### Power Electronics (Solved Numerical Problems)

A 3 phase dual converter is operated front the secondary of a delta star connected transformer of 220 volts, 50 Hz supply. If the load resistance is 10 Ω, the circulating inductance is 7.5 mH and $${\alpha _1} = {50^0}$$, find, (i) Peak circulating current (ii) Peak current of converter 1 (AMIE Summer 2023)

Solution

Secondary phase voltage

$${V_{ph}} = \frac{{220}}{{\sqrt 3 }} = 127\,V$$

Peak value of phase voltage

$$\begin{array}{l}{V_m} = \sqrt 2 {V_{ph}} = \sqrt 2 \,x\,127 = 179.63\,V\\\omega = 2\pi f = 2\pi \,x\,50 = 314.16\,rad/s\end{array}$$

Peak circulating current

$${i_{cir}}(t) = \frac{{3{V_m}}}{{\omega {L_r}}}\left[ {\sin \left( {\omega t - \frac{\pi }{6}} \right) - \sin {\alpha _1}} \right]$$

This current will be maximum when

$$\sin \left( {\omega t - \frac{\pi }{6}} \right) = 1 \Rightarrow \omega t = \frac{{2\pi }}{3}$$

$${i_{cir(peak)}} = \frac{{3x179.63\,V}}{{314.16(7.5\,x\,{{10}^{ - 3}})}}\left[ {\sin \left( {\frac{{2\pi }}{3} - \frac{{2\pi }}{6}} \right)} \right] = 53.5\,A$$

Peak current of converter 1

$$= \frac{{2{V_m}}}{R} = \frac{{3(179.63)}}{{10}} = 53.89\,A$$

$$\begin{array}{l}{i_{peak,conv1}} = peak\,load\,current + {\rm{ }}peak\,circulating\,current\\{\rm{ = 53}}{\rm{.5}}\,{\rm{ + }}\,{\rm{53}}{\rm{.89}}\,{\rm{ = }}\,{\rm{107}}{\rm{.39}}\,{\rm{A}}\end{array}$$

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