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.