On the correctness of the approximate investigation of synchronous machine rotor swinging : PMM vol. 37, n6, 1973, pp. 1007–1014

We consider the complete system of equations for the dynamics of a synchronous machine with two windings on the rotor. We indicate the conditions under which the original system of equations can be reduced to the equation of motion of the rotor. The conditions for rotor selfoscillations to arise are determined as a result of investigating this equation. The complete system of equations for the dynamics of a synchronous machine containing equations describing the electrical responses and equations for the rotor's mechanical motion are obtained in 1]. Transient responses in electric circuits were investigated next, as was the expression for the electromechanical moment under a constant rotation velocity of a rotor with one circuit, e. g., field winding. However, in many of the later works the electrical equations were used only for finding the electromechanical moment under a constant spin rate of the rotor, and the problem was then reduced to the study of the equation for the rotor's mechanical motion 2, 3]. Here the conditions for which such an analysis is admissible were not mentioned. It was established that the swinging of a synchronous machine's rotor can be revealed in the form of selfoscillations. Vlasov 4] has investigated the equation of motion of a rotor and, under the assumption of a small parameter in the first derivative term, has found the conditions for the excitation of selfoscillations. Investigation in this same direction was carried out in 5]. However, in the investigation of the selfoscillations Vlasov did not examine the responses in the electrical circuits, while the expression for the electromechanical moment was obtained from power considerations. Other works have used particular expressions for the electromechanical moment, which can not explain the selfoscillation phenomenon.