Power Factor 1

Electricity and Magnetism Level 2

A household is running the following equipment:

A single phase pump for the swimming pool is also connected and the nameplate reads:

230 V rated , 15 A , 0.83 pf 230 \text{ V}_\text{rated}, 15\text{ A} , 0.83 \text{ pf} .

What is the expected power factor for the entire house?

Hint: The following model is for illustrative purposes, do not calculate the values of the inductors or resistors

0.853 0.884 0.878 0.881 0.886 0.912 0.784

Brandon Louw by Brandon Louw , 29, South Africa

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1 solution

Brandon Louw
Jun 17, 2016

The solution to this problem is to break up the powers into its active and reactive components.

  • S = P + jQ

  • P = Heater + Geyser + (Fluorescent Globe x75 )+ (230x15x0.83)

  • Pt = 5013.5 W

  • So to find the reactive parts of the systems, you need to use pf equations

  • pf = P S \frac{P}{S}
  • S = 10 0.72 \frac{10}{0.72} x75
  • S = 1041,67 VA
  • Q = Ssin(pf)

  • Q = 722,8896 VAr

  • For the motor:

  • pf = arccos(0.83)
  • pf = 33.9
  • S = 230 x 15
  • S = 3450 VA
  • Q = 3450sin(33,90)
  • Q = 1924,72 VAr
  • Qt = 1924,72 + 722,8896

  • Qt = 2647,145 VAr

  • St = (5013,5 + j2647,145) VA

  • arctan(thetha) = 2647 , 145 5013 , 5 \frac{2647,145}{5013,5}

  • thetha = 27,834
  • pf = cos(27,834)
  • pf = 0.8834
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