Common types of voltage sags include three-phase sags, two-phase sags and single-phase sags, which have different degrees of harm to variable-frequency drives (VFDs). Accordingly, it is necessary to study the unified specifications for the tolerance characteristics of VFDs under different types of sags. This paper presented universal tolerance curve envelopes of VFDs under different types of sags by theoretical analysis, simulation and experiments. Firstly, the influence mechanism of different types of sags on VFDs was analyzed, which was verified by simulation carried out in MATLAB/Simulink later. Then a test platform was built to test 8 VFDs of 7 representative brands and 2 kinds of power (7.5 kW and 18.5 kW). The results of experiments, theoretical analysis and simulation were verified by each other, and their conclusions are basically consistent. Finally, the universal tolerance curve envelopes of VFDs under different types of sags in the rated torque and speed were obtained by dealing with the results from experiments in some way, which have practical application value and can provide efficient reference for the standard of tolerance curve for VFDs to be formulated.