After a short-circuit fault occurs at a certain location in the power system, the system voltage undergoes a dynamic process characterized by an initial drop and subsequent recovery. During the fault duration, induction motor loads experience a voltage decrease, causing the electromagnetic torque to fall below the mechanical torque, resulting in a decrease in motor speed. Following fault clearance, these induction motors absorb a significant amount of reactive power, hindering the rapid restoration of system voltage to pre-fault levels. This paper presents a multi-stage voltage calculation method for grid faults, taking into account low voltage ride-through of wind turbines and the dynamic characteristics of induction motors. The proposed method enables the swift computation of multi-stage voltages after system faults, facilitating an assessment of the impact of faults on the voltage of new energy systems with a high proportion of motor loads, and it provides insight into the spatial distribution characteristics of fault voltages.