Under the background of the "Carbon Peak and Carbon Neutrality" goals

the integration of carbon emission flow with the optimal operation of distribution networks is a key research focus. Based on this

this paper proposes an optimal operation model for distribution networks based on the carbon emission flow calculation method for lossy networks.Firstly

a network equivalence method for lossy networks using complex power is proposed

and the updated system power flow is utilized to calculate the new nodal carbon potential.Secondly

an optimal dispatch model for distribution networks based on second-order cone power flow programming is established

incorporating a demand response model. This model guides electricity users to adjust their consumption behavior during peak hours or system emergencies

enabling flexible load regulation.Thirdly

the model is constructed with the objectives of minimizing the total operating cost and carbon emissions of the distribution network.Finally

the feasibility of the carbon emission flow calculation method is verified using a two-machine four-node system

and simulation analysis is conducted on the modified 33-node system

and three comparative scenarios are provided to analyze the algorithm effectiveness.The experimental results demonstrate that the proposed carbon emission flow calculation method can improve the accuracy of carbon flow

and the proposed model can effectively reduce carbon emissions and operating costs while ensuring computational efficiency

showing promising application prospects.