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Electromagnetic Transients Program (EMTP) is widely used in power system dynamics studies. However, in most cases EMTP is found inadequate for dealing with the realistic size power systems due to the small time step resulting in relatively slow simulation speeds. To accelerate the EMTP simulations of power system dynamics, a novel frequency-adaptive methodology is proposed. In this method, a new transformation is presented. The properties of the transformation and the numerical solutions based on the transformation are discussed. The component models obtained by discretizing the differential equations at the branch level are also given which are convenient for EMTP implementation. The proposed method allows using large time steps without sacrificing accuracy, which greatly improves the simulation speed. To validate the proposed methodology, a general program has been developed. Furthermore, various case studies substantiate the claims and demonstrate the application of the method.