GATE 2016 EE (EE2) – Question 58
An ideal single-phase bidirectional VSC charges a 400 V battery at 5 kW from 220 V rms, 50 Hz mains at unity pf. Interfacing L=5 mH and switching frequency 20 kHz. Find the phase-shift magnitude between mains Vs and fundamental converter voltage VC1 in degrees.
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Correct answer: 9.1 to 9.3
Explanation
At unity input pf, source current is in phase with Vs and has rms value I=5000/220=22.7273 A. The inductor reactance is 2π50(0.005)=1.5708 Ω.
The converter phasor is VC1=Vs−jXI, so it lags Vs by $\delta=\tan^{-1}(XI/V_s)$.
Substitute XI=35.6999 V and Vs=220 V to get **δ≈9.217°**, within 9.1–9.3°. The switching frequency does not replace the fundamental frequency in this phasor reactance.