---
title: "Power transfer limit vs SIL ratio and length"
subject: "Transmission and Distribution System Design"
chapter: 2
key: "semester_8/transmission_and_distribution_system_design:power-transfer-sil-length"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/power-transfer-sil-length
site: BCT Engineering
---

# Power transfer limit vs SIL ratio and length

Transmission and Distribution System Design · Chapter 2: Transmission Voltage Level and Number of Circuits

- Asked in: 2070 Magh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/power-transfer-sil-length
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-2

## Question

Explain the dependency of power transfer limit to surge impedance ratio & length of transmission line.

## Short answer

Power transfer limit equals a multiplying factor times V²/Zc. Lower surge impedance (e.g., bundled conductors) raises SIL. The multiplying factor decreases with line length due to stability limits, so capability falls as length increases.

## Answer

**Surge impedance loading (SIL)** is the power delivered when a lossless line is terminated in its surge impedance $Z_c = \sqrt{L/C}$:
$$
SIL = \frac{V_L^2}{Z_c}\ \text{MW}
$$
At SIL the reactive power generated by line capacitance equals that absorbed by inductance, so the voltage is flat along the line.

#### Dependency on surge impedance
- SIL $\propto 1/Z_c$. Lowering $Z_c$ (bundled conductors, compact phase spacing, shunt capacitance increase, series compensation) raises SIL and hence the power limit.
- Typical $Z_c$: about 400 Ω for single-conductor lines, 250–300 Ω for bundled EHV lines.

#### Dependency on length
- Max power $P = \frac{V_sV_r}{Z_c\sin\beta l}$ (lossless line). As length $l$ increases, $\sin\beta l$ increases, so power in multiples of SIL falls.
- Short lines (< 80 km) are limited by thermal rating (about 2.5–3 × SIL); medium lines (80–320 km) by voltage drop (about 1.5–2.5 × SIL); long lines (> 320 km) by stability (about 1 × SIL or less).

| Length (km) | 80 | 160 | 240 | 320 | 480 | 640 |
|---|---|---|---|---|---|---|
| Capability / SIL | 2.75 | 2.25 | 1.75 | 1.35 | 1.0 | 0.75 |

So power transfer limit $= \text{m.f.}(L) \times V^2/Z_c$: it increases with $V^2$, decreases with $Z_c$, and decreases with line length.

## Check yourself

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

1. What is the condition at surge impedance loading (SIL) of a lossless line?
   A. Reactive power generated by line capacitance equals that absorbed by inductance, so voltage is flat
   B. The line carries its thermal limit current
   C. The receiving end voltage is zero
   D. The line is open circuited
   Answer: A. At SIL the line's capacitive VARs equal its inductive VARs, giving a flat voltage profile along the line. (Key point: SIL definition)

2. Which change raises the SIL and hence the power transfer limit?
   A. Increasing Zc by widening phase spacing
   B. Lowering Zc by using bundled conductors
   C. Using a single conductor per phase
   D. Reducing the line voltage
   Answer: B. SIL = V^2/Zc, so lowering Zc (bundling, compact spacing) raises SIL. (Key point: Effect of surge impedance)

3. As line length increases, what happens to the power transfer capability in multiples of SIL, and what limits a long line (> 320 km)?
   A. It rises; thermal rating
   B. It stays constant; voltage drop
   C. It falls; stability
   D. It rises; stability
   Answer: C. The multiplying factor falls with length (2.75 at 80 km to 0.75 at 640 km); long lines are limited by stability at about 1 x SIL or less. (Key point: Capability versus length)

## Related in Transmission and Distribution System Design

- [T/F: power transfer capability vs line length](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-power-transfer-line-length) — Transmission and Distribution System Design, chapter 2, asked 2×
- [T/F: switching surge ratio vs system voltage](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-ssr-system-voltage) — Transmission and Distribution System Design, chapter 3, asked 4×
- [T/F: X/R ratio, transmission vs distribution](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-xr-ratio-transmission-distribution) — Transmission and Distribution System Design, chapter 1
- [Power loss change on doubling line length](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Apower-loss-doubling-line-length) — Transmission and Distribution System Design, chapter 7
- [Initial line design for 200 MW over 120 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aline-design-200mw-120km) — Transmission and Distribution System Design, chapter 2
- [T/F: capability curve inversely proportional to length](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-capability-curve-inverse-length) — Transmission and Distribution System Design, chapter 2

## Related in other subjects

- [Surge impedance and velocity of 220 kV line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Asurge-impedance-220kv-200km) — High Voltage Engineering, chapter 3, asked 2×
- [Surge impedance and travel time of 400 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Asurge-impedance-220kv-400km) — High Voltage Engineering, chapter 3
- [Characteristic impedance, SIL, propagation constants](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acharacteristic-impedance-sil-constants) — Power System Analysis I, chapter 5
- [Infinite line: surge impedance and forward/backward waves](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ainfinite-line-surge-impedance-waves) — High Voltage Engineering, chapter 3