The paper describes a new model reduction procedure tailored to power systems. It uses measurement data to devise a family of reduced order nonlinear models while retaining physical interpretability of parameters and equations. The manifold boundary approximation method (MBAM) uses the Fisher information matrix calculated from measurements to identify the least relevant parameter combination in the original model. Next, it numerically constructs a geodesic on the corresponding statistical manifold originating from the initial parameters in the least relevant parameter direction until a manifold boundary is found. MBAM then identifies a limiting approximation in the mathematical form of the model and removes one parameter combination. The simplified model is recalibrated by fitting its behavior to that of the original model, and the process is repeated as appropriate. MBAM is demonstrated on the example of a synchronous generator (SG), which has been treated extensively in the literature. Implications of the proposed model reduction procedure on large power system models are illustrated on a 441-bus, 72-SG dynamical model.