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The reclosing action of the distribution network may cause multi-stage voltage sag in the grid nodes, which leads to more serious losses for sensitive users. In order to more reasonably characterize the disturbance degree of multi-stage voltage sag on sensitive equipment, a frequency evaluation method based on process immune time (PIT) and improved analytic hierarchy process is proposed. Firstly, multi-stage voltage sag waveforms caused by the reclosing corresponding action under transient fault and permanent fault are analyzed, and the PIT characteristic curve of sensitive equipment under multi-stage voltage sag is characterized. Secondly, the weight function method is used to calculate the influence degree of each stage sag. The analytic hierarchy process is improved by utilizing the correlation and influence degree of each stage sag. The weight of each stage sag is determined, and then the amplitude of the multi-stage voltage sag is calculated equivalently. The multi-stage voltage sag frequency evaluation method is proposed in the distribution network. Finally, the IEEE 30-bus system is used for simulation verification. The results show that the proposed method is more accurate and reasonable for the evaluation of multi-stage voltage sag frequency. This method provides a basis for the frequency evaluation and governance of multi-stage voltage sag. [ABSTRACT FROM AUTHOR]