Nonlinear static and dynamical aspects of power systems: a bifurcation approach

The author presents basic concepts in bifurcation theory which can be applied to study the voltage stability and nonlinear oscillations of power system networks. Dynamical systems are considered with one parameter. Changing the parameter may drive the system from one asymptotic behavior to another and result in different bifurcations. Typical static bifurcations are (i) saddle-node or fold bifurcation, (ii) transcritical bifurcation, and the( iii) pitchfork bifurcation. A typical dynamic bifurcation is the Hopf bifurcation. Numerical identification of these bifurcations is considered from a power system network point of view