SEPIC converter : why average secondary inductor is the output current?
A SEPIC converter can be simplified like this: -



Picture from here.


  why average secondary inductor is the output current?


Average current is basically a DC current and we know that DC cannot pass through C1 or C2. C1 and C2 are functionally needed of course but they do not provide DC currents. Hence, the only source has to be L2 in the picture above: -