Why do most aircraft use three phase AC electrical power? It is for the same reason most houses use two phase power, it is safer and allows for smaller wires. Chances are the power coming to your house is actually a single phase that has been split by a transformer, but from the perspective of your home circuit breaker or fuse box, it appears in two phases with a neutral wire in the middle. If your airplane has three-phase AC generators, each will probably have four large cables: three phases and a neutral wire that plays that part for all three phases.
Understanding this will help the next time you are dealing with an aircraft electrical problem on less than all three phases.
Three-phase electric power is a common method of alternating-current electric power generation, transmission, and distribution. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. It is also used to power large motors and other heavy loads. A three-phase system is usually more economical than an equivalent single-phase or two-phase system at the same voltage because it uses less conductor material to transmit electrical power. The three-phase system was invented by Galileo Ferraris, Mikhail Dolivo-Dobrovolsky and Nikola Tesla in the late 1880s.
In a three-phase system, three circuit conductors carry three alternating currents (of the same frequency) which reach their instantaneous peak values at one third of a cycle from each other. Taking one conductor as the reference, the other two currents are delayed in time by one third and two thirds of one cycle of the electric current. This delay between phases has the effect of giving constant power transfer over each cycle of the current and also makes it possible to produce a rotating magnetic field in an electric motor.
Three-phase systems may have a neutral wire. A neutral wire allows the three-phase system to use a higher voltage while still supporting lower-voltage single-phase loads. In high-voltage distribution situations, it is common not to have a neutral wire as the loads can simply be connected between phases (phase-phase connection).
Three-phase has properties that make it very desirable in electric power systems:
Figure: Household 3-Phase System, from Eddie's notes.
In a typical 120 Volt household, electricity comes from the power company in a single phase and high voltage. A transformer takes that power and steps it down to 240 volts with a neutral tap in the middle. Taking power from the two ends results in 240 volts for high demand systems, such as a clothes dryer. Taking power from the center neutral top to either phase results in 120 volts for most household needs.
Figure: G450 Integrated Drive Generator 3-Phase System, from Eddie's aircraft.
With an aircraft AC generator you will commonly have three outputs, one for each phase, and a common neutral. Unlike the household example, the voltages are not commonly combined. High demand aircraft systems will use all three phases for more power than a single phase can provide. A high demand motor, for example, may have three sets of windings to take advantage of all three phases.
I don't have a source for any of this, it just comes from years of working on two-phase systems in the various houses I've owned and trouble shooting the various three-phase system aircraft I've flown.