QUANTIFICATION OF NONLINEAR MODAL INTERACTIONS USING MODAL SIGNAL ENERGIES

Increased system stress has brought about the need for a better unders tanding of nonlinearities in power system dynamic behavior. The relati onship between system stress and the nonlinearity of the differential equations should be quantified. The similarity transformation used to determine the Jordan canonical form of a linear system provides a view of the system in a 'modal' state space where the linear parts are dec oupled and easily accounted for. The nonlinear system can also be tran sformed to the modal state space using the linear variable transformat ion. In the transformed state space the effects of nonlinearities and linearities are clearly separated and are expressed in terms of their effects on the system modes. Thus the nonlinear interactions between t he modes are viewed directly. The effects of the nonlinearities on the modes are measured by considering the signal energy associated with t he nonlinearities in the Jordan-form state space. The concept of nonli near signal energy provides a numerical value to gauge the influence o f nonlinearities on a given mode. Application to the IEEE 50-generator test system shows the relationship between interarea modes and nonlin ear interactions between low- and high-frequency modes. (C) 1996 Elsev ier Science S.A.