---
title: "Comparison of G-S and N-R load flow"
subject: "Power System Analysis II"
chapter: 2
key: "semester_5/power_system_analysis_ii:gs-vs-nr-comparison"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/gs-vs-nr-comparison
site: BCT Engineering
---

# Comparison of G-S and N-R load flow

Power System Analysis II · Chapter 2: Load Flow Analysis

- Asked in: 2078 Kartik, 4 marks; 2075 Asoj, 4 marks; 2071 Shrawan, 8 marks (asked 3 times)
- Video: [Comparison between GS and NR Method - Load Flow Studies - Power System 3](https://www.youtube.com/watch?v=1d_tI1Tx-B8) — Ekeeda
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/gs-vs-nr-comparison
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-2

## Question

Make a comparison between Gauss-Seidel method and Newton-Raphson method of load flow analysis. Mention the advantages and disadvantages of N-R method over G-S method.

## Short answer

Gauss-Seidel updates voltages sequentially with linear convergence; Newton-Raphson solves linearised equations with quadratic convergence. N-R advantages: fast convergence (3-5 iterations independent of size), reliable for large/ill-conditioned systems, no acceleration factor, Jacobian reusable. Disadvantages: complex programming, higher per-iteration computation and memory.

## Answer

Both Gauss–Seidel (G-S) and Newton–Raphson (N-R) solve the nonlinear power-flow equations iteratively. G-S updates one bus voltage at a time using $Y_{bus}$; N-R linearises all power equations together using the Jacobian matrix.

#### Comparison
| Point | Gauss–Seidel | Newton–Raphson |
|---|---|---|
| Basis | Fixed-point iteration $V_i = f(V)$ | Taylor series, linearised with Jacobian |
| Coordinates | Rectangular (complex voltages) | Usually polar ($\lvert V\rvert$, $\delta$) |
| Convergence | Linear, slow | Quadratic, fast |
| Iterations | Many (increase with system size; ~n) | Few (3–5), almost independent of size |
| Time per iteration | Very small | Large (forming and solving Jacobian) |
| Memory | Small (only $Y_{bus}$) | Larger (Jacobian, sparse techniques) |
| Acceleration factor | Needed (α ≈ 1.4–1.6) | Not needed |
| Effect of slack bus choice | Affects convergence | Hardly affects |
| Reliability | May fail for ill-conditioned systems, negative reactances, long/short line mix | Reliable for large and ill-conditioned systems |
| Programming | Simple | More complex |
| Suited for | Small systems | Large systems, OPF, contingency studies |

#### Advantages of N-R over G-S
1. Quadratic convergence: a highly accurate solution in 3–5 iterations.
2. Number of iterations does not grow with system size, so it is faster overall for large systems.
3. More reliable; converges where G-S diverges (heavy loading, series capacitors, high R/X).
4. Not sensitive to the choice of slack bus; no acceleration factor needed.
5. The Jacobian can be reused for sensitivity analysis, contingency studies and optimal power flow.

#### Disadvantages of N-R compared with G-S
1. Programming logic is more complex.
2. Each iteration takes longer, since the Jacobian is recalculated and a linear system solved.
3. Needs more memory (reduced by sparsity techniques and decoupled versions).
4. Needs a reasonably good initial guess (flat start usually works); a poor start may diverge.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Newton-Raphson convergence is:
   A. Linear
   B. Quadratic
   C. Slower than G-S
   D. Independent of initial guess
   Answer: B. N-R has quadratic convergence, needing few iterations. (Key point: Convergence rate)

2. As system size increases, the number of N-R iterations:
   A. Grows roughly with n
   B. Is almost independent of size
   C. Doubles
   D. Falls to one
   Answer: B. N-R needs 3-5 iterations regardless; G-S grows with size. (Key point: Iterations vs size)

3. A disadvantage of N-R is:
   A. Needs an acceleration factor
   B. Each iteration is longer due to Jacobian formation
   C. Cannot handle large systems
   D. Fails for heavy loading
   Answer: B. The Jacobian must be recalculated and a linear system solved each iteration. (Key point: N-R disadvantage)

4. Which method uses an acceleration factor about 1.4-1.6?
   A. N-R
   B. Gauss-Seidel
   C. Both
   D. Neither
   Answer: B. G-S uses acceleration; N-R does not need it. (Key point: Acceleration)

## Related in Power System Analysis II

- [Comparison of load flow techniques](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aload-flow-techniques-comparison) — Power System Analysis II, chapter 2
- [Bus classification in load flow](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Abus-types-specified-quantities) — Power System Analysis II, chapter 2, asked 2×
- [Need for load flow; NR and decoupled equations](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aload-flow-need-nr-decoupled) — Power System Analysis II, chapter 2
- [Significance of load flow techniques](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aload-flow-techniques-significance) — Power System Analysis II, chapter 2
- [Decoupled load flow assumptions and algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adecoupled-assumptions-algorithm) — Power System Analysis II, chapter 2, asked 2×
- [N-R load flow corrections and algorithm](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Anr-load-flow-derivation) — Power System Analysis II, chapter 2, asked 2×

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