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Hi, I'm Mike G and I'll be assisting you. Do you plan to go overhead or underground on the new service? Where are you located?
At that distance you can use either a 4/0 copper or a 250MCM aluminum. The run should be in sch40 PVC to avoid failures in the future from ground movement and the necessity of enveloping a cable in sand to protect it from rock penitrations. The conduit will need to be 2 1/2" mom.
Will it be from the same pole or an addition to the 150 ft?
Same size wire. If you cross any driveway you'll need to use galv ridgod conduit to cross it. At the pole you'll need 2 ground rods with a #4 copper loop to both disconnects and a single rod with #6 copper at the house and at the barn.
Originating on the neutral bar, connecting 2 rods 6 ft apart and returning to the neutral bar.
Codes change. Yes they may be blow the surface.
You're welcome and a great year for you.