Oscillation accidents emerge in power systems integrated with increasing penetration of renewable energy sources. The impedance of electromagnetic dynamics is investigated in recent years, where the mechanical dynamics are neglected. So far, the low-frequency oscillations are not well addressed with the impedance analysis method. A novel analytical impedance is formulated and implemented for wind energy conversion system consisting of wind turbine generators (WTGs) and wind farm, which fills the gap in the mechanical dynamics of the impedance. Instead of assuming constant values, the electromechanical dynamics of the rotor speed and the pitch angle are involved in the WTG impedance. Besides, the impedance framework is generally and modularly designed and is adaptive to different operating regions. With the developed analytical impedance, the stability assessment can cover the low-frequency oscillations, providing an in-depth insight into the mechanical parameters influencing the small-signal stability performance. As an application, the impedance characteristic and stability performance of systems with active power reserve for grid supporting are analyzed and optimized. Furthermore, the shafting torsional vibrations of WTGs in wind farms are analyzed with modal decomposition and the low-frequency impedance model. The improved accuracy of the developed analytical impedance is illustrated by comparison with commonly used impedance, which ignores the coupling between the electrical and mechanical dynamics. It is proven that the mechanical dynamics have a significant influence on the impedance, particularly in the low-frequency range. Experimental validation is carried out to validate the low-frequency impedance model and the stability performance.