Possibility of Auto- & Hetero-Parametric Resonances in Power Systems and Their Relationship with Long-Term Dynamics

The possibility of parametric resonance due to the nonlinearity of swing equation of electric power systems is described, starting with Mathieu-type equation. The resonance presented here is classified into (i) heteroparametric resonance which is caused by periodic disturbances, e.g. sinusoidal load variations, and (ii) autoparametric resonance (internal resonance) which is the interference among some dominant modes in transient state. The occurrence conditions and Equation of Envelope which govern the aspect of the resonance are presented using the method of multiple scales, and then confirmed by simulations. From the parametric resonance viewpoints, unstable phenomena of long-term dynamics with poor damping are also reviewed with nonlinear analysis and simulations.