A Hopf bifurcation in the steam electrical power plant

Electrical turbogenerators have complex nonlinear dynamics. So, many different behaviors are seen in the power systems. A common accident that occurs in many of power systems in the instability due to large suddenly disturbances. In these cases, more effective countermeasures that the linear continuous supplementary stability control must be taken immediately to balance the mechanical power input and the electrical power output and to maintain the system stability. In this paper, we relate an instability occurrence in an electrical turbogenerator to a subcritical unstable Hopf bifurcation. This is for the first time that the above mentioned phenomenon are analyzed based on the Hopf theorem and the instability is justified. Existance and stability type of the Hope bifurcation are proved and some numerical and simulation results are included.