A One-Machine-to-Quasi4nfinite-Bus (OMQIB) power system, which can be interpreted as Duffing's equation from the viewpoint of oscillation, has revealed that it may suffer the instability (the "Jump phenomena") due to the ill-combination of the system parameters. We investigate the stability problem of this kind of power system via the catastrophe theory approach. Discussions are given on the effects of the specifc combination of system parameters to make the resonance curve triplevalued and on the identified bifurcation set which can be used to assess the system stability.
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