# Capacities of three-phase symmetric system

Active power (often simply power) the three-phase siyostema is called the sum of active powers of all phases of the source of the eneryogiya equal to the sum of active powers of all phases of the receiver.

In symmetric three-phase system, i.e. system with the symmetric generator and the receiver, at any scheme of their connections for the kayozhdy phase of power of the power source and the receiver identical. In this case P = 3 USAn Federation and for each of phases the formula of active power of the sinusoidal current of the USAn Federation = is fair Ufif cos?, where? - the phase angle between the phase tension and current.

Having replaced the operating values of the phase current and tension lineyyony at connection of the power source and the receiver according to the scheme "star" and "triangle", we will receive same vyrazheyony for the active power of symmetric three-phase system:

Р =????????? =? _{3ulilcos}_{}.

In plants receivers usually symmetric or almost symmetric, i.e. power can be calculated on the stated above formula.

Generally the reactive power of three-phase system nazyyovatsya the sum of reactive powers of all phases of the power source, ravyony to the sum of reactive powers of all phases of the receiver. Reactive power of symmetric three-phase system

Q = 3qf =3ufifsin

or, after replacement of the operating values of the phase current and tension linear,

Q =? _{3ulilsin}_{}

**Ultimate power of three-phase system is called the sum of vector powers of all phases of the power source equal to the sum of vector powers of all phases of the receiver.**

Ultimate power of symmetric three-phase system - S=? _{3ulil}_{.}

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