The SVD of system matrices and modal properties in a two-area system

In this paper we present results of a comparison of participation factors with a new method that uses the singular value decomposition (SVD) of complex matrices which are functions of the state matrix A, the input matrix B, the output matrix C and the eigenvalues as measures of modal controllability and observability. The agreement between the two approaches is remarkable. We also give some results about the conditioning of single eigenvalues and eigenvectors and apply them to the same system mentioned above. We find that in some region in the parameter space the eigenvalues corresponding to the area modes approach each other coalescing into a double eigenvalue. At this point and in a region surrounding it in the parameter space the eigenvalues and the eigenvectors become very ill-conditioned rendering the information obtained from the eigenvectors meaningless.