An equivalent circuit model of a synchronous generator with diode-bridge rectifier and back-emf load is presented in this paper. The principle of harmonic balance is applied, which makes it possible to construct a state-space mathematical model for the system, The criterion of stability is obtained for the system under small disturbances. This stability criterion is more accurate than that presented in the existing literature. It is shown that the system's stability can effectively be improved by installing a short-circuited quadrature-axis winding on the machine rotor.