Incorporating Voltage-Controlled Nodes Into the Matrix-Based Successive Power Flow Method

This paper presents a novel matrix-based successive approximations method for power flow analysis in electrical power systems. Building upon the classical Gauss-Seidel approach, the proposed technique employs a structured linear algebra framework to enhance convergence speed and computational efficiency, especially in modern grids featuring renewable energy sources and complex interconnections. The approach combines the simplicity of the Gauss-Seidel method for voltage-controlled nodes with a matrix-reformulated iterative process for load nodes, resulting in faster and highly accurate solutions. Validation on benchmark systems, including a 6-bus network and the IEEE-WSCC 9-bus system, demonstrates reduced iteration counts and computation times while maintaining precise voltage profiles and power losses estimates. These findings position the method as a promising tool for real-time power system analysis and control, supporting the stability and reliability of increasingly complex and renewable-rich grids. Future research should explore scaling, integration with optimization algorithms, and robustness under various operating scenarios.