Dynamics of a minimal power system: invariant tori and quasi-periodic motions

The paper provides an extensive analysis of local and global bifurcation phenomena in the voltage-angle dynamic interactions of a minimal power system model. Using nonlinear analysis and normal form theory, it is proved that this system will experience quasi-periodic motions near certain degenerate local bifurcations which are explicitly characterized. The results in the paper provide strong analytical evidence for the possible occurrence of complicated behavior in the power system from the interactions of voltage and angle instability mechanisms. Computational methods for the detection of invariant 2-tori in higher dimensional systems using tools from center manifold theory and normal form theory are introduced briefly and these techniques are illustrated on a fourth order power system model.