Residential Power

Ordinary buildings like houses are powered by AC. As an electrical engineer, you hear stuff about phases and if you’ve ever done some electrical work you may have dealt with multiple source wires.

The terminology that electricians use is somewhat misleading. It’s based on the right concepts but if you just hear the words and try to parse them into what’s going on, it’ll lead to confusion.

Voltage, Current and Power

The source in a typical US is a single-phase AC feed. It’s a general sine wave at about 60 Hz with about 110 V RMS. An ordinary house will support anywhere from 100 A to 200 A, although there are some systems that could supply more or less. 150 A seems to be fairly common these days, for 16,500 VA total power. That’s volt-amperes, not watts, because it’s uncorrected for power factor.

Because the power factor isn’t corrected, and for other reasons, the sine wave is often dirty. For bulk AC power and with the power factor of ordinary household devices, it’s clean enough. Because it’s dirty, the frequency may drift slightly, sometimes +/- 5 Hz. My, “good,” devices list +/- 8 Hz tolerance, but that’s because they’re centered at 55 Hz to accommodate for other places in the world where 50 Hz is the center frequency.

The voltage can vary greatly from system to system but is generally fairly uniform within an individual system. That is, you can measure your outlet voltage at home and it’ll probably always be the same, but your friend in a different neighborhood may very well usually get a different number. 110 V +/- 10 V is a good guess

The current is the only systemic independent variable in the system. The breaker panel manages maximum current per circuit. In this sense, the entire system is a circuit hanging off the source system and therefore has its own maximum current, which is the source current rating. Some devices manage other variables, such as arc- or ground-fault devices, surge (inrush) protectors and UPS devices.

I’ve glossed over power factor so far. An ordinary residential system in steady state can ignore PF, inrush, backflow, standing wave reflection, and generation. They all exist and are measurable. However, UL and ETL certification (or devices that are within spec even if not certified) and code compliance demand that devices and the system tolerate the variance outside of source forcing. Systems with notable generation function, like solar installations, or high power factors, like some shop equipment, have active correction. All of these unusual cases are covered separately.

Lightbulbs

An ordinary device that’s plugged into a wall outlet, like a coffee machine, USB brick or TV, gets this 110 V. Its circuit, the subsystem it is attached to, is generally capped at 15 A or 20 A.

All the other numbers are mostly moot. The preponderance of household appliances either run fine off dirty AC with wide tolerances, or convert the AC to DC anyway. DC conversion to well below system voltage is now the most common case (device by device, and sometimes even as a share of power used) so as long as the power is there, your device doesn’t care.

Incandescent lightbulbs use dirty AC. The filament wouldn’t care much if the voltage drops to 82 V or if the source sine wave looks more like a wooly sweater at 36 Hz. Neither would a toaster heating element or, to a lesser extent, the compressor in a refrigerator. LED bulbs convert to DC. Fluorescent and CFL bulbs require a ballast (AC to AC converter) that smooths out many imperfections.

If you’ve ever designed an AC-to-DC power supply, you know that it probably doesn’t matter too much how gnarly the source looks. The feedback loop in any modern upstream converter stomps any difference like this. If you’re an electrical engineer born after about 1930 and you don’t know the fundamentals of AC-to-DC power conversion, either you haven’t learned them yet or I want to talk to you because you’re an interesting special case. If you’re an electrical engineer born before 1930 and you’ve read this far, I want to talk to you because you know things that are about to get lost below the noise floor of AC-to-DC power conversion.

Higher Voltages

Note that I didn’t write 240 V. That’s because you don’t get 240 V, or 220 V, or anything like that. Not really. This is where the phasing comes in.

The source of this residential power is a 3-phase, higher voltage system. Power transmission over long distances is much more efficient with very high voltages and three hot lines plus ground. The three phases are separated by 90 degrees, leading to a much higher RMS potential with the same absolute voltage swing. A substation somewhere nearby converts this into close to 500 V, single phase.

Most residences have, or share with a few neighbors, a transformer. This transformer does two things: it steps down the voltage to a 220 V RMS center voltage, and it is center-tapped, thus providing a new, “neutral,” return line. The neutral is very different from ground, although it should carry the same potential as an earth ground, in theory.

Thus, the power received is actually 2-phase 110 V RMS, with opposing (180 degree) phases and a floating center-tap neutral. The symmetrical opposition of the phases is guaranteed, minus aberrations, which are rare. Ordinary devices use one leg to neutral, providing 110 V RMS. If a device needs a higher voltage, the potential between the two legs is 220 V, ignoring the common center-tap neutral.

This is called, by electricians, “single-phase.” The term, “two-phase,” although misleading because single-phase actually has two phases, refers to a special case and some outdated systems. When an electrician talks about a phase, they are referring only to 90-degree phase differences.

Somehow, the concept that a phase could be 180 degrees separated from another, got dropped. In the usual case, we jump straight from single-phase to three-phase, which is the next source option, with 3, 90-degree-offset phases, and higher voltage. Essentially, a three-phase system skips a portion of the upstream substation and provides this function itself.

Electrical Code

This system isn’t designed this way just to make it simple for electricians, or because it’s easier to deliver this way. It’s actually more work, so much more that it warrants the conceptual simplification, and by a lot.

A simple method must be determined for calculation of the independent variable, breaker trip amperage, for a given circuit. This is based on a need to prevent arcing in a real system. Arcing occurs when the breakdown voltage between two conductors is less than the potential they carry. The two primary breakdown-prone media are air and insulation.

Air gaps are fairly easy to conquer. The minimum allowed space between exposed conductors is specified to be more than some given amount. This plays into exposed lead lengths and physical specifications for things like junction boxes and outlets. These specifications are also baked into consumer equipment requirements like UL listing. The minimum air gap in a 220 V system is actually fairly small, a handful of mm, so as long as stuff is either insulated or solidly fixed in space, there isn’t much to worry about with some good design.

Insulation is much harder. This is where most of the requirements come from. The short version is that the breakdown voltage of a given plastic generally changes with temperature. (Most insulation is now plastic, although the same principles hold true for most non-polymer materials used for insulation.) Like any good real-world system, breakdown potential to temperature is non-linear. A common residential electrical system has now become a complex multivariate non-linear system. Contractors need to build houses and manufacturers need to produce materials for them, with no time to solve this system for each house separately.

So we introduce electrical code. Put requirements and minimums on common materials, determine a margin of error, and calculate maximums once for the common case. Draw up charts for these cases.

The voltage in the system is fixed. Circuits operate either on 110 V or 220 V. Establish a voltage tolerance and ensure that the power supplier, the utility company, remains within it. Over-voltage surges often blow transformers, which is adequate protection. Over-voltage transients, or surges, of short duration, may be passed by transformers, or may occur downstream of the last transformer. Equipment is on its own to handle these. Heating is slow, so this should not affect insulation breakdown in the general case. Low voltage is less of a problem and is generally ignored.

Voltage drop, however, is significant. The system has impedance. Assuming a clean-ish 60 Hz sine wave potential force from the supplier, ordinary AC artifacts, like power factor, can be ignored if they’re smaller than reasonable tolerances, which are also set by code and listing. Therefore the system behaves like pure DC resistance.

The conductor material for wiring is limited to either aluminum or copper, which are the two most commonly used wiring materials. There are two charts, one for each. Hybrid materials, like the very common copper-clad aluminum, can be generalized if within specifications, lending partially to skin effect. Similarly, the size and shape of the conductor is regulated, the shape being round and the size varying according to wire gauge. The wire gauge ends up as an axis on the chart, because more wire leads to higher cost.

Insulation material is also limited, although the end user doesn’t see this much. Wire simply isn’t produced using insulation materials that aren’t within spec, partially because the price-availability curve for those materials doesn’t make sense, and partially because some materials just aren’t used. For example, peanut butter has a breakdown voltage, but there aren’t a lot of wire producers lining up to make peanut butter-insulated scandium wire. This is probably because the market for this is small. A wire manufacturer calculates once that a given gauge with a given thickness of a given insulation material matches requirements. An electrician or homeowner simply needs to know that the produced wire meets requirements.

The heat problem is complicated, because radiation and conduction can vary greatly. Many assumptions are made in this area, which comprise the bulk of electrical code. They aren’t generally electrical, such as the space that conductors may run through, which likely confuses a lot of people. Some more on that later, but for now, it will suffice that the code requires largely that the space around an insulated conductor carry away enough heat that the steady-state temperature of the conductor under load eclipses the ambient temperature immediately surrounding the wire. This is not as complicated as it seems, because the conductor is rated to operate at temperatures around 60 degrees C, which is much higher than ordinary ambient temperatures.

Thus the problem has been reduced to run-length DC resistance. Lengths of circuit runs are limited to 200 feet or less, further simplifying the problem. We are left with the, “ampere capacity,” of a given specified wire type, or ampacity.

For instance, the ampacity of a 14 gauge 3-conductor (2 live 14 gauge copper-clad lines plus an appropriate ground) structured cable like Romex at 65 C is 15 A. Therefore, if you run this wire for a branch circuit, the breaker on the panel supplying it must trip at 15 A or less. These values may be looked up on a chart. All the supply equipment on this circuit must be rated for 15 A or higher, like outlets and switches. Load equipment ratings are moot at this point: if a space heater tries to draw more than 15 A from this circuit, the breaker will trip and the circuit will go dark.

There is also a separate chart for use in confined spaces. This is named by its most common use, conduit fill. A conduit longer than a certain length does not carry heat away from conductors as well as open air. Therefore, most of the space in the conduit must be open air so that the heat convects. A trivial case of this is a, “short run,” such as a conductor passing through the hole in a framing stud; technically this is a conduit but it is of little enough practical significance that it is excepted in code. A less-trivial case is structured cabling, like Romex, where multiple conductors run in parallel with a binding shroud (for convenience of pulling). This case isn’t called out in conduit fill, but rather drastically lowering the allowable temperature. Single-conductor is specified to 90 C, while structured cable is specified at 65 C. This is a difference of 45 F, which is the same as or more than the inside-to-outside temperature differential in a great deal of residential construction.

Ramifications & Notes

Of special note, given this information, in a 3-wire system, the selection of the common neutral wire is simplified. If there were two ordinary circuits, each with 110 V potential, and a single return, the return would need to be sized for half the resistance (trivially, twice the diameter) as the hot wires. This is never the case, because the two live wires are guaranteed to be of opposing phases. 220 V load equipment ignores the common neutral. If two devices were on the opposing load lines, their instantaneous voltage would always oppose, thus keeping the maximum potential on the neutral wire at zero.

The earth-ground-ness of the neutral wire is also of some note. An earth ground is a funny thing. In an ideal world, all earth ground would always be at a potential of exactly zero with an infinite ability to sink (or source, if you use Franklinian current) electrons. Also in an ideal world, the common center tap on a transformer would always be at zero potential compared to the end taps. Neither of these assumptions holds true in the real world. The source from the power supplier often comes without ground, often to save the high cost of running a very long, very large ground conductor. In many cases, it is expected that a residential subsystem can find its own ground, which can be complicated and is usually difficult.

The ground wire is also of a smaller gauge in some circuits. It is not expected to carry steady state load, so therefore will not heat much, and can have a higher resistance. For instance, #6 structured cable (6/3 with ground) carries a #10 bare copper ground wire, which is to specification for up to 60 A ampacity.

Eating for humans

I’m going to cover the topic of eating and dieting as best I can. This is a rant.

The most important thing to consider about dieting is that our bodies are a relic of our animal roots. The system by which we function was designed (evolved, how ever you want to look at it) back in a time when food was scarce and there wasn’t a lot of bartering. We’ve been farming for a few thousand years and we’ve had a commercial society — going to the store to buy what you want to eat that’s grown by someone else — for a few hundred years. The kind of change that would move us out of this space (once again, call it evolution or not, depending on what you believe) happens on the scale of tens- or hundreds-of-thousands of years. No one alive right now is going to be converted out of the cycle I describe.

At a very base level, you convert energy in food into energy used to run your metabolic systems. This is your heart and lungs, your muscles and also your brain. They all take energy to run. We measure energy in calories, which are actually kilocalories if you’re specific, and is a grossly simplified measure of energy as used by our bodies.

One calorie is the amount of heat (roughly, pure energy) necessary to raise one ounce of water by one degree Fahrenheit. It’s a great measure of a specific thing in the physical world. Because the numbers are large in the human-dietary scale, we use kilocalories, or thousands of calories. If it says on your chocolate bar that it’s 230 calories, the chocolate could be used to raise 10 gallons of water from room temperature of 72 F to 108 F, if you burnt it right under the water in a closed system.

Interestingly, that’s actually how a lot of the, “nutritional information,” on some foods has been calculated in the past. Set it on fire, see how much energy comes out, and that’s the caloric content.

Here’s the first big problem: I don’t know of anyone who has a blast furnace in their guts. Calories measure burn energy content, not the amount of energy that a human’s metabolic system gets from the food item. The human digestive system is much more complicated than that, and when it’s done processing what’s put in it, the result isn’t pure energy.

So at best calories are an approximation of how much energy is available in food. Just because 230 calories of pure energy are available in your chocolate bar, that doesn’t mean your body is getting that amount out of it.

The math is simple if you’re willing to abide by the approximation. There are 3,600 calories in a pound of fat. This is the kind of fat used in our bodies to store energy. Fat cells aren’t created or burned, they just gain and lose energy. (This is why liposuction works fairly well. It’s also a lot of the reason why people, “gain,” and, “lose,” the fat they carry in different places.) So a pound’s worth of fat cells can hold 3,600 calories.

Information on energy used in various activities is very readily available. Depending on your size and what activity you’re undertaking, you burn some number of tens to hundreds of calories per hour. Doing nothing — just letting your heart, lungs, brain, etc. go at it without using any of the muscles on the diagrams on the machines at the gym — is an activity. You can figure out your base metabolic rate (BMR) using various methods, some of which are simple approximations and others of which are somewhat ridiculously complicated. That’s basically the number of calories you burn in a day without doing anything else.

Calories in minus calories out divided by 3,600 is how many pounds of fat you gain in a day. Basically, if your BMR was 3,600 calories and you ate nothing and did nothing, you’d lose one pound a day. Unfortunately, the fact that a calorie is a bad measurement of metabolic energy use kinda torches that equation.

Part of the complexity rides in the fact that different foods contain different chemical structures to hold the energy. If you’re just burning it in a fire, that’s pretty irrelevant. But if you’re using it in a human metabolism, it’s probably more relevant than how many calories it contains. Depending on how your metabolism runs, for a variety of reasons, one calorie of burn energy in some food could end up delivering way less to your body. (Incidentally, it’s physically impossible for that calorie in the food to deliver more energy to your body, according to Newton’s Third Law.)

How your metabolism runs is a very delicate balance that has been the subject of many a fad diet. Some genetic things play a part, which is why most of us know that person who never seems to gain weight regardless of what or how much they eat. How much exercise you do makes a very large difference, hence our doctors’ constant insistence that we get a lot of it, regardless whether we’re dieting or not. Exercise doesn’t only burn calories; getting a lot of it also causes your BMR to change in a higher-numbered direction. Your level of hydration, stress or anxiety, mental activity, and other things like that change how your metabolism works also. But a key to this is also the content of the food.

The things we call, “carbohydrates,” are probably the simplest direct connection to energy content. Some carbohydrates are very close to 1-to-1 in terms of pure energy content versus how most bodies will process them. Fat is a very dense source of calories, which is slightly harder to digest but much more rewarding to the metabolism. Protein contains calories, somewhat tangentially, but they’re still there. Water — most of what most of your food is made of — contains none if it’s pure. Most other nutritional things, like vitamins and such, don’t contain enough to tip the scales in the quantity we eat them. We also stew over things like dietary fiber and amino acids, some of which are significant in this equation and some of which aren’t.

The formula of calories-in-minus-calories-out is good in some ways. A la Newton, it does establish a maximum criterion. If you ate 1,800 calories in a day, did nothing, and your BMR was 1,800 calories, you’d never gain any weight in fat because there simply wouldn’t be enough energy in the food you’re eating to deliver a net gain for your body to store. Also, it’s simple. Oversimplification sometimes gets us into trouble but a correct amount of simplification often gets us out of trouble as well. It’s also a functionally abstract formula: given the number of factors that go into the details and how nearly impossible it is to measure the in, the middle, or the out, the system is pretty much chaotic; a simplification is as good as any other way we have to figure it out quantitatively.

But that brings us to qualitative, which is really the more important part. It’s also where the animal brain comes in and also why it’s so difficult to diet. There’s a brain connected to this whole thing.

Those factors which affected your body’s ability to use food for energy also affect your brain’s desire for you to put food into your system. If you’re dehydrated, your brain is going to make you want to eat more because most of the food we eat contains mostly water, and it’s thinking it could work towards rehydration if it just had some more food to process. Long distance runners often have some problems keeping light because exercise makes your body want more nutritional content, which, if you’re not getting your dietary content perfect, means more food.

There’s an answer to each one of the problems. If you fast — essentially, if you don’t eat minuscule amounts constantly — your body will want to store extra energy to build up reserves for later, so don’t fast. If you have a disorder like diabetes, manage your intake carefully. (Diabetes is as much a disorder as aging — none of us are in perfect, “order,” or we’d never die. Life itself is a disorder.) Don’t think too much, maintain a stress-free life, eat a perfect diet (even though it’s impossible to know exactly what’s perfect for your body at any given moment), exercise several hours a day, hydrate perfectly, and you’ll always be in your top condition. There’s the answer. Good luck with that.

Enter the diet. Something is out of perfect alignment so we’re going to try to fix it. The real fix is complicated. I once knew a guy who was in great shape whose answer to staying trim all the time was to always go to bed hungry. The other side of the coin is the lemonade diet. Everyone has enough willpower to drink lemonade so what could possibly go wrong? Surely there’s some silver bullet, “trick,” that will make our bodies think they’re getting more than enough nutrition while eating just a little bit. Appetite is suppressed, weight is lost, the clouds part, beams of sunshine radiate, and angels sing.

Some diets do work for a while. Generally, the harder they are, the more they work. The quality, “hard,” is very subjective: Weight Watchers points are exciting to calculate for some and a total drag for others. Unfortunately, your body is much better at adapting than your brain is. Eventually, anything you do other than keeping a perfect balance will get adjusted out of perfection. The only thing that works consistently and permanently is hard work.

A great deal of the information we get is meant to mask the work. We’ve invented terms like, “trans fat,” and, “good fat.” All fats are good in the right amount and bad if overdone. We need fat to live because carbohydrates alone don’t have the energy density necessary to keep a human going at full steam. Eat too much of it — and fat is delicious because our brains are still trying to plan ahead for that time they’re sure is going to come when we don’t have enough energy stored to survive — and you gain weight. Our bodies are remarkably fantastic at managing our metabolism. Regardless of how many buzzwords or trends we hear and pay attention to, our bodies are never out to exact revenge or trick us. Every minute is a new minute to them and they’re going to try their best to handle right now and the future, even trying to do what they can to clean up past mistakes.

Just keeping a decent balance, even if a perfect one is out of reach, is hard work. It means not eating that thing you want to eat sometimes. It’s a lot like unconditional love of a child: doing something good now doesn’t mean you’re banking, “good points,” so you can do something bad later. The bad you do later is bad regardless how much good you did before.

Finally, on to how to eat like a human. Eat. Follow all the really good advice — not the advice that sounds easy or fun — from your doctor and your grandparents. Enjoy eating. Don’t do it as revenge. Listen to what your body tells you because it’s the closest thing to real information that you’re ever going to get. The fewer rules you have, things you don’t eat or refuse to eat, the better your health will be. Take the effort to make the difficult choice each and ever time it’s at all possible, including eating the right thing and getting the exercise. Don’t pay too close attention to little details because we’ve all been lied to so many times it’s impossible to count them. If something is all details — most fad diets are — it doesn’t deserve much attention. Always give yourself leeway to live life and never give let yourself go overboard on anything.

Making construction materials out of shredded paper

Here’s my deal: I have a paper shredder. Back when I lived in an apartment complex where someone just came around to fetch the trash, I threw the stuff out and I was okay with that. Now that I’m out in the country, I have to pay for this service and I’m limited by volume. Shredded paper is bulky. So I want to do something else with it.

I bet I can turn this into a construction material. It’s probably one of the cheaper materials I can make, I think. The base material — the thing that makes up the bulk of it — is free.

The Paper

The paper I’m using is shredded junk mail, mostly. I don’t separate it much. The envelopes have the plastic see-through windows on them for the address; that gets shredded along with everything else. Sometimes I shred old CDs (because why would you keep CDs?) or credit cards. Pretty much whatever comes in the mail or whatever I don’t want to just throw out because it’s got sensitive information on it.

I’ve got a very standard cross-cut shredder. I think I got it online for a couple hundred bucks. It works fairly well. I have the shredded lubricating sheets which I use once in a while and I usually bag the shreds. I used to not bag them and it was an awful mess.

The Concept

I’d like to make bags full of compressed paper shreds. I’m really flexible on the result, it doesn’t have to meet very stringent requirements. I don’t want to add too much to it and I want to use standard bags. The shredder bags are fine. Regular plastic shopping bags would work too.

I don’t need a permanent material. I’m not actually building a load-bearing structure. My first need is as a liner for a graywater system. If it works well, I may use it as-is or modify it to do bigger and better things. Mostly, I want to see what the properties of it are.

The Research

My first hit came up with this thing about papercrete. It sounds a little rude but the concept looks like it’s exactly what it up my alley. They’re making blocks that I’m imagining are going to be similar to cinderblocks. They use them for actual construction and there’s no plastic bag liner. They do say that they absorb a lot of water so maybe if I modify the plan to work with a plastic liner it’ll be more water resistant.

Papercrete

The people making this stuff seem like a bunch of people just like me. They have space, tools, access to stuff, etc. and they’re looking to re-use their clean, dry trash for construction materials.

They’ve got a process and it seems like most of their stuff is based on that. I couldn’t find any recipes so I’m going to have to adapt their method to use what I have.

The core of their process is some fancy custom-built shredder thing. It’s quite clever: it’s a trailer that you run behind a truck and it uses the motion from the turning wheels to shred paper and mix it with concrete. I’ve got a cement mixer though, and my paper is already shredded. If I can adapt the process, I think I can make it work.

So he’s got a stock tank of some unspecified volume that’s 4 feet in diameter. For this setup, his proportions are a 3/4 full tank of water, 75 lbs of material and a 94-lb bag of portland cement. I’m going to have to re-scale this and I’m going to have to weigh some of my paper.

As for the tank, I found a similar-looking one on Tractor Supply’s website. It looks to be about 75% as tall and it’s half the diameter, but it’s measured at 23 gallons. Doing some math, I’m estimating that his tank is about 29.6 gallons. Let’s call it 30 gallons. So that’s about 7.5 gallons of water or, by weight, about 1.25 lbs of water for every lb of paper. Similarly with the cement, it’s about 1.6 lbs of cement per lb of water, or 2 lbs of cement per lb of paper. So paper-to-water-to-cement, by weight, should be about 4:5:8.

Modifying the directions and stuff a whole bunch, here’s what my first run is going to be:

  • 30 lbs of paper, pre-shredded by my shredder.
  • 1 60-lb bag of regular Home Depot high-strength Quickrete.
  • a 5-gallon bucket of water, mostly full.

Depending on how much volume 30 lbs of shredded paper takes up, this may or may not fit in my (3-1/2 cubic foot) cement mixer. The actual amount of water was 4.69 gallons, but that rounds well within 5 gallons — a contractor bucket — given the estimation error on this whole thing. Plus, the person who posted the papercrete block article seemed imprecise with the water and I live in a fairly dry climate. I figure that at worst, it’ll take a little time for this to dry. I’m also substituting the cheaper concrete mix for portland cement. I had a roommate in college who was a civil engineer and went to concrete lab all the time. He could probably tell me the difference between concrete and portland cement, or I could look it up. I don’t know if it matters though. 30 lbs is 3.75 gallons of water. I know without even picking it up (again) that a full shredder bag doesn’t weigh that much. I’m probably going to need 2 bags full.

More to come as I get to trying!