A generalized eigenvalue perturbation approach to coherency

It has long been recognized that the presence of weak interconnections between areas within an electric power system can give rise to low frequency, lightly damped modes representing undesirable electromechanical oscillations between generating units. To date, rigorous analyses of this phenomenon have relied primarily on singular perturbation perspectives, associating the weak interconnection with small parameters in a dynamic model. As an alternative, this paper presents a simple method for identifying slow modes based on first order sensitivities of generalized eigenvalues in a power system model composed of differential equations with algebraic constraints. By explicitly displaying (to first order approximation) the dependence of eigenstructure on line parameters and on the interconnection topology of the network, this approach provides a number of useful insights. In particular, it is used to develop an efficient new algorithm for partitioning a network into coherent areas (identifying both generator and load buses within an area).