Spot the handwaving!
The power grid of most civilized planets doesn’t use electricity. Broadcast energy is converted into electricity or light at the point of use, since electric charge is a well-understood and efficient medium for transmitting both data and energy, and light is a bit faster and has some extra quantum-mechanical goofiness for chip designers to play around with. What’s actually broadcast isn’t either of those – tesla coils’ massive magnetic fields have a hideously wasteful energy falloff (and tend to kill people) and microwave lasers need an unobstructed path from the transmitter to the target (and tend to kill people).
Instead, what’s transmitted is torque.
Nanosprings are a simple form of nanomachine, first discovered near the end of the 20th century, although for decades they were only used for cushioning impact. Modern nanosprings bear little resemblance to their ancient cousins – instead of an ultra-soft, thin film, they’re more of a pale white, gooey fluid. They’re also extremely toxic even if they aren’t charged, so you wouldn’t want to stick your finger in a vat of them. If they are charged, then not only would they soak through your skin and poison you if you stuck a finger in, but they’d rip your arm out of your socket and throw you across the room.
So don’t do that.
Nanosprings can store an incredible amount of torque per unit volume – less than antimatter, but far more than any other form of battery. Fortunately for the safety of the public, they release the energy ‘slowly’ – over the course of minutes or weeks, depending on the variety. Generally, for consumer goods, a variant (and volume) of nanospring is used that releases energy when unhindered at approximately 110% of the rated energy throughput of the device. So you don’t have to worry about your toaster exploding and killing you. The power tools in your garage… maybe.
If all they were was super-batteries, well, the world would probably look about the same, only with more recharging stations. However, there’s a certain kind of nanospring – a dangerously unstable kind, unfortunately – that is able to absorb and induce torque in ‘similar’ structures within a mile or two. Take a big vat of those, and you have an energy sink, so named because a singularity’s core is, somehow, a ‘similar’ structure, and thus the nanosprings are able to ‘cool off’ the singularity and keep it from spinning itself to pieces under repeated transformations, which would otherwise be even more of a problem.
As a side benefit, the energy sinks let you measure how fast your singularity is spinning, so you know when it’s about to explode from overspinning. This has nothing to do with a singularity exploding because its physics destabilized, or with a singularity breaking free of its containment and shooting around randomly like a bouncy ball of death – but those are measured and controlled by other means (‘the observer board’ and ‘lots of redundant repulsors’, respectively).
So the ‘powersat’ system works like so: you deliberately overspin your singularity, but surround it with a metric ton (or twelve) of dangerously unstable nanosprings in armored vats – your energy sinks. Depending on how the nanosprings are aligned within the vats (you can use magnets for that), a ‘broadcast energy field’ is created in which other, harmless nanosprings will spontaneously spin themselves up to a highly charged state and apply torque to whatever you want. Often, to a miniature electric turbine.
To power cities using powersats, the actual power satellite uses an actual microwave laser to transmit the energy to a sister station on the ground with its own set of energy sinks. Sometimes people just keep the singularity around on the outskirts of the city instead, with energy sink relays set up every mile or so to spread the love around – whether the giant microwave laser aimed at your city is more dangerous than keeping a potentially explosive black hole nearby is not a settled issue, but the satellite method is more common, thus the common term for singularities used primarily for power generation is ‘powersat’.
Another specialized kind of nanospring is known as ‘hull paint’, since the most important use is on the hulls of starships, although by both volume and visibility the most common use is as glowing neon paint to make advertisements stand out. Hull paint has fairly ordinary nanosprings in it, but also microscopic light-emitting diodes, letting it continuously emit the energy it absorbs in the form of light of the frequency of your choice and an intensity reflecting the strength of the broadcast energy field. ‘White’ is a common choice, since it’s the most efficient at dispersing energy, but the difference is small enough that many people choose to use it to make their ships look pretty. Or, in the CEC’s case, to make them all a hideous but recognizable shade of orange.
Starships without hull paint used to be utterly screwed, but eighty years ago someone developed a trick where the torque from the energy sinks could be inverted and used to spin the singularity back down. It’s not a very fast process – all but the very smallest ships disperse more energy through their paint – but it’s far, far better than nothing.
Despite being technically a nanomaterial, nanosprings are so important to modern technology that virtually all fabbers have a specialized, dedicated machine to build the common household varieties, and space-based fabbers will have machines to build hull paint and energy sinks. Nanosprings are genuinely easy to build, which helps this work – even 200 years ago, they were one of the simpler nano-scale structures to assemble.
Not all of this was made up on the spot! But I still reserve the right to change how this stuff works if plot convenience demands.