Sounds like you may have a bad battery. While holding down the Option key, click on the battery icon on the menu bar to see what the status condition is listed. Anything but "Normal" or "Good" usually means the battery is failing.
You can also run the Apple Diagnostic which may perform a slightly better check on the battery.
If the battery checks fine, then try an SMC reset and PRAM reset.
You can also take it to an Apple Store or Apple Authorized Service Provider to be checked out. Since it is a power related issue, you should take along the power adapter & cord just in case they need to be examined or tested.