A bilinear analysis technique for detection and quantification of nonlinear modal interaction in power systems

In this paper, a general nonlinear analysis framework is presented for treating nonlinear interactions between system modes. The method is based on Carleman linearization and can be used to study nonlinear behavior and mode coupling directly in physical coordinates. An efficient algorithm for finding low-order analytical approximations to system behavior around an equilibrium condition is proposed. The method improves the usual linearization of the system about an equilibrium point and allows to identify nonlinear characteristics using standard linear analysis techniques. Based on explicit forms of analytical solutions, simplified expressions are derived that allows us to compute the strength of nonlinear behavior in both, the time and frequency domains. Techniques are also suggested to quantify the magnitude and distribution of nonlinear intermode coupling. A detailed case study on a four-machine two-area test system is presented to illustrate the proposed technique