New Recursive Formulas for Eigenvalue Sensitivity Analysis

Eigenvalue sensitivity analysis represents a key discipline in many engineering system applications where the dynamic behavior of such systems is closely related to the eigenvalues of the system (state) matrix. Currently available eigenvalue sensitivity evaluation methods are based on a general form of the system matrix derivatives with respect to the sensitivity parameter of interest. In many engineering systems, however, the structure of the system matrix is such that its derivatives with respect to practical system parameters constitute special rank-one forms. This paper presents a novel application of a compact matrix exchange formula to the eigenvalue sensitivity problem, which includes rank-one derivative matrices, leading to very fast recursive sensitivity formulas with substantial savings in computation time and memory requirements. With such recursive formulas, the evaluation of higher-order eigenvalue sensitivities is therefore attainable using previously calculated lower-order sensitivities. An illustrative application to power system dynamic stability analysis is presented in which the new eigenvalue sensitivity formulas were successfully used to estimate the effect of parameter changes on the dynamic system modes