This article proposes an improved continuation method to calculate the limit-induced bifurcation associated with the power flow equation due to the encounter with reactive power limits by generators. One of the distinguishing features is that the maximum loadability characteristics of limit-induced bifurcation are used for identification so that the computation efforts can be minimized. Another distinctive characteristic of the method is that, to ensure accuracy, the tangent vector of the continuation power flow equation at the reactive power limit encountering point is used to differentiate between limit-induced bifurcation and saddle-node bifurcation, as the latter also represents maximum loadability. The proposed method also adopts the conventional schemes of secant prediction, arc-length correction, and a new stepsize control, i.e., the convergence-dependent step-size control. Numerical results of the IEEE 118-bus system are used to illustrate the improvements of the proposed continuation method in comparison with the existing one.
In this paper, the reduction approach based on the center manifold theory for parameterdependent nonlinear dynamical systems is applied to simplify the analysis of the fold bifurcation relevant to voltage collapse in a simple electric power system. This technique enables us to obtain a lower-dimensional and topologically equivalent system in the neighborhood of the bifurcation value, which is a subset in the state-parameter space. Explicit formulas are presented for the computation of quadratic coefficients of the Taylor approximations to the center manifold for the fold bifurcation in parameter-dependent dynamical systems. It is demonstrated that it is the fold bifurcation but not other static bifurcations that occurs in the reduced power system, via validating the nondegenerate conditions for the fold bifurcation. The dynamics of the reduced system are visualized by two-and three-dimensional plots, which show that the reduction method is applicable and accurate to analyze local bifurcations in the power system. Furthermore, time domain simulation and modal analysis technique for linear systems are applied to distinguish the voltage stability from the rotor (angle) stability in the electric power system.
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