Towards a theory of voltage collapse in electric power systems
Systems & Control Letters
Bifurcation analysis on a multimachine power system model
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Shifted-frequency analysis for EMTP simulation of power-system dynamics
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2009 IEEE custom integrated circuits conference
A smoothing SQP method for nonlinear programs with stability constraints arising from power systems
Computational Optimization and Applications
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This paper presents a comprehensive and detailed study of an optimization-based approach to identify and analyze saddle-node bifurcations (SNBs) and limit-induced bifurcations (LIBs) of a power system model, which are known to be directly associated with voltage stability problems in these systems. Theoretical studies are presented, formally demonstrating that solution points obtained from an optimization model, which is based on complementarity constraints used to properly represent generators' voltage controls, correspond to either SNB or LIB points of this model. These studies are accomplished by proving that optimality conditions of these solution points yield the transversality conditions of the corresponding bifurcation points. A simple but realistic test system is used to numerically illustrate the theoretical discussions.