# Back to Basics: Power Factor Correction

**Arun Ananthampalayam, Power Marketing Applications Engineer, CUI**

8/21/2013 12:15 PM EDT

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The advent of the switching power supply has made it possible to deploy high-efficiency power conversion into a wide range of applications. But monetary and environmental considerations are driving changes and improvements in their design. These will ultimately reduce the cost of supplying electricity to the growing array of electronic systems used worldwide.

Most power throughout the world is generated and distributed as AC power rather than DC power. The voltage and current of linear AC systems are sinusoidal and can be described by a magnitude, phase offset, and a radial frequency.

Instantaneous power is the product of the instantaneous voltage, and instantaneous current. The resulting power waveform has twice the frequency of the voltage and current waveforms, as shown below.

While the instantaneous values have their uses, the voltage, current, and power of an AC system is often described in terms of their root-mean-square (RMS) values. The RMS voltage and current represent the DC values that would produce the same heating effect when applied to a purely resistive load. For sinusoidal signals, such as the AC voltage, the RMS value is equal to the magnitude of the sine wave divided by the square root of 2.

The power dissipated by a purely resistive load is the product of RMS voltage and current. In this special case, the voltage and current are in phase; in other words, their phase offsets are equal.

The situation becomes more complex when the load contains a reactive component (inductance and/or capacitance). The reactive component causes the voltage and current to be out of phase; phase shifts are no longer equal.

If the RMS voltage and current seen at the input of the load were the same as the case of the purely resistive load, then their product will be the same and it would be easy to assume that both loads would dissipate the same amount of power. In fact, if we look at the product of the instantaneous voltage and current of the above figures, we see that the first has a much larger phase shift than the second, meaning that it is dissipating less power.

In the case of the first figure, the load is purely reactive and dissipates no power. If, on the other hand, we were to have two devices that each required 100 watts to operate, one being purely resistive and the other being somewhat reactive, we would find that, while both devices produced the same amount of work, the reactive device would have a higher RMS input current than the purely resistive load.

It has been shown above that, unlike in DC power, in AC power the product of voltage and current into a load does not represent the work done. The product of RMS voltage and current is known as the apparent power (S, measured in volt-amperes). The apparent power is the vector sum of two components: the real or true power (P, measured in watts) and reactive power (Q, measured in volt-amperes reactive). The real power component is the component that results in work being done by the system.

For example, in a motor, only the real power produces torque. The reactive power is stored in the reactive components of the load and then returned to the source where it is dissipated by the power lines in the form of heat. It is often helpful to draw the apparent power as a vector sum of the real and reactive power, as shown below. Using this figure we can easily see that if Q increases so does S without any increase in real power.

Power factor is defined as the ratio of real power to apparent power. In the case of a purely resistive load, the power factor is 1, and apparent power equals the real power. In a purely reactive load, the power factor is 0, and the real power is 0.