Reliable synchronous machine modeling is key to accurate power system planning, operation and post event analysis, especially in the emerging smart grids. In the literature, various models of a synchronous machine with different number of parameters have been used while little attention has been paid to the significance of each parameter in an originally nonlinear model. In this paper, first, a shrinkage and term selection method is extended to the identification of nonlinear systems. Then, the extended method is applied to the synchronous machine identification problem in order to determine which parameters have more substantial impacts on the machine response, i.e., the model parameters are partitioned into well and ill-conditioned sets. It is shown that the ill-conditioned parameters can be set to typical values to allow for significant improvements in the identifiability and speed of convergence of the estimated parameters without loosing the capability to characterize the system. As a result, the parameter estimation is done for a reduced-order optimization problem, which leads to a more reliable estimation with lower variances and faster convergence, especially in on-line measurements. The performance and effectiveness of the proposed nonlinear term selection method is demonstrated using numerical simulations and compared to the results of two existing approaches. (C) 2016 Elsevier Ltd. All rights reserved.