Identification of generic bifurcation and stability problems in power system differential-algebraic model

Based on the structurally represented power system differential-algebraic model and its Jacobian matrix. This paper develops a much more complete and systematic classification of the types of bifurcation and stability problem in the power system model. It is theoretically shown that bifurcations cannot occur due to the row dependence of the network Jacobian matrix (causality matrix) associated with the rows of the active and reactive power balance equations at a single bus or at a subset of buses, resulting in several of the classified bifurcations being nongeneric. The generic types of bifurcation and instability problems are then identified: static bifurcation dynamic bifurcation, loss of causality, and loss of single-machine stability; the later two are further shown to be very improbable. This paper also proposes an equivalent test for static bifurcation-static/algebraic bifurcation test whose advantages are disclosed. The identification of generic bifurcation and stability problems in power systems provides the foundation of the further study on static and dynamic voltage-angle stability problems