How it works
Four bus types: slack (reference) bus fixes |V| and δ = 0°; PV (generator) bus specifies P and |V|; PQ (load) bus specifies P and Q — the unknowns being |V| and δ. Gauss-Seidel iterates Vi(k+1) = (1/Yii)[Pi − jQi)/Vi*(k) − ΣYij Vj(k)]; converges in 20–50 iterations for well-conditioned networks but slowly for large systems. Newton-Raphson forms the Jacobian matrix of mismatch equations ΔP/Δδ and ΔQ/Δ|V| and converges quadratically — typically in 3–5 iterations regardless of system size.
Key points to remember
Convergence criterion: mismatch |ΔP| and |ΔQ| at all buses must fall below typically 0.0001 pu. Fast Decoupled Load Flow (FDLF) separates P-δ and Q-V equations because ∂P/∂|V| ≈ 0 and ∂Q/∂δ ≈ 0 in power systems, halving the matrix size. Y-bus is sparse (mostly zeros) for real power networks and is built from line admittances; diagonal Yii = sum of all admittances connected to bus i; off-diagonal Yij = −yij. FDLF uses constant B' and B' matrices, making each iteration cheap — suitable for real-time security assessment.
Exam tip
Every Anna University load flow question asks you to perform two iterations of Gauss-Seidel for a 3-bus system — set up the Y-bus from the line data, write the GS equation for each PQ bus, and substitute numerical values carefully for each iteration.