Okay, couple things.
Silver, manufacturing capital/power plants do not apply to mining. However, moons do-except when the aforementioned structures are present. Additionally, economic starbases apply, as well as (obviously enough) racial passives. I've tested this quite thoroughly and it's the same in DA and TA. Unless my version is bugado, anyway.
Also, Loupdinour makes an extremely valid point regarding TA-the Drengin and Korath are production monsters.
More ontopic:
First level power plants aren't worthwhile. From a build cost and research cost standpoint, second level power plants might be-250 industry to produce versus 400 for third level (quantum), and 20% as compared to 30% increase in production. The kicker here is the fact that quantum is 5000 RP/TP by itself, whereas the first two levels of power plants total 2000.
For a quantum with normal factories, you gain a benefit by using a power plant when you have one or more factories (16+6=22, 22>20). For a quantum with industrial sectors, you gain a benefit by using a power plant when you have three or more industrial sectors (16+48=64, 64>54). For an antimatter (second level) with normal factories, you gain a benefit when you have three or more factories (two doesn't quite cut it-16+12=28, 28<30, but 16+18=34, 34>30). For an antimatter with industrial sectors, you gain a benefit when you have four industrial sectors or more (16+64=80, 80=80).
As pointed out by CaptainYar (and potentially others), there is also the issue of maintenance. Additionally, by the time you reach industrial sectors, which cost 400 industry a piece to produce, 450 for a quantum power plant is quite valuable.
With all of this said. While it is not advisable to build the first level power plant, and circumstances can decide the usage of the second and third levels for you, it is worth noting that the manufacturing capital, even though it has been reduced to 33% from its former 100% (now 50% in DL, but I remember those days...), it is still useful, both late game to turn an otherwise borderline world into a reliable source of ships, and early game for either the homeworld or something large nearby to increase colony ship build quality or capacity.
As an addendum, a long long time ago in a galaxy far far away, if you guys can remember back that far, power plants gave 25%, 50%, and 100% with the varying levels. At that point in time, they were most definitely useful, but also most definitely overpowered as well.