“…The significance of the bifurcations theory in stability analysis was identified in the 1980's [14]; it is showed the presence of chaotic motions in the two-degree freedom swing equations. Subsequent applications of this theory have been directed to the following studies such as voltage collapse [15], sub synchronous resonance [16], Ferro resonance oscillations [17], chaotic oscillations [18], and design of nonlinear controllers [19]. Furthermore, this theory has been applied to assess the dynamical behavior of nonlinear components such as induction motors [20], load models [21,22], and tap changing transformers [23], power system stabilizers [24] and static VAR compensators [24,25].…”