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Dynamical Behavior and Singularities of a Single-machine Infinite-bus Power System

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Abstract

This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at P Tc = 3.4382, SIB at P T0 = 2.8653 and HB at P Th = 2.802 for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as P T is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.

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Authors and Affiliations

  1. Department of Mathematics & LIMB of the Ministry of Education, Beijing University of Aeronaut and Astronaut, Beijing, 100083, China

    Jin-liang Wang

  2. Department of Electrical Engineering, Tsinghua University, Beijing, 100084, China

    Sheng-wei Mei & Qiang Lu

  3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, Hong Kong

    Teo Kok-lay

Authors
  1. Jin-liang Wang
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  2. Sheng-wei Mei
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  3. Qiang Lu
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  4. Teo Kok-lay
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Corresponding author

Correspondence to Jin-liang Wang.

Additional information

Supported by the National Natural Science Fundation of China (No.50377018) and a research grant from Research Office of the Hong Kong Polytechnic University(G.63.37.T494).

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Wang, Jl., Mei, Sw., Lu, Q. et al. Dynamical Behavior and Singularities of a Single-machine Infinite-bus Power System. Acta Mathematicae Applicatae Sinica, English Series 20, 457–476 (2004). https://doi.org/10.1007/s10255-004-0184-9

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  • DOI: https://doi.org/10.1007/s10255-004-0184-9

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