This paper presents a new general method for computing the different specific power system small signal stability conditions. The conditions include the points of minimum and maximum damping of oscillations, saddle node and Hopf bifurcations, and load flow feasibility boundaries. All these characteristic points are located by optimizing an eigenvalue objective function along the rays specified in the space of system parameters. The set of constraints consists of the load flow equations, and requirements applied to the dynamic state matrix eigenvalues and eigenvectors. Solutions of the optimization problem correspond to specific points of interest mentioned above. So, the proposed general method gives a comprehensive characterization of the power system small signal stability properties. The specific point obtained depends upon the initial guess of variables and numerical methods used to solve the constrained optimization problem. The technique is tested by analyzing the small signal stability properties for well-known example systems.

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