what size fuse for 150 amp alternator

How long is the run of cable? It will probably be the weak link in the power chain (fuse for the weakest link).
 
I would try to use a 125 amp fuse, as 4 AWG is good for around 130 amps at the distance you require. It would have been better to use 2 AWG, as that's more appropriate for the hypothetical load, and allows the circuit protection to better match the alternator's output.

MHO,
Good luck.