On Efficient Methods for Detecting Hopf Bifurcation With Applications to Power System Instability Prediction

Abstract

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse or instability point) is one of the key problems in power system operations and planning such an index indicates the severity of a power system with regard to voltage collapse or instability. While much work has been done on the former problem, the latter problem poses a more severe challenge both to the engineering and mathematical communities. This paper first presents a review of the main methods for detecting Hopf bifurcation in the general field of bifurcation theory and then attempts to generalize the previously studied fold detection and index methods to the Hopf case. The proposed Hopf test functions should be of wide interest while the proposed test function based index method gives an indication of the distance of the current operating point from the Hopf instability. Promising numerical results have been obtained using some standard dynamical test systems.

Bifurcation tracking by Harmonic Balance Method for performance tuning of nonlinear dynamical systems

“…These minimally extended systems are implemented in MATCONT [8] software. A comprehensive review of the methods suitable for detecting bifurcations can be found in [19] while in [42] authors focus on Hopf bifurcations.…”

Development of an efficient bifurcation tracking method

“…Both of these direct methods use an iterative solver and as such need an accurate initial value. This involves finding an initial guess to the critical eigenvalue, which can be difficult as usually the evolution of eigenvalues with a parameter is not linear [10]. We compute an initial guess for the direct bifurcation methods by employing a continuation method until a bifurcation has been detected.…”

Multivariable Adaptive Hybrid Control Model for Interconnected Power Systems at the Inception of Voltage Collapse

“…A general voltage collapse graph and decreases the interconnected power system security margin is shown in figure 1. Switching of shunt capacitors as load increases can have the tendency to rise to voltage and increase the amount of power that can be transmitted (Hussein and Chen 2003 ;Niglye et al 2006). Voltage collapse was identified and analyzed for simple power systems in the first half of this century.…”