Power-flow (load-flow) solution methods solve the nonlinear algebraic relationship between bus power injections and complex bus voltages in an electrical network; the Gauss-Seidel method iterates a fixed-point update using the most recently computed voltage values (optionally accelerated by a scalar factor), while the Newton-Raphson method linearizes the nonlinear power-balance equations via a first-order Taylor expansion around a current estimate, expressed through a Jacobian matrix, and iteratively solves the resulting linear system for a state-vector correction. Because Newton-Raphson converges in a nearly constant number of iterations independent of system size (unlike Gauss-Seidel, whose iteration count grows with system size), it is preferred for large systems, and its linear correction step is efficiently solved by Gauss elimination (LU-style triangularization and back-substitution) rather than by explicit matrix inversion, which is computationally prohibitive for large sparse systems. This belongs to power system analysis, specifically numerical methods for power-flow computation, and relates to the broader discipline of numerical linear algebra and iterative nonlinear equation solving.
Power-flow (load-flow) solution methods solve the nonlinear algebraic relationship between bus power injections and complex bus voltages in an electrical network; the Gauss-Seidel method iterates a f…