Practical values of power factor

The calculations for the three-phase example above are as follows:

Pn = delivered shaft power = 51 kW
P = active power consumed

[math]\displaystyle{ P=\frac {Pn}{\rho}=\frac{51}{0.91}=56\, kW }[/math]

S = apparent power

[math]\displaystyle{ S=\frac{P}{cos \phi}=\frac {56}{0.86}= 65\, kVA }[/math]

So that, on referring to diagram Figure L5 or using a pocket calculator, the value of tan φ corresponding to a cos φ of 0.86 is found to be 0.59

Q = P tan φ = 56 x 0.59 = 33 kvar

Alternatively:

[math]\displaystyle{ Q=\sqrt{S^2 - P^2}=\sqrt{65^2 - 56^2}=33\, kvar }[/math]

Fig. L5: Calculation power diagram

Average power factor values for the most commonly-used equipment and appliances

(see Fig. L6)

Equipment and appliances			cos φ	tan φ
Common induction motor	loaded at	0% 25% 50% 75% 100%	0.17 0.55 0.73 0.80 0.85	5.80 1.52 0.94 0.75 0.62
Incandescent lamps Fluorescent lamps (uncompensated) Fluorescent lamps (compensated) Discharge lamps			1.0 0.5 0.93 0.4 to 0.6	0 1.73 0.39 2.29 to 1.33
Ovens using resistance elements Induction heating ovens (compensated) Dielectric type heating ovens			1.0 0.85 0.85	0 0.62 0.62
Resistance-type soldering machines Fixed 1-phase arc-welding set Arc-welding motor-generating set Arc-welding transformer-rectifier set			0.8 to 0.9 0.5 0.7 to 0.9 0.7 to 0.8	0.75 to 0.48 1.73 1.02 to 0.48 1.02 to 0.75
Arc furnace			0.8	0.75

Fig. L6: Values of cos φ and tan φ for commonly-used equipment