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This paper presents a mathematical dynamic model of single-phase four-quadrant (4Q) converters employed at the input stage onboard high-speed trains. A new stability analysis capable of considering the time-variant nature of the system for the correct tuning of the feedback proportional-integral (PI) controller has been implemented. In particular, the innovation regards the application of a current-controlled modulation technique instead of the traditional PWM control currently used in high power traction converters. A dedicated model of a real converter installed onboard Italian high-speed trains has also been implemented in order to simulate its behavior and validate the theoretical analysis. Finally, a scaled-down prototype has been developed.