Deals with the problem of identification of the network parameters and the desired equilibrium in applications of excitation control for synchronous generators. Our main contribution is the construction of a new nonlinear identifier that provides asymptotically consistent estimates (with guaranteed transient bounds) of the line impedance and the equilibrium for the classical three-dimensional flux-decay model of a single generator connected to an infinite bus. The behavior of the scheme is illustrated in two simulated case studies with the interconnection and damping assignment passivity-based controller previously proposed by the authors.