Supercapacitor PSU how to charge quickly?

Using a NTC to "charge" a supercap sounds to me like an error of reasoning. It's resistance drops within seconds maximum, but expected charging times are in a minute range, so what should it be good for?

NTCs are meaningful as current inrush limitation for rectifier filter capacitors, achievable time constants are in a 100 ms to a few seconds range. The important feature is that they stay at low resistance after charge phase to pass the regular operating current.

I agree, but this is an unusual situation where there is little or no voltage overhead in the secondary circuit and during the beginning of the charge cycle the transformer will be under almost short circuit conditions. The optimal solution has already been suggested, a voltage monitor across the capacitor that controls a current limiter in the transformer primary. I suppose the simplest solution is a thermistor on a heatsink to slow it's temperature rise but my main concern would be the transformer burning out while the current is so high. When the capacitor has charged, the primary current would be very small so even if the thermistor resistance increased again to say 25 to 50 Ohms, it would only drop a small voltage.

A slow reacting inrush NTC would be the ideal component but as far as I know none are available. I don't consider relays shorting out milliohm resistors in the secondary a good solution, the relay contacts themselves may have higher resistance than the resistors they shunted. I would also rule out any active power control in the primary because it would either dissipate a lot of heat or be pulsing current into a very low impedance inductive load. Whichever way you aproach the problem there is no 'simple' solution but many complicated ones, at least in consideration that all this does is charge a capacitor.

Brian.

Omron has 600V > 100A relays with a typical resistans of 0.2 mOhm. (but they are not cheap) Or Look in the automotive sector.
I agree with FvM for the NTC, the resistance will drop much to fast and if such a slow heavy duty NTC will be slow enough it must stay hot enough to stay low after the cap current drops a lot after a few RC so you do'n lose the time after all.