1. A computer-based method for contingency analysis of oscillatory stability in an electrical power transmission system, said method using at least one processor, said method comprising: receiving, by the at least one processor, a plurality of component inputs from a plurality of system components within the electrical power transmission system; generating a nominal matrix for the electrical power transmission system, wherein the nominal matrix includes a set of equations at least partially modeling the electrical power transmission system; calculating eigenvalues and eigenvectors of the nominal matrix; identifying a contingency representing a postulated disturbance of the electrical power transmission system; and estimating a contingency eigenvalue for the contingency using the eigenvalues and eigenvectors of the nominal matrix.