A b s t r a c t -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. I. I N T R O D U C T I O NModern power grid:; are becoming more and more stressed with the load demands increasing rapidly. The voltage collapses which occurred recently have again drawn much attention to the issue of stability security margins in power systems [I]. The small signal stability margins are highly dependent upon such system factors as load flow feasibility boundaries, minimum and maximum damping conditions, saddle node and Hopf bifurcations, etc. Unfortunately, it is very difficult to say in advance which of these factors will make a decisive contribution to instability. Despite the progress achieved recently, the existing approaches deal with these factors independently -see [a], [3] for example, and additional attempts are needed to get a more comprehensive view on small-signal stability problem.To study the power system small signal stability problem, an appropriate model for the machine and load dy- (differential) variables, x~ is the vector of algebraic variables, y is the vector of specified system parameters, and T is a parameter chosen for bifurcation analysis. In many cases y is a function of T.In the small signal stability analysis, the set (1) is then linearized at an equilibrium point to get the system Jacobian and state matrix. The structure of the system Jacobian J is shown in Fig. 1 The problem addressed here is that these different small signal stability conditions correspond to different physical phenomena and mathematical descriptions [13]. Saddle node bifurcations happen where the state matrix J" = J 1 1 -JlzJ,-,lJzl becomes singular and, for example, a static (aperiodic) type of voltage collapse or angle instability may be observed as a result. Hopf bifurcations occur when the system state iiiatrix J has a pair of conjugate eigenvalues passing the imaginary axis while the other eigenvalues have negative real parts, and the unstable oscillatory behavior may be seen. Singularity induced bifurcations are caused by singularity of t...

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