A numerical study of the effect of degenerate Hopf bifurcations on the voltage stability in power systems

• A numerical study is presented to assess how the voltage stability of a power system is affected by the presence of codimension-2 degenerate Hopf bifurcations.
• The effect of degenerate Hopf bifurcations and the StatCom on the topological structure of a feasibility region associated with the voltage stability problem is analyzed through a multiparameter bifurcation analysis.
• The application of a StatCom is proposed to eliminate sustained voltage oscillations and the appearance of degenerate Hopf bifurcations.

Bifurcation theory has been employed to qualitatively explain the mechanisms of voltage stability problems occurring in electric power systems by relating the voltage collapse and voltage oscillatory problems to the appearance of saddle node and Hopf bifurcations, respectively. The results obtained by bifurcation analysis have revealed the existence of degenerate Hopf bifurcations when two parameters of the system are varied simultaneously; however, the mechanisms of voltage stability problems when the system is operating near these kinds of bifurcations have not yet been investigated. Bearing this in mind, the main scope of this paper is to assess how the voltage stability of a power system is affected by the presence of codimension-2 degenerate Hopf bifurcations. From the multiparameter bifurcation analysis, the existence of degenerate Hopf bifurcation points are identified and a trajectory stability diagram is then computed for classifying the type of degenerate Hopf bifurcations. This classification is used for establishing the voltage dynamics’ behavior when the power system is operating near these bifurcations. Finally, the application of a StatCom is proposed to eliminate sustained voltage oscillations and the appearance of degenerate Hopf bifurcations.