To address the computational errors and infeasibility caused by non-convex constraint relaxations in distribution network optimization

this paper proposes a sequential modified second-order cone (SMSOC) optimization method to enhance both accuracy and efficiency under distributed generation penetration. The proposed method transforms the non-convex problem into a bilevel programming structure and employs the S-procedure and Schur complement to construct a strong duality gap condition between the primal and dual problems. This mechanism iteratively corrects relaxation errors and ensures convergence to the Karush- Kuhn-Tucker (KKT) point of the original problem. The effectiveness of the method is verified using two case studies: a reactive power optimization model and a photovoltaic carrying capacity assessment model. Numerical results demonstrate that the SMSOC method achieves a convergence precision of 1×10-6 and reduces computation time by 1.5’4.7 times compared with existing algorithms. The results indicate that the proposed method reduces convex relaxation errors while maintaining high computational efficiency

providing a practical and accurate tool for large-scale distribution network optimization.