This chapter introduces the hyperbolic power flow approximation for monopolar DC networks, a novel approach designed to address the inherent nonlinearity in power flow equations. The methodology involves applying Taylor’s series expansion to the hyperbolic relationship between voltages and powers in the power equilibrium constraint, enabling the transformation of the original non-convex problem into a simplified and computationally tractable form. By leveraging a first-order Taylor series expansion, the power-voltage relation is approximated with sufficient accuracy for initial calculations. To mitigate the approximation errors introduced by the first-order expansion, a recursive solution framework is employed, iteratively refining the results to ensure convergence toward a highly accurate solution. The proposed hyperbolic approximation offers significant advantages, including reduced computational complexity and enhanced numerical stability, making it particularly suitable for large-scale network analysis. The recursive process systematically improves the quality of the solution, reducing the mismatch between the approximated and true power flow equations. To validate the effectiveness and robustness of this approach, a numerical case study is conducted using Julia, a high-performance programming language well suited for mathematical modeling and optimization. The results of the case study highlight the ability of the hyperbolic approximation to achieve accurate and efficient solutions for optimal power flow (OPF) problems in monopolar DC networks, demonstrating its potential for real-world applications in modern power systems.