To address the challenges of complex topology identification in low-voltage distribution networks and low recognition accuracy caused by missing statistical data, a topology identification method based on longest common subsequence-dynamic time warping(LCSS-DTW) was proposed. In low-voltage distribution networks, users on the same voltage phase exhibit similar voltage fluctuations. Based on this characteristic, a distance matrix between users was calculated. The method combines the local alignment capability of LCSS with the global alignment of DTW to better capture the similarity of users' time-series voltage data and ensure data completeness. A clustering algorithm was used to identify the phase association of users in the distribution network. Random missing data and abnormal data interference were introduced for validation. The results show that the proposed method exhibits strong robustness. Under different missing data and interference conditions, the recognition accuracy remains above 95%, which is significantly higher than that of traditional methods. The method effectively reduces the impact of data loss on topology identification accuracy.