Calculating average power reactive power and the power facto

Calculating average power, reactive power, and the power factor To use information about the power provided by a source or absorbed by a load to calculate average power, reactive power, apparent power, and the power factor. Before completing this tutorial, make sure you are familiar with the relationships between average, reactive, and apparent power and the power factor. A load absorbs S = 85 kVA at a leading power factor of pf = 0.90. Use this information to calculate the average (P) and reactive (Q) power for the load. Enter comma separated numerical answers with three significant figures. Calculating apparent power and power factor A load operates at a voltage of V_x = 425 V-rms and absorbs P = 27 W and Q = 30 VAR of power. Use this information to calculate the apparent power (S) and the power factor (pf) for the load. Enter comma separated numerical answers with three significant figures.

Solution

part-A:

S=85 KVA

power factor=0.9

average power=S*cos theta=85*0.9*10^3=76,500 watts.

reactive power=S*sin theta=85*10^3*sin(inverse cos of 0.9)=37050.64 VAR.

part-B:

voltage=425 volts.

p=27 watts.

Q=30 VAR.

Q/P=(visin theta)/(vicos theta)=tan theta.

30/27=tan theta.

theta=inverse tan of(30/27)=48.012 degrees

power factor= cos theta=cos(48.012)=0.6689

apparent power=vi=p/cos theta=27/0.6689=40.36 VA.

part C:

p=55007 watts.

power factor=0.56

i=0.1 amps.

p=vicos theta=v*0.1*0.56=55007

v=982267.85 volts.

impedance=v/i=982267.85/0.1=9822678.571 ohms.