Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
For stability and economic reasons we operate the transmission line with power angle in the range
10° to 25°
30° to 45°
60° to 75°
65° to 80°
30° to 45°
Transmission lines are operated with a power angle (δ)between 30° and 45° to maintain an optimal balance between steady-state stability limits and economic conductor utilization. Operating at lower angles provides high stability margins but requires larger, more expensive conductors, while angles above 45° rapidly approach the pull-out torque (stability limit) of the system.
Transmission lines are operated with a power angle (δ)between 30° and 45° to maintain an optimal balance between steady-state stability limits and economic conductor utilization. Operating at lower angles provides high stability margins but requires larger, more expensive conductors, while angles above 45° rapidly approach the pull-out torque (stability limit) of the system.
P=XVsVrsinδ — Steady state power transfer equation
dδdP=XVsVrcosδ — Synchronizing power coefficient
The power transferred across a transmission line is governed by the equation P=XVsVrsinδ. As the angle δ increases, the power transfer capability increases, but the stability margin (how far the system can move before losing synchronism) decreases. The range 30° to 45° is chosen as a 'sweet spot' where the system is stable against small disturbances while utilizing the line's reactance economically.
The power angle δ is the phase difference between the sending-end and receiving-end voltages.
A higher δ allows more power transfer but reduces the stability margin.
Economic operation requires minimizing transmission losses (I²R) while maximizing line capacity.
Exceeding 90° results in total instability as dδdP becomes negative.
Maintains sufficient transient stability margin
Prevents oscillations under small load fluctuations
Optimizes the use of line thermal limits
Lower capacity utilization compared to theoretical limits
Requires reactive power compensation (like SVCs) to stay within the range at heavy loads
EHV (Extra High Voltage) transmission line planning
Load flow studies and power system stability analysis
If δ exceeds 90°, the line reaches the steady-state stability limit.
Option A (10⁻²⁵°) is too low, resulting in under-utilization of the transmission line capacity.
Options C and D (above 60°) are too high, leaving negligible margins for sudden power swings or faults.
B is correct — Operation in the 30° to 45° range provides an optimal compromise between high power transfer efficiency and a sufficient stability margin against system perturbations.
Always remember that for a lossless line, the maximum power transfer occurs at δ=90°; therefore, operating anywhere near that limit is dangerous for system reliability.