Nonlinear H∞ control of a third-order synchronous generator model

The objective of this paper is to design a group of nonlinear H
_∞
controllers for a third-order model of a synchronous generator to attenuate external disturbance. It is supposed that an unknown mechanical perturbation is added to the nominal mechanical power so that drives the power system to an unknown equilibrium point. We will obtain the Hamilton-Jacobi-Isaacs (HJI) inequality related to disturbance attenuation problem of synchronous generator. For this system, HJI inequality is a complex problem to solve and direct solution is hardly reachable as a result, Taylor series approach will be used to solve HJI inequality until fourth order. It will be shown that in addition to stabilization of the system in vicinity of equilibrium point, the controllers also significantly diminish the effect of perturbation and in a limited time drive the states to their nominal values. Simulation results demonstrate the effectiveness and robustness of the nonlinear H
_∞
controllers.