Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This manuscript presents a novel approach utilizing computational graph strategies for solving the power flow equations through the synergistic use of Newton-Raphson (NR) and Gradient Descent (GD). As a foundational element for operational and strategic decision-making in electrical networks, the power flow analysis has been rigorously examined for decades. Conventional solution techniques typically depend on second-order processes, which may falter, especially when faced with subpar starting values or during heightened system demands. These issues are becoming more acute with the dynamic shifts in generation and consumption patterns within modern electrical systems. Our research introduces a dual-mode algorithm that amalgamates the principles of first-order operation. This inventive method is adept at circumventing potential local minima traps that hinder current methodologies, thereby reinforcing the dependability of power flow solutions. We substantiate the effectiveness of our advanced algorithm with comprehensive testing on established IEEE benchmark systems. Our findings reveal that our approach not only expedites the convergence process but also ensures consistent performance across diverse system states, signifying a meaningful progression in the realm of power flow computation.