Electronic – Correct power factor formua

powerpower-factor-correction

My instructor asked me why have I written the power factor formula as

If \$\varphi\$ is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, \$cos\,\varphi\$:
$$|P| = |S|\,\cdot\,cos\,\varphi$$

with his reasoning that \$P\$ must always be positive with the exception when the resistance is negative, so I should not have the absolute value there.

Now I cannot remember the reason why, but I am pretty sure I have found it somewhere, but since I did a poor job with references, now I cannot find the origin of this formula.

I have found it on wikipedia.

Is this formula wrong? If yes, how can it be written correctly in this form. If no, can you forward me to some more reading on this? Many thanks.

Best Answer

I would say that the most general formula is:

$$P=Re\{\underline{S}\}=Re\{\underline{V}·\underline{I}^{\star}\}=S\cos{\theta}$$

where I'm using underline to identify phasors.

S is the module of \$\underline{S}\$ and it is always positive (it is simply the voltage amplitude times the current amplitude).

\$\theta\$ is the angle between voltage and current. If this angle is bigger than 90º it means that the load is in reality providing active power to the source and not the other way around.

Therefore P can be positive or negative.