Power factor: Dissipating the Myths

By David Stonier-Gibson, SPLat Controls

Power factor is one of those subjects about which there seems to be a great deal of confusion and many misconceptions. The culprit is the the assertion thatpower factor = cos(Φ), Φ (Phi) being the phase shift between voltage and current. While this is true under certain ideal conditions, there are many real-world instances where it is quite incorrect. This article will give you a basic introduction into power factor, and explain why cos(Φ) is not the whole answer.

The Basics

Figure 1

If you connect a sinusoidal voltage source to a resistor, current will flow, power will be dissipated in the resistor and the resistor will heat up. The current is given by I = V ÷ R and the power is given by P = I × V or P = V² ÷ R. The voltage and current are the rms values.

Figure 1 shows the waveforms for this experiment. The top blue waveform is sinusoidal voltage. The voltage is 1V rms giving a peak voltage of 1.414V, The red waveform is the current. It is 1A rms, 1.414A peak. (If you are awake you will deduce that the resistor is 1Ω). The green waveform is the instantaneous power, i.e. the product of voltage and current from moment to moment. For example, at the lefthand vertical line the voltage and current are both at their peaks, so the power is

1.414V × 1.414A = 2W

At the righthand vertical line we are at the negative peaks of voltage and current. Here the instantaneous power is

-1.414V × -1.414A = 2W

i.e. the product of two negatives giving a positive. It should not take too much imagination to see that the average of the power waveform is 1W.

Figure 2

Suppose we now replace the resistor with an inductor. The current in an inductor