A ground, or earth, conductor is never included in the conductor
count. So, a three-phase, three-wire, system has three line
conductors, whereas a three-phase, four-wire system, has three line
conductors and a neutral conductor.
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A two-phase system is archaic and you are unlikely to find it in use anywhere these days, so it is mainly of historical interest. A two-phase, three-wire system, consists of two phase voltages, displaced from each other by 90 electrical degrees, and a phase voltage which is 1.414 x phase voltage.
A three-phase system consists of three phase voltages which are displaced from each other by 120 electrical degrees. In the case of a three-phase, three-wire, system, the line voltages are numerically equal to the phase voltages; in the case of a three-phase, four-wire, system, the line voltages are 1.732 x phase voltage.
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A three phase four wire system allows for two voltages from a
single three phase transformer. The transformer configuration is a
wye or star connection. It is used in commercial and industrial
applications. Apartment buildings are now starting to use a three
phase four wire service distribution system. Some wye connection
voltages are 120/208 volts, 480/277, and 600/347. The lower voltage
is derived from the sq root of 3 divided into the three phase
voltage.