On-line control of Hopf bifurcations in power systems

This paper discusses the on-line control of Hopf bifurcations in multiple-parameter space of loads in power systems. In power systems, the variation process of loads and the control decision-making process are at different time scales. The former is slowly, compared with the latter. So, in general, the loads should not change remarkably during the control decision-making process. Based on the above fact, this paper proposes an on-line method to control Hopf bifurcations in power systems. The method involves the process as follows. Firstly, monitor Hopf bifurcations by computing the eigenvalues of the Jacobian matrix of power systems at the current equilibrium point. If there is a pair of conjugate eigenvalues close to the imaginary axis, then use the pair of conjugate eigenvalues to compute the approximate normal vector to the Hopf bifurcation set. Finally, regulate control parameters to avoid a Hopf bifurcation in multi-machine power systems described by DAEs (differential algebraic equations). The validity of the method is demonstrated by regulating the reactive power loads in a 14-bus power system.