Power-flow (load-flow) analysis solves the nonlinear algebraic relationship between complex power injections and voltage magnitude/angle at every bus of a network, derived from the bus admittance matrix relation between injected currents and bus voltages; because loads are uncontrolled disturbance variables and generation is control-adjustable, one generator bus (the slack/swing bus) must absorb unknown system losses by having its voltage magnitude and angle fixed rather than its power. The Gauss-Seidel method solves this nonlinear system iteratively, starting from a flat voltage guess and repeatedly updating each unknown bus voltage using the latest available values (including already-updated values within the same iteration) until successive iterates converge within a tolerance; solving the resulting linear systems (as in the related Newton-Raphson approach) can alternatively be done directly via Gauss elimination and back-substitution rather than by matrix inversion. This is core theory within power system analysis, specifically network/load-flow modeling in electrical power engineering.
Power-flow (load-flow) analysis solves the nonlinear algebraic relationship between complex power injections and voltage magnitude/angle at every bus of a network, derived from the bus admittance mat…