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A new procedure to determine the stability of a steady-state solution based on a sequential continuation scheme, Floquet theory and the limit cycle method is presented in this paper. The continuation scheme relies on an efficient predictor-corrector scheme, where the correction is accomplished through the limit cycle method. Furthermore, a comprehensive variable frequency transformer (VFT) Park model is proposed to study the stability of asynchronous links. The VFT Park allows the simulation of multiunit VFTs operated in parallel in order to increase the power transfer between two electric power networks. Each VFT unit consists of a wound-rotor asynchronous machine, a dc motor, and a control system, which provides power transfer regulation using power and speed controllers. The steady-state operating point of a VFT Park consisting of three 100-MW VFT units is computed with the limit cycle method for a set of heterogeneous operating scenarios. Stability diagrams are reported for changes of the VFT parameters, power transfer, and frequency on both sides of the asynchronous link. Even though the VFT is operated within its rated power transfer limits, simulation results reveal that a VFT may become unstable not only for changes of power transfer but also for variations of frequency.