Under the background of low-carbonization of distribution networks, an active distribution network expansion planning model that considers low-carbon and flexible loads is proposed. The objective is to provide the investment strategy with the minimum total cost under the premise of satisfying network operation constraints and CO2 emission limits. Decision variables include replacing overloaded lines, constructing new energy and energy storage devices,and constructing voltage control devices such as stabilizers and capacitor banks. The model proposes a polynomial form of voltage-related flexible load characteristics. To address the non-linear constraints in the flexible load model and network reconstruction constraints, the paper proposes a segmented McCormick envelope method and a virtual demand method to transform them into mixed-integer second-order cone optimization. Considering the uncertainty of new energy output,load, and energy prices, a two-stage stochastic optimization method based on scenario clustering is used for solving. The proposed model is tested on a 69-node system, and theions.