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This chapter presents a second-order cone programming (SOCP) approximation for solving the optimal power flow (OPF) problem in monopolar DC networks. The proposed approach transforms the original non-convex problem into a convex formulation by leveraging the properties of second-order cones, enabling efficient and scalable optimization. The methodology is validated using numerical simulations implemented in Julia, employing the JuMP package and solvers such as Ipopt and Gurobi. The results demonstrate that the SOCP model closely approximates the exact OPF solution, with minimal error differences. Additionally, the impact of the solver choice on accuracy and computational efficiency is analyzed, highlighting the robustness of the proposed method in power flow optimization. The findings confirm that SOCP provides an effective and computationally efficient alternative for OPF analysis in DC networks.

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Third Conic Approximation

  • 章节

  • 发表日期：

    2026年

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  • Oscar Danilo Montoya Giraldo,
  • Walter Julián Gil-González,
  • Alejandro Garcés Ruiz

摘要

This chapter presents a second-order cone programming (SOCP) approximation for solving the optimal power flow (OPF) problem in monopolar DC networks. The proposed approach transforms the original non-convex problem into a convex formulation by leveraging the properties of second-order cones, enabling efficient and scalable optimization. The methodology is validated using numerical simulations implemented in Julia, employing the JuMP package and solvers such as Ipopt and Gurobi. The results demonstrate that the SOCP model closely approximates the exact OPF solution, with minimal error differences. Additionally, the impact of the solver choice on accuracy and computational efficiency is analyzed, highlighting the robustness of the proposed method in power flow optimization. The findings confirm that SOCP provides an effective and computationally efficient alternative for OPF analysis in DC networks.