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T/F: stability criterion implies thermal criterion

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.

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.

TRUE (for long lines).

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

Line lengthGoverning limitTypical loadability
Short (up to about 80 km)Thermalabout 3 × SIL
Medium (80–320 km)Voltage drop (about 5%)1.5–3 × SIL
Long (above 320 km)Steady-state stabilityabout 1 × SIL or less

The stability limit P=VsVrXsin⁡δP = \dfrac{V_sV_r}{X}\sin\delta (with δ\delta kept to about 30°–35°) falls as the line length increases, because XX grows with length. The thermal limit 3VIrated\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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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