Structural bifurcation tests for voltage collapse and low-frequency oscillation in multimachine power systems

This dissertation systematically develops a fairly complete differential-algebraic power system model, classifies the bifurcation and stability problems, establishes necessary conditions for each bifurcation and stability problem, and identifies the generic types of bifurcation associated with steady state angle stability, voltage instability, and low frequency oscillation. The three generic types of bifurcation in the differential-algebraic power system model are shown to be: (1) Static/Algebraic Bifurcation due to the singularity of the equivalent static/algebraic Jacobian matrix; (2) Static Bifurcation and (3) Dynamic Bifurcation due to the equivalent system Jacobian matrix having eigenvalues with zero real parts. The prerequisite for the static/algebraic bifurcation test is the single machine stability; the one for the static and dynamic bifurcation tests is the causality condition. These two special stability problems are shown to be improbable in a practical sense.; The static/algebraic and static bifurcations are shown to be equivalent under the assumption that single machine stability and causality condition hold. Voltage-angle bifurcation in the load flow model is shown to be an excellent approximation to the static/algebraic bifurcation. This dissertation suggests utilizing the static/algebraic bifurcation test rather than the static bifurcation test since the static/algebraic bifurcation test avoids inverting causality matrix, and can be performed by slightly modifying the load flow program. Both analytical and simulation results for the load flow bifurcation test and the static/algebraic bifurcation test illustrate the important role of maintaining the reactive generation reserves at generators in preventing voltage collapse and steady state stability.; Three types of static/dynamic bifurcation are identified and necessary conditions for each are established; in mechanical dynamics, in flux decay dynamics, and in both mechanical and flux decay dynamics. Experimental results indicate that tests for various types of static/dynamic bifurcation actually classify the type of bifurcation. Such identification is shown to be more precise than eigenvalue analysis. It is expected that the structurally represented test conditions for various types of static/dynamic bifurcation will be useful in establishing the factors of these bifurcations. The proposed approach provides a basis for static/dynamic point of collapse/oscillation method to detect the unstable modes.