Burned 25uF Cap Was Used in a 400W HPS Floodlight

I vote for the mystery spike thats already come and gone

Electrolytic capacitors are polarized and only should be used on DC circuits. Nonpolarized paper, polystyrene or other types of wound cap are used in HD lighting

The fixture reached a temperature greater than the design allowed.

HPS lighting normally runs at very high temperatures.

In many cases the lighting fixtures were not designed for HPS and instead are retrofitted with a HPS kit.

Check the internal equipment temperature rating then energize the fixture and take a temperature reading on the fixture after it has been operating for 1-2 hours to find out if this is the cause.

IF it is not, then the fixture may be experiencing high voltage, a component failed, or it could be the result of a lightning strike.

I found in one of the website it was recommended 55uf, 300V(which is =0.0165Coulombs) and I installed 25uf, 250V (which was= 6.25e-3=.00625Coulombs) may be thats why the ballast got over heated and burnt.

another website has a capacitor of 25uF(same as the old burnt one) but with 400V (which is equal to 0.001Coulombs) so I think capacitor selection should be done by knowing the coulombs. Correct me if I am wrong.

But still the capacitor was connected between Line and Neutral and if the caps. burnt my L-N should not short and the whole fixture should still work with ignitor when started again.

"so I think capacitor selection should be done by knowing the coulombs. Correct me if I am wrong."

Proper capacitor selection should have been done by putting a new one back in that matched the specs of the old one. HID ballasts are ferroresonant transformer circuits that need to have the proper value of capacitance in their circuit to work properly.

The odds are if you put one in that was way to small (25 uf when it needed 55 uf) the bulb never reached its proper working voltage and currents so the pulse ignitor circuit kept running, which as it is designed to do, kept making continuous high voltage pulses in the immediate circuits ultimately killing the capacitor.

The should help you sort out what you need to know.

HID ballast troubleshooting guide.

Bear in mind electrolytic capacitors are probably the most unrelable electronic component and they are usually +/- 20% tollerance. They should be over-rated on voltage to about twice what you think they will be subjected to.
Del

It would help the diagnosis if we knew whether the lamp worked properly prior to the capacitor burning out. I suggest you replace the capacitor with one of the same capacitance and the same or higher voltage rating.