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A single-phase bi-directional voltage source converter $(VSC)$ is shown in the figure below. All devices are ideal. It is used to charge a battery at $400$ V with power of $5$ kW from a source $V_{s} = 220$ V (rms), $50$ Hz sinusoidal $AC$ mains at unity p.f. If its $AC$ side interfacing inductor is $5$ mH and the switches are operated at $20$ kHz, then the phase shift $(\delta)$ between $AC$ mains voltage $(V_{s})$ and fundamental $AC$ rms $VSC$ voltage $(V_{C1})$, in degree, is __________.

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