The DC$-$DC boost converter boosts the PV panel voltage Vpv to the high$-$voltage dc bus Vbus. The bus voltage Vbus has negligible ripple and is essentially dc$.$ The inverter

switches SW$1$ to SW$4$ are controlled such that the switch output voltage v $($t$)$ has the

s

same low$-$frequency average as the ac utility voltage vac$($t$).$ The inductors connected between the inverter switches and the utility grid have small switching ripple but small impedance at the grid frequency, and iac$($t$)$ is essentially a line$-$frequency sinusoid that is in$-$phase with vac$($t$).$ All losses can be neglected.

Typical waveforms for a residential PV system in the USA are Vbus $=400$ V$,$ vac$($t$)=2(240$ V$)$ sin$($t$),$ and iac$($t$)=2(1$ A$)$ sin$($t$).$ The ac line frequency is $60$ Hz$,$ and hence $=2$$60.$

The duty cycles of switches SW$1$ and SW$2$ are controlled so that v $($t$)$ has an average

over each switching period that is equal to vac$($t$),$ with a switching frequency of $50$