This chapter introduces a recursive optimal power flow (OPF) formulation tailored for monopolar DC networks. The methodology leverages an innovative conic relaxation approach to accurately model constant power loads. Specifically, these loads are represented using an auxiliary variable that captures the expected demanded current, enabling its relationship with voltages and powers to be expressed through a convex conic formulation. To address the inherent nonlinearity between power and voltage at the generation nodes, an iterative relaxation mechanism is employed. At each iteration t, the expected voltage value is updated and used as a reference to compute the next voltage profile by solving an equivalent conic approximation of the OPF model. This recursive process systematically reduces or eliminates the approximation error introduced by the initial voltage assumptions, ensuring convergence to a near-optimal solution. The proposed methodology is particularly advantageous for improving computational efficiency and scalability in the analysis of DC networks, where conventional methods struggle to balance accuracy and tractability. To validate the efficacy and robustness of the proposed approach, a numerical case study is implemented using Julia, a high-performance programming language ideal for mathematical optimization. Results from the case study highlight the model’s ability to achieve precise OPF solutions while maintaining computational efficiency, underscoring its potential for real-world applications in DC power systems. This chapter contributes to the growing body of research on conic optimization techniques in power systems, providing a promising framework for addressing the challenges of OPF in DC networks with constant power loads.