Abstract: In the context of low-carbon distribution network, this paper proposes a mixed-integer second-order cone programming model for active distribution networks considering carbon emissions and flexible loads, with the investment strategy with minimum total cost. Considering the uncertainty of renewable energy, load and energy price, a scenario clustering method based on K-means is proposed. The decision variables of the model are the replacement of overloaded lines, the construction of new energy and energy storage devices, and the construction of voltage control equipment such as voltage regulators and capacitor banks. The polynomial voltage-dependent flexible loads, network reconfiguration and carbon emission constraints are considered. Aiming at the non-convex nonlinear characteristics of the planning model, the virtual demand method is used to model the network reconstruction as a mixed integer linear programming form, and an improved second-order cone relaxation method based on Taylor expansion is proposed to solve the problem of traditional second-order cone relaxation caused by flexible load model. The model is tested with a 69-node system, and the results show that the proposed model not only has a lower overall planning cost, but also helps reduce carbon emissions.