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battery powered inverter- large swing of battery current

dear All E2E,

please suppose a single phase inverter powered from a L-Ion battery.

as you may know there is a pulsating power and so on the battery should be of a large swing shape.

i have three questions:

1) is such a large swing current permissible/tolerable?

2) is it permissible/tolerable to current pass to negative in this swing amplitude?

3) is there any techniques to decrease the swing?

regards, Rasool