Under the “dual-carbon” goal, a low-carbon economic optimization method for distribution networks based on “source-grid-load-storage” coordinated control is proposed. First, a model is developed with the objective of minimizing the comprehensive costs of the distribution network, considering factors such as wind and solar curtailment costs, flexible load and energy storage dispatch costs, and carbon emission costs. Second, second-order cone relaxation technology is employed to transform the problem into a mixed integer convex programming model for improving computational efficiency. Then, a modified IEEE 33-bus system is used to demonstrate the superiority of the proposed method in reducing both economic costs and carbon emissions. Finally, a sensitivity analysis is conducted on the different carbon reduction measures in the coordinated optimization of “source-grid-load-storage”. Based on this, the trade-off between coordinated low-carbon economic operation and traditional economic operation is explored, identifying similarities and differences between the two approaches under various environmental conditions.