Three-phase

In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating current voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y) (also denoted as wye in some areas). A wye system allows the use of two different voltages from all three phases, such as a 230/400 V system which provides 230 V between the neutral (centre hub) and any one of the phases, and 400 V across any two phases. A delta system arrangement only provides one voltage magnitude, however it has a greater redundancy as it may continue to operate normally with one of the three supply windings offline, albeit at 57.7% of total capacity. Harmonic currents in the neutral may become very large if non-linear loads are connected.

Definitions

In a star (wye) connected topology, with rotation sequence L1 - L2 - L3, the time-varying instantaneous voltages can be calculated for each phase A,C,B respectively by:

where:

Phase

Phase or phases may refer to:

In science

In physics

Planetary phase

Refers to the periods of time during which a planet's surface reflects different amounts of sunlight, revealing different portions of the planet's surface from the perspective of a given point in space.

Inferior planets

The two inferior planets, Mercury and Venus, which have orbits that are smaller than the Earth's, exhibit the full range of phases as does the Moon, when seen through a telescope. Their phases are "full" when they are at superior conjunction, on the far side of the Sun as seen from the Earth. (It is possible to see them at these times, since their orbits are not exactly in the plane of Earth's orbit, so they usually appear to pass slightly above or below the Sun in the sky. Seeing them from the Earth's surface is difficult, because of sunlight scattered in Earth's atmosphere, but observers in space can see them easily if direct sunlight is blocked from reaching the observer's eyes.) The planets' phases are "new" when they are at inferior conjunction, passing more or less between the Sun and the Earth. (Sometimes they appear to cross the solar disk, which is called a transit of the planet.) At intermediate points on their orbits, these planets exhibit the full range of crescent and gibbous phases.

Phase (waves)

Phase in sinusoidal functions or in waves has two different, but closely related, meanings. One is the initial angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the wave cycle that has elapsed relative to the origin.

Formula

The phase of an oscillation or wave refers to a sinusoidal function such as the following:

where , , and are constant parameters called the amplitude, frequency, and phase of the sinusoid. These functions are periodic with period , and they are identical except for a displacement of along the axis. The term phase can refer to several different things:

It can refer to a specified reference, such as , in which case we would say the phase of is , and the phase of is .

It can refer to , in which case we would say and have the same phase but are relative to their own specific references.

In the context of communication waveforms, the time-variant angle , or its principal value, is referred to as instantaneous phase, often just phase.