THE STUDY OF THE AUTONOMOUS SYNCHRONOUS GENERATOR MODES

The importance of the problem of the static stability of the stationary mode of the power system for its operation is extremely high. The investigation of the static stability of the power system is a subject of a number of works, but the problems of static stability of the stationary points of an autonomous synchronous generator are given little attention. The article considers transient and resonant (stationary) modes of the generator under active-inductive and active-capacitive loads. Mathematical model of transients in a natural form and in the coordinate system d, q are plotted. It is discovered that the mathematical model of the transition process of an autonomous synchronous generator is identical to the mathematical model of the transition process of the synchronous machine under three-phase short circuit. Electromagnetic transients of an autonomous synchronous generator are described by a system of linear autonomous differential equations with constant coefficients. However, the equivalent circuit of a generator contains dependent sources. We investigated the stability of stationary motion of an autonomous synchronous generator at a given angular velocity of rotation of the rotor. The condition for the existence and stability of stationary points of an autonomous synchronous generator is derived. The condition for the existence of stationary points of such a generator does not depend on the active load resistance and stator windings, and inductance of the rotor. The determining of stationary points of the generator is reduced to finding roots of a polynomial of the fourth degree. The graphs of electromagnetic torque dependencies on the angular velocity of rotation of the rotor (mechanical characteristics) are plotted. The equivalent circuits, corresponding to the equations of the transition process of an autonomous synchronous generator, are featured as well.