3-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 current in the neutral may become very large if non-linear loads are connected.

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:

Generally, in electric power systems, the loads are distributed as evenly as is practical between the phases. It is usual practice to discuss a balanced system first and then describe the effects of unbalanced systems as deviations from the elementary case.

An important property of three-phase power is that the power available to a resistive load, ${\displaystyle \scriptstyle P\,=\,VI\,=\,{\frac {1}{R}}V^{2}}$, is constant at all times.

To simplify the mathematics, we define a nondimensionalized power for intermediate calculations, ${\displaystyle \scriptstyle p\,=\,{\frac {1}{V_{P}^{2}}}P_{TOT}R}$

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