Bifurcation analysis is a very useful tool for power system stability assessment. In this paper, detailed investigation of power system bifurcation behaviour is presented. One and two parameter bifurcation analysis are conducted on a 3-bus power system. We also examined the impact of FACTS devices on power system stability through Hopf bifurcation analysis by taking static Var compensator (SVC) as an example. A simplified first-order model of the SVC device is included in the 3-bus sample system. Real and reactive powers are used as bifurcation parameter in the analysis to compare the system oscillatory properties with and without SVC. The simulation results indicate that the linearized system model with SVC enlarge the voltage stability boundary by moving Hopf bifurcation point to higher level of loading conditions. The installation of SVC increases the dynamic stability range of the system, however complicates the Hopf bifurcation behavior of the system. (6 pages)