Abstract
This study presents a study of bifurcation in a dynamic power system model. It becomes one of the major precautions for electricity suppliers and these systems must maintain a steady state in the neighborhood of the operating points. We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from a subcritical or supercritical Hopf bifurcation by computing the first Lyapunov coefficient. The MATCONT package of MATLAB was used for this study and detailed numerical simulations presented to illustrate the types of dynamic behavior. Results have proved the analyses for the model exhibit dynamical bifurcations, including Hopf bifurcations, Limit point bifurcations, Zero Hopf bifurcations and Bagdanov-taknes bifurcations.
Highlights
Voltage control and stability problems in the transient regimes are becoming one of the most important issues in the power system due the intensive use of the transmission network (Avalos et al, 2009; Echavarren et al, 2009)
We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from a subcritical or supercritical Hopf bifurcation by computing the first Lyapunov coefficient
Power-voltage curve provides very important information for voltage stability analysis (Kumkratug, 2012), the importance appear in the results found when we analyse the continuation in Hopf, limit point and zero Hopf bifurcation point
Summary
Voltage control and stability problems in the transient regimes are becoming one of the most important issues in the power system due the intensive use of the transmission network (Avalos et al, 2009; Echavarren et al, 2009). Voltage stability is defined by the capacity of the power system to maintain acceptable voltages at all nodes in the system under normal condition and after being subject to a disturbance (Abro and Mohamad-Saleh, 2012; Subramani et al, 2012). The dynamic of this power system are generally described by the following Ordinary Differential Equations (ODE) Equation (1): xɺ = f(x, α) (1). The continuation method demonstrated the limit point bifurcations characterized by its period and Normal form coefficient. The Hopf Bifurcation generates a limit cycles which are stable if it is supercritical or unstable if it is subcritical, the limit cycle is asymptotically stable if all other Floquet multipliers lay within the unit circle.
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