Phases in Electricity

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The electrical grid relies on alternating current.  The power that runs our civilization is produced by generators in bulk, at 35 thousand volts, and converted to much higher levels to permit transmission.

A major consideration of electrical engineers is resistance, which increases as the load carried by a conductor (e.g., a cable) increases.¹ Several methods can be used to reduce resistance, such as arranging things so the electric transmission doesn't have as far to go (resistance increases in direct proportion to distance); increasing the cross-section of the wire; and selecting an optimal conductor for the circuit, like copper or aluminum.  Another method is to transmit electricity in more than one phase.

Alternating current generates voltage in a sine curve: as the rotor spins, it induces an electric current in the wire coils (windings).  The voltage produced follows the pattern of a sine curve over time: typically, the generator spins at 60 revolutions per second, resulting in a standard oscillation of voltage from its positive to negative and back to positive, 3600 times per minute.  Many generators are designed to generate three electrical streams concurrently, 120 degrees (one third of a revolution) "out of phase," that is to say, offset so that the three currents fill out the empty spaces in the sign curve.²

There are several advantages to this.

One is that a current that is balanced in three-phase transmission produces a lot less resistance for a given wattage,³ than does a single phase.  One can run 3 currents of the same wattage through the same conductor with only √3 times the resistance, provided the phases are offset equally.

Likewise, a three-phase motor puts out 1.5 × as much output as a single-phase motor of the same size.  Moreover, there is no tendency for the toque to pulse, as with a single-phase motor.  Lastly, a rotating field can be set up by passing three-phase current through stationary coils.

The downside is simply complexity.  Most of the time, single-phase motors are adequate for household use, and domestic grid configurations are single-phase after branching from the main line to the individual house.

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NOTES

1. Resistance is an expression of the mechanical work required to force a current through a wire.  Ohm's Law: V is voltage; R = resistance; and I = current in amperes (i.e., coulombs per second).  See "Ohm’s Law - How Voltage, Current, and Resistance Relate," All about Circuits.  This is usually written as I = V/R.  The amount of power, or wattage, is just I × V, so if you could just get electrical resistance super extremely low, it would revolutionize the whole electricity business.


2. Some electrical circuits need a "DC current" generator, which I put in quotes because it's DC in the sense that the voltage of the output doesn't change sign.  AC current, of course, alternates between positive and negative voltage.  A DC generator has a commutator attached to the rotor that switches the polarities as it spins, so that the voltage is always in the same direction.
   
   It's a bit like if a friend was pushing you around the office on a swivel chair with wheels.  You're too tired, and so your friend tries to "give you energy" by pushing you in a loop around the entire city block while you try to look dignified. That's DC.  AC is where the two of you don't leave the cubicle—your friend pushes you a very short distance, then suddenly pulls you the opposite direction.  You actually travel 80 centimeters each way, until you make your friend stop because it's giving you a headache.
   
   A DC generator is an in-between scenario in which your friend pushes you around the city block, but in 80-cm bursts that average out to moving as fast as if you were moving in a constant brisk walking seed. These 80-cm bursts alternate between complete stops and accelerating to 15 Km/h.


3. Wattage: the amount of mechanical work per second that a current carries. In AC, this is complicated by the fact that the voltage is continuously changing, but you can imagine the current required to run three coffee grinders concurrently, versus that required to run only one. 

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SOURCES 🙵 ADDITIONAL READING

C. van Amerongen, "Electric Generator (Dynamo)" (Volume I, p.64), 🙵 "Generator (Dynamo)" (Volume II, p.322), The Way Things Work: an Illustrated Encyclopedia of Technology, New York: Simon 🙵 Schuster (1967)

R.K. Rajput, A Text Book of Electrical Machines, 4th Edition, Laxmi Publications (2006); link goes to Google Book listing.