Stability area of a synchronous generator nonlinear model with multiparametric excitation controller

Abstract

We take as the research object the well-known system of nonlinear differential and functional equations that describes a synchronous generator. PIDD2-control was carried out through the excitation block. Effective values of the steady state in relative units and the preliminary settings of suboptimal controllers were obtained earlier using a linearized model. Disturbing surges (spikes and slump) in bus voltages were modeled as line impedance changes. The system stabilization was studied at various surges values and controller parameters by means series of numerical experiments; the calculations were carried out by the methods of Runge-Kutta and Dorman-Prince. The main attention was paid to various transient types, both stabilizing and diverging, as well as a configuration of the stability region boundary in the controller parameters of and a surge magnitude; the paper presents the results for the proportional control parameter are as the most informative. We've identified five types of transients and several important features of the model's behavior near the stabilization area boundary. Thus, the nonlinear model turned out to be unstable to small and stable to bigger perturbations in the unstable area of its linearization. The steady-state oscillations at the boundary have a lower amplitude with increasing of an initial perturbation, etc.