Identification of the functional relationship between singularity induced bifurcation points and load change

This paper presents preliminary results in the identification of algebraic singularities of power system models. A differential-algebraic (DAE) model is used to represent the dynamic behavior of the system. The DAE model of the power systems may exhibit different bifurcations such as saddle node, Hopf and singularity induced bifurcations. Singularity induced bifurcation indicates the existence of singular points where the Jacobian matrix of the load flow equations becomes singular. This paper investigates the singular points and their behaviors through time domain simulation analysis. A variant of the 4^th and 5^th Order Runga-Kutta-Fehlberg method adapted for the DAE model is used to watch trajectories of the system when state variables are perturbed from their equilibrium values. The convergence properties of the trajectories help approximately identify singular points at a given parameter value. Simulation results are presented for a 3-bus power system