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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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With 100% series compensation of lines
Low transient voltage
High transient voltage
Current is series resonant at power frequency
Both (b) and (c)
Both (b) and (c)
Quick Summary: With 100% series compensation, the inductive reactance ($X_L$) of the transmission line is perfectly neutralized by the capacitive reactance ($X_C$) of the series capacitor ($X_L = X_C$). This leads to series resonance at the power frequency, resulting in high transient voltages during faults or switching operations.
With 100% series compensation, the inductive reactance (XL) of the transmission line is perfectly neutralized by the capacitive reactance (XC) of the series capacitor (XL=XC). This leads to series resonance at the power frequency, resulting in high transient voltages during faults or switching operations.
Xtotal=XL−XC — Net line reactance
fr=2πLC1 — Resonant frequency formula
The total impedance of the line becomes Z=R+j(XL−XC). When XL=XC (100% compensation), the impedance is limited only by the line resistance R. At power frequency, this creates a resonant condition where the voltage across the capacitor can rise to dangerous levels due to high fault currents, and transients are severely amplified.
100% compensation implies the line behaves as a purely resistive network at fundamental frequency.
Series resonance at 50Hz/60Hz causes massive current surges during faults.
Voltage across the capacitor VC=I×XC can become extremely high during transients.
In practice, transmission lines are typically compensated between 40% and 70% to avoid resonance issues.
Increased power transfer capability
Improved steady-state stability
Better voltage regulation
Risk of sub-synchronous resonance (SSR)
High overvoltage risks during faults
Complexity in protection relaying
Long EHV and UHV transmission lines
Improving transient stability limits
Option B is correct because the series resonance condition significantly amplifies the transient recovery voltage.
Option C is correct because the inductive and capacitive components cancel each other out at the fundamental power frequency, leaving only ohmic resistance.
D is correct — 100% series compensation results in power frequency resonance, causing dangerously high transient voltages.
Always remember that in power systems, resonance is generally avoided as it leads to uncontrolled voltage and current magnification; series compensation is always designed with a margin to keep resonance frequencies away from the power system operating frequency.