I have built a Raspberry Pi NAS and it is powered by a lithium-ion battery through a 5 V step-up module - the one used in powerbanks. The battery is a 18650 Li-Ion battery which is kept continuously at 3.7 V by an adjusted LM2596 module.
I am not directly powering the Pi through a 5 V mobile charger because of two reasons - brownouts and blackouts will cause the NAS to reboot. Second, no cheap-ish mobile charger's output is free from AC ripples and Y-cap leakages, which might shorten the life of the Pi. And it'll be overkill to buy a well-constructed Apple charger that's fairly foolproof.
Now, I was wondering, is it harmful for the lithium-ion battery to be kept at 3.7 V? Does it cause continuous trickle charging, that is harmful for lithium-ion batteries? Or does the battery take zero current once it's at 3.7 V?
The circuit is like this: