Determining Static Stability Boundaries Using A Non-Iterative Method

Static voltage and angle stability conditions (and saddle node bifurcations) are often associated with singularities of the power flow Jacobian matrix. This paper presents a new method based on singularity conditions written in Cartesian coordinates to determine static stability boundaries. The Cartesian coordinates instead of the traditional polar coordinates are used, allowing non-iterative locating saddle-node bifurcation points of the power flow problem. The singularity problem is formulated and then is easily reduced to a linear set of equations with respect to the real and imaginary components of nodal voltages. Because the linear problem can be singular in its turning point, singular value decomposition is used to find its solutions. The proposed method allows quick exploration of static stability boundaries in the state space, which is essential for developing real-time wide-area and local system security assessment applications. This paper demonstrates some very promising initial results of a pilot research using a 3-bus power system.