This thesis proposes the unified margin boundary tracing framework and its application to Saddle node and Hopf bifurcations. Note that Hopf bifurcation is detected with computationally efficient method without eigenvalue calculation; Voltage stability is also addressed from the viewpoint of optimization. Margin control optimization with continuation optimal power flow is proposed; From the perspective of time domain, local parameterization based time domain simulation is proposed to study dynamic voltage stability. Unified algorithm is presented that could be applied in both multi-time scale and quasi-steady state (QSS) time domain simulation to avoid numerical difficulty. All numerical results are demonstrated with New England 39 bus system.