A Structural Stability Analysis of Voltage Collapse on Power Systems

Abstract

Voltage collapse has been associated with a bifurcation of both the load flow and the transient stability model. The bifurcation can occur when the jacobian of the model that describes the equilibrium is singular. Under certain specified conditions presented in the paper the bifurcation of the load flow model is associated with bifurcation of a subset of the transient stability model equations. The structural cause, of voltage collapse in a power system is shown to be the weak transmission boundaries that surround groups of buses called voltage control areas. An algorithm for determining voltage control areas is presented that guarantees there is a small eigenvalue associated with each voltage control area. The weakness of the boundary, measured by an eigenvalue estimate Λp of the small eigenvalue associated with each voltage control area, indicates the proximity to voltage collapse when there is no reactive generation reserve (no PV buses) in the voltage control area. The eigenvalue estimate Λp measures the reactive reserve on the voltage control area boundary, which is the only source of reactive power when all generation reactive reserve in the voltage control area is exhausted. The exhaustion of reactive transmission reserves on the voltage control area boundary (Λp approaches zero) following the exhaustion of reactive generation reserves is shown to result in possible voltage collapse due to bifurcation of both the transient stability and load flow model since Λp is an upper bound on the small eigenvalue associated with voltage control area p in both models.