Abstract
A Lyapunov function is presented for a one-machine, infinite-bus system schematized by means of a seventh-order dynamic model. This model takes into account five state variables describing the synchronous machine (namely: the rotor angle, the electric speed, the field flux, and the direct and quadrature axis damping fluxes), and two additional variables referring to a first-order linear speed governor and to an equivalent first-order voltage regulator, respectively. A synthetic and closed-form condition for ‘stability in the small’ is derived which extends the well known condition applicable to a second-order machine model. Also, a closed form condition for ‘stability in the large’ is derived, which may be regarded as representing the generalization of the condition expressed by the classical equal-areas criterion. Because of the direct method of accounting for the effects of the damper winding fluxes, the results represent significant progress on previous work reported in the literature.
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