A method for evaluating the performance of PSS with saturated input

In this paper, we report upon a method for estimating an ellipsoid, which resides entirely in the stability region of a linear system with saturation nonlinearities. To reduce the conservatism in the estimation, a procedure to transform the estimation problem into a simple convex optimization with linear matrix inequality (LMI) constraints is presented. As an application of this development, a method is introduced to estimate the stability region of a multi-machine power system with power system stabilizers (PSS) subject to saturated feedback. The idea is to check if the system state after a disturbance resides inside the estimated stability region. Thereby a sufficient condition is derived to conclude the effectiveness of saturated PSS controls. Numerical results of a test power system with three generators and five buses are described, indicating the reliability and simplicity of this approach.