Yes, if outlet electricity costs 10c/kwh, car electricity probably costs 50cents.
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I was thinking more on the line of just having the thing there just to maintain battery power level, not to get the car down the road, just as a backup when you can't plug it in.
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Ummm... right. What do you think "maintaining the battery level" is exactly, as it powers or after it has powered the vehicle down the road?
Maybe in some (most?) cases an onboard genset would be an OK range extender or "range anxiety fix", but I keep thinking of my driving pattern and it's usually totally within EV range or way, way beyond it. For within, no ICE; for beyond, ICE to the wheels.