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Basic electricity - 3 phase installation powered

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Consider the following:
A 3 phase installation powered by 400V 50Hz is composed of 6 machines.
(Please see the attached table)

a) Total apparent power
b) Total absorbed current (line current)
c) Installation power factor
d) The power of the capacitors that should be installed to have a power factor of 0.95
e) Total absorbed power after the power factor as been corrected.

A step by step explanation is required.

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Equations Used: For a 3-phase installation

P = sqrt(3)* V * I * (PF) Watts, PF = Power factor = Cos (Theta)

S^2 = P^2 + Q^2 VA

PF = Cos(Theta) = P/S

I = P / [sqrt(3)* V * (PF)] Amps

V = 400 Volts

Now, let us compute all the unknown quantities for all the 6 machines using the above equations.

N = 2458 for all except N = 2.458 for I(Current computation)

Machine 1:

P = 5N; Q = 2N

Hence, S = 5.39N; PF = 0.93;
I = 0.00776N = 19.1 A

Solution Summary

Three phase installation powered is examined. The total apparent power is analyzed.

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