Topology identification (TI) is an essential problem in the distribution network due to exponentially growing power grid size in recent years. In this study, it is reformulated as a regularised alternating convex optimisation problem. Then an application based on the current injection model is proposed. Compared to the traditional algorithm optimising l1‐norm, which may lead to overfitting, a new l2‐norm minimisation problem with l1‐norm regularisation is proposed to solve the trade‐off problem with non‐convex constraints. The proposed method reduces the size of the training data set compared with the traditional TI method. Simulation results show that the recovery performance of the proposed algorithm is superior to the traditional one in additive white Gaussian noise scenario. [ABSTRACT FROM AUTHOR]