I use my AC500 to run a portable air conditioner in my bedroom at night. Sometimes at night the batteries get too low and the wall outlet connection kicks in (you set it in the ups priority menu). This gives me maximum use of my partial off-grid system. Come morning, the batteries start recharging while I’m still sleeping.
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Instead of using a nearby 15 amp wall outlet, I wanted to use the 20 amp outlet farther away, so I used a power tool cable on a wind up spool to reach the outlet. Some weeks later I woke up to a sickly sweet kind of rubber/plastic smell. The room was filled with a haze but it wasn’t smoke. The extension cord spool was hot and the insulation was melting on the wire that was still in a coil. So it was like a big transformer, and was producing quite a bit of heat ( the uncoiled part of the cable was only slightly warm.)
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If it had been a cheaper cable the wires likely would have shorted out and tripped the circuit breaker. Instead it made a big mess of melted and stinky plastic and insulation. At 4 am I’m running around opening all the doors and windows and using fans to try and clear out the haze filling the house. 
This is a VERY good point. Many 
house fires start with overloading bad and/or cheap extension cords or power strips. Many extension cords are not made to handle high wattages and big power stations like the AC500 can easily overload them. Either do not use extension cords or use those heavy duty extension cords that are rated for 3500 watts, with at least 1.5mm pure copper conductors, made by reputable manufacturers. Shorter cables are better as well. (This is for European 230 volts, if you live in a lower voltage country (Like 110v) you probably need even beefier conductors)
Many no-name extension cords and power strips use thin conductors, made of aluminium instead of copper, and may make bad contact with the power plug. This will work fine with low-power devices like a couple of phone chargers but plug in something heavy like an electric heater, water kettle or a big power station and you can burn your house down.
The Dutch fire departments constantly warn about these.
If you’re concerned about overloading your power strip of extension cord you can also lower the charging wattage/amperage of your power station in the settings. This will be easier on the battery as well.
It’s not surprising that there was overheating of the un-wind cable.
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I’m using a 50m cable drum which has a thermo breaker.
16 A are no problem but only if all the cable is uncoiled.
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This summer, with the cable drum in full sun and a consumer of ca. 2400 W
(= ca. 10-11 Amp, 230V) and most of the cable coiled
the breaker interrupted after a few minutes.
You should always uncoiling an extension cable when running high amperage/wattage loads, this phenonium is well known in the motorhome/caravanning community which have seen a few melted cable drums and the potential for fires due to not uncoiling the cable completely.
Oh yea, an electrical wire reel should ALWAYS be fully unwound before use to prevent overheating of the cable. This should be warned for on the reel as well.
Think of it this way; A strip heater i.e. infra red ilk, is a coil of wire, wound around an insulator. Its resistance causes heat. do that with an insualed extension cable and the first thing to melt or burn is the insulation.
Golden rule for all power cables AC & DC - Never use coiled up for that very reason. Plus with DC cables, you might end up creating an electro magnet that might affect nearby devices and not in the way you want. Cable gauge and quality help, but even the best quality can’t escape this effect.
Don’t use a 10A cable to power a 15A load, that applies to the 120VAC U.S. or the 240VAC EU/AU power systems. As @TheQuickFox mentioned, here in AU cable reels do have that Warning on them, it’s Law. The other downside is, if you have a fire and the insurance investigators search through what’s left and determine that is what caused the fire, your insurance will likely be voided. So a $10 cable might cost you 100s of 1.000s of $$$$. 
More precisely, with DC through a coil you get an electromagnet. With AC through a coil you get a Transformer because the current alternates 60 times a second. The changing magnetic field fights against the current and you get extra heat from eddy currents and such.
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It’s funny how I’ve known all this stuff since my Ham Radio days from the 60s. It’s just that I’ve used wound up power cords for powering saws and drills. It’s normally not a problem for short term use.
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All my extension cables are extra heavy duty, including some 30A RV cables.
Never wind power cables, they create heat by induction.