The grid‐connected dual‐PWM adjustable speed drives (ASDs) modulate the energy of the motor torque oscillation and inject it into the power system, potentially causing low‐frequency oscillation (LFO) in the grid. In this study, considering the motor torque oscillation and harmonic common‐modulation of the both‐side converters, the precise sequence impedance models are derived for dual‐PWM ASDs using the harmonic linearisation method. Based on the derived impedance of dual‐PWM ASD, the torque oscillation, which is equivalent to the time‐varying impedance, causes a series of discontinuities at the torque‐oscillation‐related frequencies on its amplitude‐frequency curve. Moreover, these discontinuous drops make it more likely to intersect with the amplitude‐frequency curve of the grid impedance, which may lead to LFO of the grid. Then, by applying the proposed impedance model and Bode plot, the stability of the grid‐ASD cascade system with motor torque oscillation is assessed. The conclusions of stability analysis demonstrate the exact mechanism that the mechanical system oscillations lead to the grid‐converter cascade system instability through the common‐modulation and coupling of the dual‐PWM ASD. Finally, experimental results on a 3 kW ASD system in the laboratory and measured results on the distribution grid in the Shanghai Yangshan Deepwater Port area verify the correctness and effectiveness of the proposed model and stability assessment.