Basin delimitation and stability assessment for power systems in the projective space

This paper presents a method for determining the global basin boundary of the power systems. To show the general outline of the basin, the power system is shrink to the projective space. First, a new vector field is induced according to Poincare's method. After the transformation, the structural stability of the system remains the same. The singularities at infinity are obtained by the proposed shrinking-projection method. The boundary of the basin which is extended to the infinity are complemented by the singularities at infinity in the projective space. The stability of the power system is then evaluated based on the distribution of the singularities at infinity. Finally, the proposed method is applied to the power system with perturbations to study the characteristic of the stochastic basin boundary. The validity of the proposed method is demonstrated on a 9-bus, 11-bus and 68-bus test system.