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

# G-S vs N-R and decoupled assumptions

Power System Analysis II · Chapter 2: Load Flow Analysis

- Asked in: 2082 Baishakh, 4+2 marks
- Video: [Comparison of GS, NR and FDLF Methods](https://www.youtube.com/watch?v=JgZME8MjMmk) — Basic Electrical
- 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-decoupled-assumptions
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-2

## Question

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.

## 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.

## Answer

#### 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
1. Transmission lines have high X/R ratio, so $G_{ik} \ll B_{ik}$.
2. Voltage angle differences between connected buses are small: $\sin(\delta_i - \delta_k) \approx 0$, $\cos(\delta_i - \delta_k) \approx 1$.
3. 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: $\Delta P = J_1\Delta\delta$, $\Delta Q = J_4\Delta|V|$.

## Check yourself

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

1. How does convergence of G-S compare with N-R?
   A. G-S is quadratic, N-R is linear
   B. G-S is linear and slow, N-R is quadratic and fast
   C. Both are quadratic
   D. Both are linear
   Answer: B. G-S converges linearly with many iterations; N-R converges quadratically in 3-5 iterations. (Key point: Convergence comparison)

2. How does the number of iterations vary with system size?
   A. G-S grows with size; N-R is nearly independent of size
   B. N-R grows with size; G-S is independent
   C. Both are independent
   D. Both grow equally
   Answer: A. G-S needs many more iterations for larger systems, while N-R stays at 3-5. (Key point: Iterations vs system size)

3. Which assumptions are made in decoupled load flow?
   A. R >> X and large angle differences
   B. X/R is high and angle differences are small, so J2 and J3 are about zero
   C. Voltage is zero at all buses
   D. Only slack bus exists
   Answer: B. High X/R and small angle differences give G << B and sin about 0, cos about 1. (Key point: Decoupling assumptions)

## Related in Power System Analysis II

- [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×
- [Bus quantities and decoupled load flow steps](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Abus-types-decoupled-steps) — Power System Analysis II, chapter 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
- [Decoupled equations and FDLF assumptions](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adecoupled-equations-fdlf-assumptions) — Power System Analysis II, chapter 2
- [Basis and advantages of decoupled load flow](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Adecoupled-basis-advantages) — Power System Analysis II, chapter 2
- [Sequence components decoupled for power flow](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asequence-decoupled-complex-power) — Power System Analysis II, chapter 4

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