Voltage collapse ia a loss of stability in large scale electric power systems which causes blackout when voltages decrease catastrophically. Explanations of voltage collapse involving various subsystems (generators, transformers, loads is unknown). The main purpose of the research is to determine which subsystems and parameters are primarily responsible for voltage collapse so that a simple power system model capturing the main causes of voltage collapse may be developed. Such a model would form the basis for the scientific understanding and prevention of voltage collapse. Voltage collapse is generally associated with bifurcation of the nonlinear power system equations; that is, the disappearance as parameters vary of the stable equilibrium at which the power system is normally operated. The goal of the proposed research is to determine how the subsystems and parameters contribute to the bifurcation (and hence the voltage collapse) by studying the geometry of the bifurcation and reducing the condition for bifurcation to a simpler form. Other parameterised nonlinear systems lose stability in a similar way and most of the techniques developed will apply generally.