In the United States, most power entering people's homes is one-phase power. The power generated at the electricity power plant, however, is three-phase power. This is the idea behind those large transmission lines you see attached to tall towers – these lines are supposed to transmit as much voltage as is feasible over long distances before this power is "tapped" and delivered to neighborhoods at a greatly reduced voltage.

Single-phase power is sufficient for virtually all household appliances, whereas industrial settings featuring heavy equipment require three-phase power. But what if you need three-phase power and all you have is the single-phase power entering your home?

Imagine yourself and two of your (obviously bored) friends walking back and forth at a brisk speed of 2 meters per second (about 4.5 miles per hour) along a path that runs north-south and measures 60 meters from end to end. Each of you starts at the midpoint of this path, walks to the northern end, returns to the start, continues walking to the opposite end, and returns again to the middle, thereby completing one 120-meter "lap," or cycle. Because each of you is walking at 2 meters per second, one round trip takes each person exactly 60 seconds.

Assume further that at the starting point, the "status" each of you is zero. You gain one unit of status for every meter you walk north and lose a unit of status for every meter you walk south. Thus whenever one of you reaches the northern end of the path, that person has a status of 30, while anyone making the turn at the southern end has a status of -30. You recognize that the three of you can maximally separate yourselves from one another by starting 20 seconds apart, because each circuit takes 60 seconds and there are three of you, and 60 divided by 3 is 20. If you do the algebra, you find that when one of you has maximized your "status" at a value of 30 by reaching the northern end, the other two are passing each other halfway along the southern section, one headed north and the other headed south, where each walker has a status of -15. If you add your status values together at such a time, they sum to 30 + (-15) + (-15) = 0. It is possible to show that, in fact, the sum of all of your status values at any time is 0 as long as the three of you are perfectly staggered as described.

This offers a model of what three-phase electrical power looks like, except that "voltage" is substituted for "status" and instead of one cycle occurring every 60 seconds, 60 voltage cycles occur each second. Plus, instead of each person passing the starting point twice per minute, the voltage passes through the zero point 120 times per second.

Because of the way power, current and voltage are related mathematically, three-phase power remains at a constant, nonzero level even though the three individual voltages add to zero at any time. This relationship is:

P = V²/R

Here P is power in watts, V is voltage in volts and R is electrical resistance in units called ohms. You can see that negative voltages contribute to power because squaring a negative number yields a positive value. The total power in a three-phase system is just the sum of the power of the three individual power values of each phase.

Also, if you ever found yourself wondering how alternating current (AC) got its name, you now have your answer. Voltage is never steady in either single-phase or three-phase systems, and as a result, neither is current; these are related by Ohm's law, which is V = IR, where I stands for the current in amperes ("amps").

To extend the pals-walking-back-and-forth analogy to one-phase power, simply imagine that two of your friends are called home to dinner while you continue walking, and there you have it. That is, three-phase power is literally just three one-phase power sources mutually offset by a third of a cycle (or in trigonometric terms, by 120 degrees). In a single-phase power supply, each time the single voltage briefly becomes zero, so does the power output. You can perhaps understand now why small appliances, which are not affected much by very brief lapses in power, can run on single-phase power, whereas large machines that operate at high wattage (power) levels cannot; they require a large and steady power supply.

All of the foregoing is more easily understood by consulting a graph of voltage vs. time for a three-phase power supply (see Resources). In this graph, the individual phases are graphed in red, purple and blue lines. These always sum to zero, but the sum of their squares is positive and constant. Thus given an unchanging value of R, the power P in these set-ups is also constant owing to the relationship P = V²/R.

For a one-phase supply, there are no voltages to sum up, and the voltage of single phase passes through the zero point 120 times per second. At these instants, power drops to zero but recovers quickly enough so that smaller lights, appliances and so on do not experience noticeable interruptions.

If you have a three-phase motor in a larger device such as an industrial-sized air compressor and do not have ready access to three-phase power owing to the way your local grid is set up, there are workarounds you can use to get your equipment properly powered. (One of these is to simply replace the three-phase motor with a one-phase motor, but this is not nearly as clever as other solutions.)

Numerous types of three-phase converters are available. One of these, a static converter, takes advantage of the fact that while a three-phase motor cannot start on single-phase power, it can stay running on single-phase power once it is started. A static converter does this with the help of capacitors (devices that can store charge), which lets the static converter stand in for one of the phases, albeit in an inefficient way that is assured of decreasing the motor's effective life span. A rotary phase converter, on the other hand, acts as a sort of combination of a substitute three-phase motor and an independent generator. This device includes an idler motor, which, once it is set in motion, does not turn any moving parts in the parent machines but instead generates power so that the entire set-up can mimic a three-phase power system reasonably well. Finally, a variable frequency drive (VFD) makes use of components called inverters, which can be used to create alternating current at almost any desired frequency and replicate most of the conditions inside a standard three-phase motor.

None of these converters are perfect, any more than a bread knife can be used to cut meat with ease. But a bread knife is better than your bare hands, and so these converters are actually good to have on hand if you often work with power-hungry machinery and tools.