This study introduces a comparative analysis of the Newton-Raphson and quasi-Newton techniques for addressing the power flow problem in monopolar DC distribution networks within a quasi-dynamic framework. The proposed approach is tailored for simulations with a time resolution of one minute, facilitating real-time or large-scale system assessments. Two variants of the Newton-Raphson method, differing in their Jacobian structures, are evaluated alongside three quasi-Newton algorithms employing constant Jacobian approximations. Validation is performed on the DC equivalents of test systems comprising 33 and 69 nodes, considering performance metrics such as convergence speed, computational efficiency, and precision in power losses estimation. The results indicate that, while Newton-Raphson methods tend to converge in fewer iterations, quasi-newton approaches—especially those using fixed Jacobian matrices—achieve reduced computation times, demonstrating their suitability for fast, quasi-dynamic power system analysis.