao & Jin Ma & Wei Li & Albert Y. Zomaya, 2018. "An Input-to-State Stability-Based Load Restoration Approach for Isolated Power Systems," Energies, MDPI, vol. 11(3), pages 1-17, March.
    3. Ziquan Liu & Wei Yao & Jinyu Wen, 2017. "Enhancement of Power System Stability Using a Novel Power System Stabilizer with Large Critical Gain," Energies, MDPI, vol. 10(4), pages 1-15, April.
    4. Xingbao Ju & Ping Zhao & Haishun Sun & Wei Yao & Jinyu Wen, 2017. "Nonlinear Synergetic Governor Controllers for Steam Turbine Generators to Enhance Power System Stability," Energies, MDPI, vol. 10(8), pages 1-16, July.
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