iMac shutdown unexpectedly, must unplug the power cable to power on it again

What model and year is your iMac?

That's indiction of a failing power supply. Had the same issue with a 2015 27 iMac. I had contacted Apple and they had me erase the drive and install a new system without migrating any of my user data. This was to verify that it was a hardware issue and not a software one. It was hardware. Luckily I was still under AppleCare so it was taken care of by Apple.

Make sure you have a full and current backup of your boot drive. Contact your nearest Apple Genius Bar or Apple Authorized Service Provider for a full evaluation. If your Mac is not on the obsolete list Apple will perform the evaluation for free. The AASP will probably charge from the evaluation.

It will help us get a good idea of what is causing your problem if you provide a report of your system, that way we do not have to play 20 questions with you. The report we are requesting does NOT provide any personal information and is extremely safe to use. Please navigate to www.Etrecheck.com and download the free version of EtreCheck. Once you have you downloaded the app and installed it, please run the report and save it. This report will help us get a good idea what has been installed on your system and help us be able to diagnose what may be wrong.

When you have your report, you can attach it when you reply to this message and we can then review it and help you determine what is needed to get your system running well again. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message please click How to use the Add Text Feature When Post… - Apple Community