1. A computer-based method for improving 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; estimating a contingency eigenvalue for the contingency using the eigenvalues and eigenvectors of the nominal matrix; performing a time-domain simulation on the contingency if a contingency stability value is greater than a pre-determined threshold value; adjusting a plurality of generation sources or loads or both in the electrical power transmission system based on the results of the time-domain simulation for improving the oscillatory stability; wherein estimating the contingency eigenvalue comprises using a first-order approximation of a Taylor series expansion when a faster computation is required and using a second-order approximation of a Taylor series expansion when higher accuracy is required; and wherein when the first-order approximation is used, the contingency eigenvalue is given by λ i ⁡ ( post ) 1 ⁢ ⁢ st ≈ λ i + ψ i ⁢ Δ ⁢ ⁢ A sys ⁢ ϕ i ψ i ⁢ ϕ i where λ i(post) 1st is the contingency eigenvalue, λ i , ϕ i , and ψ i are the eigenvalue, right eigenvector, and left eigenvector, respectively, corresponding to mode i and A sys is the nominal matrix.