why is my battery light coming on sometimes when accelerating hard

Hard to tell - with anything like this you need to begin by isolating the fault as much as possible - the smell could be wires or it could be your alternator belt - the alternator is what charges the battery. Locate the Alternator and check the belt first, see if its loose on the pulley - if its lose tighten it and test it. If its not lose then you need to get hold of a volt meter set to (DC) and connect it up to your battery - being careful of the wires and the moving parts - start up the engine and see what the voltage raises to - from cold it will be around 11 or 12 volts - with the engine running it should be 13.5 - next you can rev the engine and monitor the volt meter for changes - if it stays at 13.5 when its revving at say 4000RPM then its not the alternator and you need to check your cables if it goes past that voltage then you need to replace the alternator as this usually indicates its the regulator thats faulty and this can cause over charging - check online if this is the case many parts places carry alternators by make and model to make it easier to replace - usually they are exchange items (they want your old one first).

I just fixed this on my 2003 Mini after an annoying year of problems with it. When I accelerated my power would surge, the battery light would come on, the speedometer would drop out and I would lose power steering... and it burned up the wires in my low beams. It turned out that there was a loose electrical ground wire in the engine compartment. In my case, there were premium spark plug wires that needed to be grounded. When I tightened the loose wire, all the problems went away. You should start by checking the main engine ground and then all other grounds. I'll bet one is loose or rusted and that is the culprit. Good luck. My total cost = $0 (Mechanics quoted thousands of dollars from a bad CPU, alternator, battery, etc etc)