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Basic electricity - 3 phase installation powered

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

Find:
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
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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)
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Machine 1:
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P = 5N; Q = 2N

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

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

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