Comparison of load flow techniques

The main load flow techniques are Gauss-Seidel (G-S), Newton-Raphson (N-R) and the decoupled / fast decoupled load flow (FDLF). All solve the same non-linear power-balance equations by iteration.

Gauss-Seidel

• Updates one bus voltage at a time: $V_i = \frac{1}{Y_{ii}}\left[\frac{P_i - jQ_i}{V_i^{*}} - \sum_{k\ne i}Y_{ik}V_k\right]$.
• Merits: simple to program, little memory, short time per iteration.
• Demerits: linear convergence; the number of iterations grows with system size; may fail with heavy load, negative reactance or a poorly chosen slack bus; needs an acceleration factor (about 1.6).
• Use: small systems and teaching.

Newton-Raphson

• Solves $[\Delta P;\ \Delta Q] = [J][\Delta\delta;\ \Delta|V|]$ in each iteration.
• Merits: quadratic convergence (3 to 5 iterations for any size); reliable; accurate.
• Demerits: Jacobian must be formed and solved every iteration; more memory and time per iteration; harder to program.
• Use: large systems, accurate planning studies, optimal power flow.

Fast decoupled

• Uses $R \ll X$ and small angle differences: $\Delta P/|V| = -B'\Delta\delta$, $\Delta Q/|V| = -B''\Delta|V|$ with constant $B'$, $B''$.
• Merits: much faster per iteration than N-R; constant matrices factorised once; needs less memory than N-R.
• Demerits: less accurate model, so more iterations; poor convergence for high R/X ratio (distribution feeders).
• Use: on-line studies, contingency analysis.

Comparison

Limitation common to all: the solution is only as good as the data, and all need suitable starting values (flat start) and care with generator Q-limits.