Theoretical rechargeable battery capacity question
This is not an easy &quot;compact battery&quot; application.
Required:

Battery that stores 500 Wh (Watt.hours) of energy.

Assumed means of converting battery power to mains power.

Conversion efficiency assumed to be 100%  adjust to whatever converter is used.


Required Battery Ah (amp-hours) = Watt.hours /  battery voltage.
ie Ah = Wh/V
So:
Lithium Ion:
A single LiIon cell at 3.6V mean nominal requires
Ah = Wh/V = 500/3.6 ~= 140 Ah.
A good 18650 cell is 3300 mAh (3.3 Ah) so you'd need 140/3.3 ~=  42 of them [!!!].
Recent 21700 LiIon cells may have 4 AH capacity for high power cells and up to about 5 Ah for high energy (and lower peak power) cells. So you'd need 140/4 or 140/5 = 36 or 28 of these respectively. 28 x 21700 cells at 21mm dia x 70mm long could be arranged in a 4 x 7 stack of about 100mm x 175mm x 70 mm (about 4&quot; x 7&quot; x 3&quot;).
Reputable cells from a trustable supplier cost in the $5 - $7 range each.
600 Watts peak draw = 600/28 ~= 21 Watts/cell. [Yes, that IS a valid equation :-) ].
I at 21 Watts/cell = W/V = 21/3.6 = 5.8A. That's about 1.5C or less and available from all except the lowest power rated 21700 cells.
Once you know the required battery size you still need to know how to safely configure them into a battery of series and parallel cells and then operate an inverter from them. Unless you are severely $ constrained it is usually a good idea to buy battery packs &amp; chargers 'off the shelf' and also you need to be sure to not lower the battery voltage too low during discharge.
I'll repeat - &quot;this is not an easy compact battery question&quot; - it's all doable, but it's also easy to do it wrong enough to be disastrous, sadly.
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Lead Acid
Using a 12V battery Ah needed = 500/12 = 42 Ah. That's a largish car battery fully discharged.
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Internal combustion engine:
A small internal combustion engine driving an alternator using alcohol or &quot;petrol&quot; would typically require around 0.5 litre of fuel to supply 500 Watt hours of energy.
[Fuel energy content ~~ 10 kWh/litre. Assume all up somewhat pessimistic 10% efficiency in energy conversion].