Efficient Power Flow Solution in Monopolar DC Networks Using a Derivative-Free Steffensen Method

This paper proposes and evaluates advanced solution techniques for nonlinear power flow analysis in monopolar low-voltage DC networks. The key contribution is the systematic comparison between the classical Newton-Raphson method and a derivative-free multivariable Steffensen method, demonstrating that the latter offers a practical alternative with superlinear convergence, reduced computational complexity, and simpler implementation. Numerical simulations on benchmark 33-bus and 69-bus systems show that both methods converge rapidly within fewer than six iterations, with Steffensen’s method maintaining competitive solution times and accuracy while significantly lowering the effort needed for Jacobian evaluations. The findings confirm that the Steffensen method is highly suitable for real-time, large-scale power system analysis, especially where derivative calculations are expensive or unreliable. Overall, the results endorse the Steffensen approach as a robust, efficient, and scalable solution method for modern DC power systems, paving the way for improved operational reliability and integration of renewable energy sources.