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GATE 2017 EE – Question 63

Power Electronics · Single and three-phase configuration of uncontrolled rectifiers · 2 marks · Numerical answer

The figure below shows an uncontrolled diode bridge rectifier supplied from a 220 V, 50 Hz, 1-phase ac source. The load draws a constant current $I_o = 14$ A. The conduction angle of the diode $D_1$ in degrees (rounded off to two decimal places) is ________.

A single-phase source of 220 V, 50 Hz in series with a source inductance $L_s = 10$ mH feeds a four-diode bridge ($D_1$ to $D_4$). The load is a constant current source $I_o = 14$ A.

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Correct answer: 220 to 230

Explanation

The source inductance delays the current transfer between diode pairs, giving an overlap angle $\mu$. It satisfies $\cos\mu = 1 - \frac{2\omega L_sI_o}{V_m}$. Here $\omega L_s = 3.1416\ \Omega$ and $V_m = 220\sqrt{2} = 311.1$ V, so $\cos\mu = 1 - \frac{2 \times 3.1416 \times 14}{311.1} = 0.7173$ and $\mu = 44.2°$. A diode conducts for $180°$ plus the overlap, so the conduction angle of $D_1$ is $180° + 44.2° = 224.2°$.