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3 amps at 120v to power the PPS, so it will need at least 30 amps BATTERY POWER at 12v then you have to figure in the "losses" :-(
That's why I said 35 amps (Battery Power), cuz the raw math said 33.3 amps
PANEL POWER can be a lot less, cuz it is just to top off the batts.

no...I don't thinkso.
I can fill a swimming pool (battery) l with an 36in irrigation pipe.
or a 1/4 inch plastic tube....
one is just quicker...than the other.
same amount of water.

Your Swimming Pool is constantly being drained by a 1" line, in this example ;)

But we have no idea if the PPS will just charge slower, or cut off.
I'm betting it will cut off. You can try tho...

Get the panel(s) but the math says you will need 4 or 5.
1 or 2 with batteries before the 400w inverter.

3 amps is what the PPS needs at 120v AC, that is 360 watts.
So you need at least a 400w inverter and 500w solar, by the book.
All these devices have cut offs for low voltage, that is how they are
made so you don't hurt anything...

I was saying 30+ amps of battery, the solar charge can be lots less, like I said before.
(Edited the above post for Clarity) ;)