how would them being in parallel help with sustaining a high power draw? Does it contribute directly to voltage sag or voltage droop?
Yes, the voltage will 'sag' in proportion to the current. If you put another string of batteries in parallel, then except for the minor differences in the wiring (one pack internal with short leads, one pack external with longer leads) they will basically split the current requirement so each pack only flows around half the total amps. In doing so their voltage will 'sag' proportionally less, and keep the inverter above its low voltage cutoff point.
And also since you mention needing a foot of wire, I am questioning the wire used in the UPS as well. Which gauge of wire should I get for a 600-700w load on a 12v battery or 24v battery? 12awg is currently used.
It's good that you noticed that as a potential bottleneck. We're talking about a 25-30amp draw during that 600-700w load (700w / 24v = ~29amp) and 12awg will support that for a while before its temp gets too high. With short duty cycle circuits like this there are often things that are intentionally left kinda crappy because it's like the situation of being chased by a bear.. you just have to be faster than the slowest guy.
So even if that 12awg wire is technically undersized for that current and eventually overheat under a continuous 30amp current, it's still going to take a certain amount of time for its temp to rise, and with such a small battery pack the battery will drain and not be able to sustain the 30a, before the wire actually gets too hot. The wires that go to starter motors in cars are the same way.. Technically too small, but it's ok because they don't run long enough to overheat.
So that's just talking about temp. The heat COMES from the voltage that gets dropped across the wire, so making heat = losing volts. In terms of voltage drop, yes the 12awg wire is probably dropping several tenths of a volt while flowing the peak current. But, it may be very tedious to improve that part of the device because the 12awg wire probably gets soldered directly into a through-hole on the inverter circuit board and while you may be able to solder a 2nd set of leads onto it in parallel with the existing leads, or replace the existing 12awg leads with a single set of larger leads into those through-holes or solder pads on the circuit board, it is
probably more work for less gain vs just adding the second string of batteries in parallel and feeding it through the existing 12awg wires.
What if I got 2x 24v 5ah batteries to run in parallel would that work better for this type of load of 600w for 1-2 seconds?
It depends what kind of batteries they are. Lithium iron phosphate (lifepo4) batteries do not have much voltage 'sag' under load so even if you replaced the SLAs with Lithium of a smaller Ah rating, they would likely sustain higher voltage under the brief load condition. With lead acid it is basically 'settled science' to the point that if you have 5lbs of lead acid wired one way or 5lbs of lead acid wired another way, it will basically give the same result given that you have to keep it 24v regardless. So replacing 2x 12v 9ah in series, with 2x 24v 5ah in parallel, might allow you to still fit everything into the existing case but probably won't address the voltage sag issue because you still essentially have 'the same amount of battery' or pretty close to it.
So to substantially reduce the voltage sag under load, you either need to make the battery 'bigger' by paralleling an external pack, or replacing the single internal pack with a lithium replacement which will not suffer as much voltage sag under load.
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