Since carbon emission allowances will be a limited public resource under the carbon peak and carbon neutrality targets, this paper focuses on the user-side to carry out the research of carbon reduction. Considering the differences in the development and resource statuses between regions, this paper applies the carbon flow theory based on the proportional sharing to measure the user-side carbon emissions. A non-convex mixed-integer nonlinear optimal power flow model based on the carbon flow theory and the user-side carbon emission allowances is established, where the power flow direction problem of the user-side carbon emission constraints is solved. Then, a particle swarm algorithm based on a power flow calculation update is used to solve the model. A case study illustrates that, introducing carbon allowances on the user-side can not only meet the user's carbon emission demand for electricity, bult also take into account the fairness principle of the emission reduction responsibility of the power sector in the dispatching. The proposed algorithm has a significant advantage in computational speed compared to the exact solution in the small-scale cases. In the large-scale cases, the proposed algorithm has a significant advantage in convergence compared with the common nonlinear programming solver. The problems of convergence and parameter tuning in the traditional particle swarm algorithm are solved.