Hello @Mchank 
If the smart plug turn on by itself:  

1. Please try to remove Schedule / Away Mode/ Timer/ Smart Action/ Scene settings on smart device  in case those settings affects tapo:

How to set up schedule, away mode and timer for Tapo smart devices (smart plug, smart bulb,smart switch)

1. If it works with any third party smart app , like Alexa /Google /Home automation etc., please unbind or remove settings temporarily while test 
2. Confirm device firmware and app are both up to date. 
3. Factory reset tapo device and reinstall it from app and see if issue is gone

How to factory reset the Tapo smart plug

If still the same issue, can you help confirm some details here, thank you.
1. Please describe phenomenon  as detailed as possible,   e.g. at 8:00 UTC+1, xx light turn off by itself and stay off, power led on plug went off, need manually press power button to turn it on, or turn it through APP
2. How often does this happen?   Does it turnregularly at certain time or randomly,
3. Do you use any third-party software except for Kasa app
4. Did you recently add any new network device in the home network? The model of router, does plug connect to router directly or through extenders? 
5. How many smart devices have this issue, can you share the Mac address of certain unit to us via private message, thank you.