Since acquiring a US-spec Kill-a-Watt device, I've been measuring the power factor on my US ballasts and stuff. The worst by far is the Philips Goldeye 18W SOX fixture, with an appalling power factor of 0.24. It also runs extremely hot, which may well be due to this.

What would be a suitable value for a PFC capacitor to go across the supply here..? I know what the value is for a 240V 50Hz 18W SOX ballast, but the value will be different here.

Some people will be itching to tell me I don't need PFC on a single lamp or fixture, please don't. I want it, simple as that. Can anyone help, please..?

I would expect the ballast being ridiculously hot to be caused by the frequency musmatch (= saturating primary, plus at least 20% extra current not counting shunt saturation) and not that much by the missing PFC capacitor. Or if the capacitor is connected directly to mains, it can not be caused by it missing.
Have you checked the currents? Without the capacitor the output should be (obviously)the 0.36A, the input around 1.55A.

And yes, the power factor of 0.23 is normal for an 18W 0.36A discharge, fed from around 240V OCV ballast. Higher OCV means lower power factor.
The capacitor should be about 16uF at 120V 60Hz, 20uF at 120V 50Hz and about 5uF at 240V 50Hz.

The ballast is running on 120V 60Hz from my inverter, so there is no frequency mismatch. Thank you for the capacitor values, I will try 16µF.

And the inverter is really a true sinewave?

Otherwise the 120V ballasts tend to be quite hotter than we are used to. Because the step up transformer function just means more than double total winding loading.

And the capacitance depends on the ballast OCV. The 16uF is for 240V, higher OCV would mean higher capacitance.
Any way, it won't change the ballast operating temperature, just reduce the inverter loading (assume it is really a true sinewave; otherwise it would kill it or best case trigger an overload protection)...

Yes, it's a true sine wave inverter. Only 400W but enough for my needs, larger lamps tend to be compatible with UK/EU ballasts anyway.

I have plenty of 8µF capacitors, as these are used for 80W MV here, so a couple of those will give me 16µF.

Ok, update. 16µF has improved the PF to 0.58 - 0.6 so we're moving in the right direction. It's definitely running cooler, anyway 

And a final update. A capacitor of 24µF (well 2 x 12µF actually) gives me an almost perfect PF of 0.95. Can't ask for better than that 

Still runs a bit hot though, but it's a lot better than it was 

On my first generation Goldeye I tried a 17.5uf capacitor (commonly used  here for 175w MV CWA gear) and it dropped the current draw from the nameplate 0.93A to 0.37A. Power consumption was around 42w, which results in a power factor of 0.92. Much better than the original power factor. However I did not notice a change in operating temperature.

Maybe I'll try with a second generation Goldeye and see what results I get.

I don't remember what the power consumption was, somewhere around 35W I think, but not sure. I'll measure it next time I fire it up. I'd like to find the lamp current, not easy though, with the wiring to the lampholder all enclosed