The present paper introduces a novel method for identifying voltage sags in time-variant power distribution networks, effectively addressing the challenges arising from the temporal variability of network topology and data. The proposed method is founded on the concept of inheritance, which is bifurcated into breadth and depth inheritance strategies. The breadth inheritance strategy employs transfer learning to manage topological temporality, utilizing the Euclidean distance between samples to ascertain the sequence of sample migration, and implements multitask learning to share feature representations across different tasks. The depth inheritance strategy, on the other hand, utilizes incremental learning to handle data temporality, building upon the initial model parameters to learn new sample features, which in turn reduces the time required for model updates and enhances the accuracy of target tasks. Case study findings validate the suitability of the proposed methods for reconstructing fault identification models in scenarios characterized by topological temporal variability and for rapidly updating fault identification models in scenarios with data temporal variability. The approach presented herein holds significant implications for the enhancement of power supply reliability and the adaptability of electrical grids.