How does power work in this game?

[LightAsAFeatha]

I'm a pretty new player in the city-building genre, so all of this is pretty new to me. I have a city with a population of 19k. I've been using the coal power plants a lot and eventually I had to increase my budget of power to 150%. However, a lot of the different industrial, commercial, and residential districts seem to be weird with power. I try putting more power plants in the city and nothing changes. I tried using power lines and connected other areas with power to the areas struggling for power. Nothing happens. It seems like sometimes it works whenever I connect power lines completely surrounding the area that needs electricity, but other times it doesn't work. Am I missing something here?
Like I said, I'm very new at this, and this is my first city I have really ever built. (Also have problems with garbage and traffic as well)

[Tankfriend]

When you go into the power info overlay, or when you build power lines, you can see a blue area around buildings. That area represents the local power grid. To make sure that a power plant supplies power to an area of your city, the blue areas of the power plant and your city either have to touch directly (forming one large area), or the gap between them has to be bridged by power lines.

Besides, power production across all your city's power plants *is not shared*. That means that every power plant only provides the power it produces to the areas it's connected to. You could build a nuclear power plant somewhere in your city that's connected to nothing and its output will show up in your power production/consumption statistics, but your city won't actually be able to use that power without a connection.

To fix your problem, make sure that every single power plant and every area of your city are connected with each other either via direct local power grid connection, or by power lines.

['Strict]

What he said, but also, it's almost never a good idea to raise the budget over building a new building (if you have the money to build it). Raising the budget by 50% means you'll get 25% extra power or places in schools for example.
Lowering it by 50% means you'll only get 25% of the power or seats in the schools.

[leftbehind]

Where possible, prefer renewable power - not only is it generally cheaper, because you don't need to import as much ecocide, but it will reduce traffic as well because it doesn't need fuel delivering all the time.

[Waggy]

Maybe the coal plants aren't receiving coal from the delivery trucks due to traffic. Industry generates the most traffic in the game.

Try moving the power and garbage buildings to their own little separate area, away from industry zones.

[leftbehind]

and maybe give them their own harbour or cargo train station so that the only deliveries made to it are for the power station and it's not getting clogged up with other industry goods

[LightAsAFeatha]

Thanks for the replies, everyone. My city is much better in terms of power and I understand it much better than I did before. :)