# Power Factor

Power factor is a measure of how far out of phase the flow of current in alternating current (AC) circuit with respect to voltage. We will examine power factor in detail in this article and explain power factor (PF) with diagrams and present a power factor simulator in Excel that can be used to visualize this concept.

## Why would the flow of current be out of phase with the voltage?

In a purely resistive circuit, the flow of current is in perfect phase with the applied voltage. When the flow of current is completely in phase with the applied voltage, the power factor (PF) is 1.

In an AC circuit that has inductance (a circuit that has capacitance or inductance, such as an electric motor), the flow of current will be out of phase with the applied voltage. The degree to which the flow of current is out of phase with the applied voltage is the power factor (PF).

## Power factor can be leading or lagging

### In a circuit with inductance, the current lags with respect to the current flow (lagging power factor).

A common example would be a SCIM (squirrel cage induction motor). An SCIM presents a resistive load with inductance to the source. During operation at full load a typical SCIM might present a power factor of 0.7 to 0.8 lag. A chart is shown below of an example of the relationship between voltage, current, and instantaneous power.

##### Download an Excel spreadsheet to visualize power factor and produce charts like the ones shown here (free!).

### In a circuit with capacitance, the current leads with respect to the voltage (leading power factor).

A common example of this type of load is a capacitor such as in a power supply. The chart below shows an example of 0.8 or 80% leading power factor (PF).

##### Download an Excel spreadsheet to visualize power factor and produce charts like the ones shown here (free!).

### In a circuit that presents a purely resistive load to the source, the current is in phase with the applied voltage, and the power factor is 1 (unity power factor).

A common example of a purely resistive load is a heating appliance such as an oven or a light bulb. These types of loads do often present a small but negligible amount of reactance in addition to the resistance. A power factor of 1 is often referred to as 'unity power factor'.

## Power Factor Correction

Industrial and commercial power consumers often apply power factor correction to their plant if their power factor is much lower than 0.9. Many utility companies charge a power factor penalty if the power factor presented by the plant is much less than 0.9.

For example, an industrial plant with many induction motors might employ a bank of power factor correction capacitors to get the power factor of the overall load of the plant presented to the utility to be greater than 1.

Larger industrial power consumers who might have large synchronous electric motors may set the rotor field on the motor to present a slightly leading power factor to compensate for lagging power factor presented by other loads in the plant.

## Power Factor Penalty

Many utility companies charge a power factor penalty to commercial and industrial consumers if the power factor is below a certain threshold. In some contracts, the power factor penalty applies for an entire billing period (i.e. month) if the power factor presented by the plant drops below the threshold at any point during the month.

One reason for the penalty is that although the real power of the load in Watts may be a certain value, the peak power of the load is higher, and thus the utility must be sized to provide the peak power. What actually happens with a non-unity power factor is that during each cycle, the plant gives back some of the power it consumed.

Looking at the example power factor charts above, we can see points in each green instantaneous power waveform where the instantaneous power is negative. At those times the plant is actually driving power back into the grid. However, the utility must still provide the power on the positive portions of the cycle and must be sized for this load, only to be given part of this power back during another part of the cycle, thus lowering the average (and typically billable) power.

However, when we look at the unity power factor chart example above, we can see that the instantaneous power never goes negative.

## Power Factor Losses

Moreover, power transmission line (wire/cable) heating losses are purely a function of the amount of current travelling through the line and the resistance of the line. This loss is expressed as I^{2}R losses (I squared R). So another difference we can see is that a non-unity power factor is less efficient for power transmission. The average power in a non-unity load is less than it would be in a load of unity power factor; however the I^{2}R losses are the same (because voltage does not matter in the caclulation of this loss).

## Non-linear load Power Factor

Other types loads such as switched mode power supplies, rectifiers, and fluorescent and arc lamps often present a non-linear load the source. These produce non-sinuoisodal current loads to the source that might have sharp peaks.

#### If you have questions, please post a comment or visit the forum.

#### About the Author

This article was written by Lewis Werner. It was last updated December 9, 2010 and first published November 22, 2010. If you have questions about the article, please click here to view the author's contact information including e-mail address, telephone number and mailing address.

- | Trackback URL |

## Post new comment