Study on prediction-correction homotopy method of tracking Hopf bifurcation point

A new method named prediction-correction homotopy method is proposed to calculate Hopf bifurcation points associated with the parameter dependent differential algebraic equations (DAE) which are used to model power systems dynamics. It uses the secant prediction method to track the Hopf bifurcation homotopy path. Compared with the tangent prediction method, the computation load is much less because it is not related to the matrix inversion computation. At the same time, the automatic step-size control strategy ensures the calculation accuracy and speed to effectively implement the step-by-step correction. Finally, it is proved that this algorithm can be used accurately and effectively through WSCC 3-machine 9-bus system and NewEngland 39-bus system.