We have that in my part of the US, but my utility calls it a "connection fee". It's what you pay just to be connected to the grid, not for the actual electricity you use.
We also have one of the higest rates of residential rooftop solar here, you get relatively little payback for exporting in Perth (its hard to get more than about $20/month) but can save quite a bit on what you self-consume during the day.
As a result, this Daily Supply Charge has been steadily going up over the last decade, much more than the per-unit fee. Currently it's $1.13 AUD/day + $0.316/kWh (that's 74c USD/day + $0.21 USD/kWh)
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