Application of the ACT5S Numerical Method for Solving Power Flow Equations in DC Monopolar Systems

This paper presents an advanced numerical approach for solving the direct-current (DC) power flow equations in distribution networks, which leverages the high-order ACT5S iterative method. The unique nonlinear formulations of the DC power flow problem are outlined, and their Jacobian structures are derived to facilitate the development of efficient solution strategies. The proposed methodology integrates the ACT5S scheme, known for its fifth-order convergence, to improve convergence speed and robustness when compared to the traditional Newton-Raphson method. Extensive numerical tests on the 33-bus and 69-bus systems demonstrate that the ACT5S method significantly reduces the number of iterations required, with comparable computation times and high solution accuracy. The results highlight the potential of high-order iterative algorithms for reliable and efficient power flow analysis in modern DC distribution networks, which is increasingly critical in applications involving renewable energy, energy storage, and electrification initiatives.