This is true if you want to export the power back to the grid (aka grid tied), however, some solar controller systems can operate without this happening, and do not require any form of permission to operate.

Generally homes are grid tied unless they have batteries, simply for the fact that the solar power is generally available when power isn't in high demand, and not available when power is in high demand. So the daytime power is pushed to batteries, and the batteries are consumed during usage time (usually near or after sunset).

Systems can be augmented to use grid power when solar/batteries are insufficient, and do so without sending any excess power back to the grid.

These systems are generally more expensive than grid tied systems, but they have obvious upsides to power availability when the grid is not delivering power. Another caveat is that most solar systems are not built to be able to handle the full power load from a household, so some things will be solar while many others will not be.

Unless you're exporting the power, a permit is not required for generating power with solar. Installing it, however, you may want a permit for that....

decreasing certain plant outputs.

let's be honest, this is the real threat, oil/coal/natgas based power production would take a hit midday, because at the end of the day, the shareholder is simply more equal than you are, and he is owed the income