Prorating binary state structures (Radar/Stealth)

Option 3 could also be confusing: "The radar is on, it has power, so why doesn't it work?"

I think there's two parts to preventing confusion, and they're somewhat related:
1) We want someone totally new to the game to be able to see the symptoms of an energy shortage and realize it's an energy shortage
2) We want someone who has been playing the game for some time to rapidly recognize the symptoms of an energy shortage

I think there's a very quick way to illustrate a power shortage: put cosmetic lights on structures. The lights flicker or go out when the power runs out.

There are, of course, other UI tricks to highlight a shortage, but that seems like the most intuitive to me. If you want a specific vote, I lean towards option 2 for simplicity and obviousness to player. Proportional range is a neat idea, but (similar to the shortage scenario for option 3) in a severe power shortage it could be difficult to diagnose what the problem is.

Make radar work like force fields. Radar have batteries. When their batteries are drained, they take a nap for a while until their batteries are fully charged again. You can then have them charge up proportional to your power production.

This solves the flickering and this works with the flow economy. Structures take naps until they are recharged. You can also then balance how things react to power shortages. Metal extractors could keep running for a very long time before they have to take a nap. It would give you time to react to the situation and perhaps power down things you don't currently need.

Yeah I think this is the best option.

I'd also add a flickering graphical effect that doesn't prevent you from detecting things but lets you know your radar is about to go out. It kicks in as your radar's energy consumption exceeds your spare power production that can go to your radar. Basically whenever your radar's batteries go under a 100% charge, and then the flickering is more noticeable as the batteries go down.

So build in energy storage with a bar in UI?

Kinda like that, I guess. It could work, as long as the battery charging doesn't impact the building's overall energy drain (so whether the battery is full or just charging up, the building always uses 5 energy/second) otherwise it'll get confusing because the building sometimes chews a lot of energy and sometimes a little. Also it'll mean that getting out of a stall will be harder, because all your buildings are not only battery-dead, but also draining more energy than normal because they are trying to charge.

I also like the idea of building a power station next to a building as a way of prioritizing. Simplest one I've seen yet, and works pretty well in this situation.

But it must be this way if.
Or you can abuse it and effectivly half the energy drain of a building by turning the normal energy on and off: charge up turn off drain energy turn on charge up and so forth.

That's a very risky strategy, where you are sacrificing your reserves to save on operational costs. I don't neccesarily see a problem with it; it'd mean that if your power goes down just as you've drained all your batteries, you're in trouble.

(Alternative easy fix; you only have "on" which drains power and "off" with shuts down the building without using the battery, leaving the battery charged for when you turn it back on)

I think whatever method is chosen, it must be made clear to the user what happens, and how to rectify it so that noobs can pick up the concepts quickly. Whether this is through a tutorial, FAQ or some other method, I'm not sure.

Equipment in PA should have levels of efficiency and some should be auto on and some should be power level 1-10 and have different effects at each level.

I would think a priority system is better. Just give Low, Normal, High priority buttons to things that suck resources. And then allocate incoming resources to them from High to Low.

The 1s power on/off flickering is a sign of trouble and yes, its vulgar and very distracting. That's the point! An energy stall is very Very bad and it should jump up and down and spit in your face to get your attention to solve it.

with a proper UI, I don't see the problem with having radar scale to the % that it is powered.

Perhaps the biggest question of all is What can and can't be binary? I think you'll find that ANYTHING can have a binary function without exception or issue. However, not everything can work properly with only partial resources. The latter issue means that every single device needs to be considered and given its own rule set for when power runs short.
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In TA, everything was binary with minimal exception. An energy stall would cause everything to shut down for a second, eliminating the energy usage. This gave a surge of energy for storage, giving a few more seconds of stable operation until the stall happened again.

The only devices that were irreconcilable in TA were self-repair and unit upkeep costs. These costs were almost insignificant, and virtually every unit created equal or excess energy for its own upkeep anyway. Creating a permanently flat bar was virtually impossible. Interestingly enough, late game mods did not allow extractors to be shut down by a stall, creating a priority system that existed even in TA.

In Supcom, the prorating economy created a great number of issues as devices would simply malfunction. The status of stealth/cloaked units was completely unknown, and radar facilities would flicker in unpredictable ways. The only thing that worked without issue was a fair and even distribution of build power. I think it looked cool, but ultimately caused more headaches than it tried to solve.
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I dunno about you, but TA's "burst prorate" system was so much more obvious and effective on every level. When things flickered, you knew exactly that it was offline, how badly it was stalling, and could see when the next outage was going to happen. Besides, the server is only going to spend so much bandwidth on telling you where your money is at. The numbers don't need to update every 1/10th of a second to still count as a streaming economy.