I've been having trouble keeping power supplied to the Living Quarters, amongst other rooms.

As an experiment, I built some power generation rooms directly over the two priority Living Quarters to see if I could keep them permanently "on".

That experiment failed and I destroyed the rooms since it wasn't achieving the goal.

My Vault is consistently running on low power levels since I don't have the personnel necessary to run both major generator rooms simultaneously.

Is there something I am not getting about power generation?

What rooms are deemed high priority when it comes to power?

And a side question, when I acquire a Nuclear Power Station, does it actually need to be near the rooms it is powering?

I am planning to put it as physically far from the rest of the Vault as possible, because I am not comfortable with having it close to any of the major areas.

But will this diminish the power over distance supply?

The game says rooms furthest from the power supply shut down first and if the NPS is so far away, will it be inefficient at supplying power?

It doesn't need to be near the rooms, however the first rooms to shut down are the ones farthest from the reactor, same as the power rooms. I have 9 (merged into 3) reactors and I still have a hard time powering everything (82 dwellers). Ultimately you always need to choose whether you would rather have 1 room working at peak, or a set of 3 working less than peak, or 3 sets of 3 at less than peak. Early on I built everything in triples and I always found it better to have two triples staffed with 4 each than 4 individual power rooms fully stocked. Now my biggest problem seems to be keeping the dwellers all fed.

The more INDIVIDUAL rooms you have, the more power you consume. Merging rooms saves in power consumption.

Then make more. Find people who have high Strength to breed to increase your odds of kids with inherently higher strength.

Get a weight room to buff them up a bit first. Army fatigues are great for buffing with clothes too.

If your vault dwellers take too long to get jiggy, put some Nightwear on them to move things along (Charisma shortens the time before they do the horizontal tango). Also, zoom in all the way on the room to see if they're saying anything about "spending time with family", as dwellers won't breed with kin and it can get hard sometimes to remember who's related to whom. Get a radio room and staff it with high CHA people to not only bring in new people, but fresh genepool water. And yes, any celeb vault dwellers you have will breed too. I... kinda turned Moira Brown into the Vault Bicycle in an effort to propogate her redhead genes...

Also DO NOT DEMOLISH ANY LIVING QUARTERS WHILE YOU HAVE PREGNANT WOMEN. You can induce the Perma-Preg bug that way.

Production rooms are vitally important to the Vault. So when you say "I don't have enough Dwellers to properly staff the power generators" then, you need more Dwellers. However, with more Dwellers that means you need more Food, Water, and Guns to ward off Radroach attacks.

I know guns are not really what you are concerned about in your OP but it's still important since what you need means a population increase. I just sent out the 16 new Dwellers I have into the Wasteland with no Outfit or Weapon so they could get a Weapon. All my dwellers always have a Weapon. My next goal will be to send out everyone with a BB Gun that does 0-x Damage. I want them to all have a 10mm Pistol or better. Dwellers will equip a better gun if they find it so while they are adventuring I will be able to see that the found a new weapon once they are no longer holding the BB Gun. Once you recall them and they arrive at the Vault Door, before you click Collect you can toggle the BB Guns so they are sold rather then going into Storage.

In http://www.gamesas.com/topic/1521786-enhanced-vault-dwellers-survival-guide/ I have some Examples of Vaults from 10 to 68-ish Dwellers that show what I had for resources. I never updated it but I do talk about my pitfalls after going form 50 to 55 Dwellers. At 50 Dwellers I thought I had the right amount of resources but after getting only 5 more dwellers the Vault could not sustain them. I had to build more Food, Water, and Power in order to get it balanced again. Currently I have 123 Dwellers and I have about 2100 Power Storage and 975 Food and Water Storage. I have been finding I am low on power reserves. So while I have plenty of storage I can't keep up with the power drain from all the Vault Rooms I have. I have to build another Power Generator and see if I can max my power reserves.

I'm getting way too nerdy and geeky with the math but here is something I figured out. I have 34 Rooms according to the vault list for my main vault. I was Consuming 0.93 power every second however, I was making 1.33 power every second. Wasn't that good. To speed that up all I have to do is shorten the time when I can collect power from the power stations. If I can collect power from any of the 5 power stations every 1m 51s then I will make 2.20 power every second. Which should be a better ratio.

More simply put, a fully upgraded 3 wide Power Station should be collected every 1m 51s or less. Which can be done by having Dwellers with a high strength. I figure I need each Dweller to have 6 Strength which includes the bonus from the Outfit. So an outfit of 2 strength and 4 base strength, equals 6 Strength. I have 5 Power stations so once I can collect them that frequently I feel I should be stable. I need to do more testing.

EDIT: In fact once i had all my dwellers to 6 or higher including outfits, everything was smoother. I maxed out all three of my resources. Which is good because I have 16 people Adventuring and once they return then I will have more demand on my Food and Water reserves. Power should stay the same since, "Rooms run on power, Dwellers run on Food and Water."