How does convergence of G-S compare with N-R?

G-S is linear and slow, N-R is quadratic and fast

G-S is quadratic, N-R is linear

How does the number of iterations vary with system size?

G-S grows with size; N-R is nearly independent of size

N-R grows with size; G-S is independent

Which assumptions are made in decoupled load flow?

X/R is high and angle differences are small, so J2 and J3 are about zero

R >> X and large angle differences

2082 Baishakh · 4+2 marks

G-S vs N-R and decoupled assumptions

Short answer

G-S uses iterative substitution one bus at a time, linear convergence, many iterations. N-R uses Jacobian and Taylor series, quadratic convergence, few iterations, better for large systems. Decoupled load flow assumptions: X>>R, small angle differences, so P-δ and Q-|V| problems can be solved separately.

How G-S method is different from N-R method for the load flow analysis? Write down the assumptions are to be made for decoupled load flow analysis.

Difference between G-S and N-R methods

Point	Gauss–Seidel	Newton–Raphson
Principle	Iterative substitution, one bus at a time	Taylor series linearisation using Jacobian
Variables	Complex voltages (rectangular)	$\lvert V\rvert$ and $\delta$ (polar)
Convergence	Linear, slow	Quadratic, fast
Iterations	Many; grow with system size	3–5; nearly independent of size
Time per iteration	Small	Large (Jacobian formed and solved)
Memory	Low	Higher
Acceleration factor	Needed	Not needed
Reliability	May diverge in ill-conditioned systems	Reliable
Suitable for	Small systems	Large systems

Assumptions for decoupled load flow

Transmission lines have high X/R ratio, so $G_{ik} \ll B_{ik}$ .
Voltage angle differences between connected buses are small: $\sin(\delta_i - \delta_k) \approx 0$ , $\cos(\delta_i - \delta_k) \approx 1$ .
Hence $\partial P/\partial|V| \approx 0$ and $\partial Q/\partial\delta \approx 0$ , so the P–δ and Q–V problems are solved separately: $\Delta P = J_1\Delta\delta$ , $\Delta Q = J_4\Delta|V|$ .

✓ Answer checked by Claude Sonnet 5.5

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