Abstract The proposed method enables the modeling and integration of synchronous machinery models in accurate and efficient simulation of power systems over diverse time scales that cover electromagnetic and electromechanical transients. The underlying models make use of frequency-adaptive simulation of transients (FAST) where analytic signals are used since they lend themselves to the shifting of the Fourier spectra. The shift frequency appears as a simulation parameter in addition to the time step size. When setting the shift to the common carrier frequency of either 50 or 60 Hz, the method emulates phasor-based simulation that is very suitable for extracting envelope information at relatively large time step sizes. At zero shifting, instantaneous values are being tracked. It is shown how this shifting plays a critical role in integrating synchronous machine models that are represented using the Park transformation with the network model. In a further step, it is illustrated how the modeling approach is modified if the Park transformation is not applied. For illustrative purposes, the integration is first validated for a single-machine-infinite-bus system. In a following multi-machine test case involving four machines in two areas, the added value of the proposed methodology becomes clear as both electromagnetic transients and electromechanical transients are emulated accurately and efficiently within one simulation run.