An efficient method to compute singularity induced bifurcations of decoupled parameter-dependent differential-algebraic power system model

In this paper, we present an efficient method to compute singular points and singularity induced bifurcation points of differential-algebraic equations (DAEs) for a multi-machine power system model. The algebraic part of the DAEs brings singularity issues into dynamic stability assessment of power systems. Roughly speaking, the singular points are points that satisfy the algebraic equations, but at which the vector field is not defined. In terms of power system dynamics, around singular points, the generator angles (the natural states variables) are not defined as a graph of the load bus variables (the algebraic variables). Thus, the causal requirement of the DAE model breaks down and it cannot predict system behavior. Singular points constitute important organizing elements of power system DAE models. This paper proposes an iterative method to compute singular points at any given parameter value. Generator angles are parameterized through a scalar parameter in the constraint manifold and identification of singular points is formulated as a bifurcation problem of the algebraic part of the DAEs. Singular points are determined using a second order Newton-Raphson method. Moreover, the decoupled structure of the DAE model is exploited to find new set of parameters and parameter increase pattern which will result in a set of equilibria including singularity induced bifurcations. The simulation results are presented for a 5-bus power system and singular and singularity induced bifurcation points are depicted together with equilibria to visualize static and dynamic stability limits.