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UPS inrush current in battery mode - can it kill the battery/UPS?

I’ve been reading up on the combination of UPS and Active PFC power supplies, as they are common here in the EU. Seems you need to take 2 things into account. First, some A-PFC PSUs cannot work with the modified square wave output of some UPSs. You need a pure sine wave version. Though it may work (as Seasonic says in their FAQ, just try it out).

Secondly, A-PFC PSUs have a high inrush current up to their specced capacity (i.e. a 1000W PSU can pull that 1000W briefly at startup)

I tried my workstation, with a Seasonic Prime Ultra Titanium 1000W on an Eaton Ellipse Eco 800VA (550W). It works, when I pull the plug during a 450W load, the Eaton switches to battery power, and the workstation just keeps working. Seasonic says it should not be a problem and the PSU cannot be damaged by the modified sine wave output of the Eaton.

However, using the monitoring software from Eaton, I do see a very high inrush current peak when switching to battery mode (I could briefly see 650W but it may be higher as it’s just a very brief peak). I planned on a higher capacity UPS anyway, I just had the 800VA lying around and wanted to see if its wave output form would work on the Seasonic.

But I am still worried, as the highest Eco type can handle 1000W, so barely the max inrush peak of the workstation. And I’d like to add a few small devices to the UPS as well (not much extra load).

So I asked Eaton, and they kinda danced around the inrush current subject and advised to buy a pure sine wave UPS from the 5P line. These are twice as expensive and also bloody loud. Not something I want on my desk. Seems they just want to make a sale (as the 5P tower models only go up to 1000W too)

So my question is: can the inrush current peak damage the UPS or battery, or is the worst that can happen just the UPS overcurrent protection kicking in and shutting down? It seems the protection of the Eco did not activate in my test, even if it went into the red zone for a very brief moment. Not sure if that means it’s OK, or if the Eco’s overcurrent protection is crap.

Any insights would be much appreciated.