Among a wide variety of topics that are covered by Dynamic Security Assessment (DSA), maintaining synchronous operation and acceptable voltage profiles stand out. These two stability categories are mostly jeopardized in the seconds after a large contingency occurs. Therefore, this thesis tackles the two aspects of large disturbance stability of power systems in the short-term time scale. The classical DSA methods deal with the short-term loss of synchronism by analyzing one operating point and one contingency at a time. However, a small change in operating point may turn a stable system unstable. The first part of the thesis overcomes this gap by proposing the idea of parametrizing the stability boundary. The newly introduced method constructs the parametrized security boundaries in polynomial forms based on a reduced amount of Time Domain Simulation (TDS) data. Such a method retains the positive traits of TDS while being able to estimate a measure of stability even for those points that do not belong to the “training" set. The polynomial coefficients are further improved via SIME parametrization that has a physical meaning. Finally, when being subject to a constraint by the means of Quadratic Programming (QP), SIME parametrization also becomes competitive with direct methods in the sense of conservativeness. Nevertheless, if TDS fails, any TDS-based DSA approach is useless. Most often, the dynamics of the non-linear power system is described by the set of Differential Algebraic Equations (DAE). TDS can face problems when the DAE model experiences singularity due to the loss of voltage causality. This thesis introduces Voltage Impasse Region (V IR) as the state-space area where the voltage causality is lost due to the non-linear modeling of static loads. The entrance of a dynamic trajectory to a V IR was shown to be accompanied by non-convergence issues in TDS and significant voltage drops. Appropriate Voltage Collapse Indicators (VCIs) are also derived for each load model of interest. The thesis concluded that V IR is a structural problem of the DAE model that should always be accounted for when the short-term stability is assessed.