I had the same issue. I called support first. The gent had me reset the PRAM, no fix. He had me re-install High-Sierra over the top - no fix. Next I reformatted and re-installed High-Sierra. During the re-install setup steps it would crash when I would enter in my AppleID information. Coming back in to re-do the setup it started crashing when setting up the wifi connection. Next I made an appointment with the Genius Bar. They bypassed the AppleID and sped through setup and ran hardware tests. All passed.....ugh. They were suspecting it was a High-Sierra issue so they downgraded to Sierra and couldn't reproduce the issue and sent me on my way. When I got it home the crashing started again (exact same random black screen for several seconds then total power shut down on Sierra this time. I made another trip to the Genius Bar. On this second trip I left it with them to run extensive diagnostics. They reformatted the HD (which I had done already 3 times) and re-installed Sierra with a generic AppleID then ran it for 48 hours straight streaming looping videos - no crash. I took it home, plugged it in and all good........until I unplug it. I have just left it plugged in for now but that random shutdown is looming for me next time I go mobile with it.
They offered to ship it off and have all the internals replaced for $575 US which isn't bad.
I bought it refurbished so no warranty.
Hope this helps someone. I have no hair left after dealing w/this thing.