As more and more DGs are built and connected to the DN, the DN exhibits a notable degree of stochasticity and volatility. This stochasticity and volatility can result in an imbalance of active power in real-time, which may ultimately lead to a collapse of the DN. Therefore, in order to achieve a balance between carbon emissions and economic efficiency, this study introduces a strategy aimed at enhancing the PBC of the DN by employing a collaborative optimization approach involving DG, FL, and ES. The main contribution of this paper is to find a methodology for the co-optimization of DG, FL, and ES, which optimizes the PBC of the DN and the absorption rate of DG to the best conditions. Firstly, a model of DG-FL uncertainty in multiple scenarios is developed, and typical operational scenarios are extracted by effectively quantifying the DG-FL uncertainty of the distribution network. Secondly, a quantitative evaluation method for the balance degree of DG-FL based on IET is proposed. Finally, a two-stage optimization model for DG-FL-ES collaboration is established. The scientific rigor and practical applicability of the proposed method for improving the PBC and facilitating the integration of renewable energy sources are demonstrated through a case study of the power grid in a specific region of Zhejiang Province. The results demonstrate that the method proposed in this paper can enhance the BDODF by 43.44 % and achieve a 100 % absorption rate of renewable energy.