This thesis presents a thorough analysis of saddle-node bifurcations for power system dynamic models, including a third order representation of high voltage direct current (HVDC) transmission, classic ac generator dynamics with reactive flows, and voltage and frequency dependent load models. Extensions of the Point of Collapse and Continuation methods, initially used in ac system voltage stability studies, are applied to the determination of these bifurcation points. These methods are compared and used for calculating bus voltage profiles ( "nose" curves) and collapse points on ac/dc systems of up to 2158 buses, considering a variety of operational limits and controls, namely, ac/dc regulating transformer tap limits, voltage and reactive power limits, and area interchange control. AC generator reactive power limits, HVDC firing angle limits and voltage dependent current order limits (VDCOL) are shown to affect the stability and loadability of these systems.

A vector Lyapunov function approach is employed to define a system wide energy function that can be used for stability analysis. This thesis describes the derivation of individual component Lyapunov functions for simplified models of HVDC links connected to “infinitely strong” ac systems, along with a standard ac Lyapunov function. Then, a novel method is proposed for obtaining the weighting coefficients that link both energy components into the overall system energy function. Practical solutions devised to improve stability predictions obtained from energy function analyses are presented and discussed. The use of the new energy function for transient stability and voltage collapse analyses is illustrated in systems of up to 121 ac buses with multiple HVDC links.