For a long time, the low-voltage distribution network has the problems of untimely management and complex and frequently changing lines, which makes the problem of missing grid topology information increasingly serious. This study proposes an automatic grid topology detection model based on lasso algorithm and t-distributed random neighbor embedding algorithm. The model identifies the household-variable relationship through the lasso algorithm, and then identifies the grid topology of the station area through the t-distributed random neighbor embedding algorithm model. The experimental results indicated that the lasso algorithm, the constant least squares algorithm and the ridge regression algorithm had accuracies of 0.88, 0.80, and 0.71 and loss function values of 0.14, 0.20, and 0.25 for dataset sizes up to 500. Comparing the time spent on identifying household changes in different regions, in Region 1, the training time for the Lasso algorithm, the Constant Least Squares algorithm, and the Ridge Regression algorithm is 2.8 s, 3.0 s, and 3.1 s, respectively. The training time in region 2 is 2.4s, 3.6s, and 3.4s, respectively. The training time in region 3 is 7.7 s, 1.9 s, and 2.8 s, respectively. The training time in region 4 is 3.1 s, 3.6 s, and 3.3 s, respectively. The findings demonstrate that the suggested algorithmic model performs better than the other and can identify the structure of LV distribution networks.