According to zxcvbob :

If I understand your question, the "connection" you want is a big breaker
in your service panel; for that kind of distance, I'd use a 60A 2-pole
breaker and run #4 wire. You can use a 100A breaker with #4 wire, but 100A
breakers are expensive.

Not compared to the wire. Price out 150' of #4 and be prepared for quite
a shock. This is one of the (few) times to consider aluminum wire[+]. When
installed properly (with appropriate connectors and grease), it's perfectly
safe. But check with a inspector.

At this ampacity range and for this purpose/length, there's not a lot of
point to oversizing the wire and _not_ having the breaker match it. In other
words, if you only need 60A, but you're gonna run #4, you might as well
put a 100A breaker in even if it costs a bit more.

[+] in a similar situation a slightly shorter length of #4 copper feeder
would have cost me almost $800CDN. In #3 aluminum, it was ~$400.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.