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This manuscript combines the recently developed nonlinear moment-matching (NLMM) technique with dynamic mode decomposition (DMD) to obtain a simulation-free reduction framework for power systems. Unlike the conventional model reduction methods for power systems, where the external area is linearized, we consider the nonlinear effective network (EN) and the synchronous motor (SM) power grid models. First, the reduced system is constructed from the solution of the underlying approximate Sylvester equation by exciting the system with user-defined inputs from a representative exogenous system. Then, a non-intrusive reduction is performed using DMD to approximate the nonlinear function via Koopman modes in an equation-free manner. The advantage is that a "simulation-free" nonlinear model order reduction framework is obtained to approximate the response of the large-scale power grid models. Finally, we substantiate our observations using numerical simulations of reduced EN and SM models of the IEEE 118 and IEEE 300 bus systems for realistic fault scenarios. Results show that the overall CPU times of the reduced-order models are lowered to half as compared to the original models while maintaining the fidelity. The results are also compared with POD-DEIM for reference. • The study presents the dimensionality reduction of large-scale power system models. • The intrusive MOR is achieved using approximated nonlinear moment-matching technique. • DMD is used to obtain a low-rank approximation of the underlying nonlinear function. • The overall combination yields an efficient reduction framework for power grids. • Results show considerable savings in the CPU times of the ROMs thus obtained. [ABSTRACT FROM AUTHOR]