---
title: "T/F: stability criterion implies thermal criterion"
subject: "Transmission and Distribution System Design"
chapter: 4
key: "semester_8/transmission_and_distribution_system_design:tf-stability-implies-thermal"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-stability-implies-thermal
site: BCT Engineering
---

# T/F: stability criterion implies thermal criterion

Transmission and Distribution System Design · Chapter 4: Conductor and Support Selection

- Asked in: 2079 Chaitra, 1+3 marks; 2070 Magh, 1+3 marks (asked 2 times)
- 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/tf-stability-implies-thermal
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-4

## Question

State and justify whether the following statement is TRUE or FALSE: While designing the long transmission line, if the stability criterion is met then the thermal criterion is also met.

## Short answer

TRUE. On long lines (above about 320 km), the steady-state stability limit is much smaller than thermal rating because reactance grows with length. If the stability criterion is satisfied, the current is well below the conductor's ampacity, so the thermal criterion is automatically met.

## Answer

**TRUE** (for long lines).

The power a line can carry is limited by three criteria (St. Clair loadability curve):

| Line length | Governing limit | Typical loadability |
|---|---|---|
| Short (up to about 80 km) | Thermal | about 3 × SIL |
| Medium (80–320 km) | Voltage drop (about 5%) | 1.5–3 × SIL |
| Long (above 320 km) | Steady-state stability | about 1 × SIL or less |

The stability limit $P = \dfrac{V_sV_r}{X}\sin\delta$ (with $\delta$ kept to about 30°–35°) falls as the line length increases, because $X$ grows with length. The thermal limit $\sqrt{3}VI_{rated}$ does not depend on length.

For a long line, the stability-limited power is therefore much smaller than the thermal capacity of the chosen conductor. If the line is designed so that the stability criterion is met, the current is well below the conductor's ampacity, so the thermal criterion is automatically met.

The converse is not true. A long line that meets the thermal criterion may still fail the stability criterion.

## Check yourself

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

1. For a long line, meeting the stability criterion also meets the thermal criterion. This is:
   A. False, thermal limit is always smaller
   B. True, because the stability-limited power is far below thermal capacity
   C. False, stability is independent of length
   D. True for short lines only
   Answer: B. On long lines the stability limit is much lower than the thermal capacity, so the current stays within ampacity. (Key point: Verdict)

2. Which limit governs loadability for a long line (above about 320 km)?
   A. Thermal limit
   B. Voltage drop limit
   C. Steady-state stability limit
   D. Corona limit
   Answer: C. St. Clair's curve shows long lines are limited by stability, near 1 x SIL or less. (Key point: Governing limit)

3. Why does the stability limit fall with line length while the thermal limit does not?
   A. Reactance X grows with length, but thermal limit sqrt(3)VI_rated is length independent
   B. Resistance falls with length
   C. Voltage rises with length
   D. The conductor heats more on long lines
   Answer: A. P = VsVr sin δ / X falls as X rises with length; the rated current limit does not depend on length. (Key point: Length dependence)

## Related in Transmission and Distribution System Design

- [T/F: 765 kV stability limit vs thermal limit](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-765kv-stability-vs-thermal) — Transmission and Distribution System Design, chapter 2
- [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
- [T/F: thermal limit design urban, losses rural](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-thermal-limit-urban-loss-rural) — Transmission and Distribution System Design, chapter 7, asked 3×
- [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×
- [Justify higher voltage/more circuits for more power](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ajustify-higher-voltage-more-circuits) — Transmission and Distribution System Design, chapter 2
- [Justify: trending method for large area forecast](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ajustify-trending-large-area-forecast) — Transmission and Distribution System Design, chapter 6

## Related in other subjects

- [True/false: CT secondary kept open](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-false-ct-secondary-open) — Electrical Machine, chapter 2
- [True/false: derivative controllers always used with others](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Aderivative-always-with-others) — Control Systems, chapter 7, asked 3×
- [True/false: series motor started at no load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-dc-series-motor-start-noload) — Electrical Machine, chapter 4
- [True/false: rotor core loss neglected](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-rotor-core-loss-neglected) — Electrical Machine, chapter 5