Power factor
Non-linear loads
Non\-linear loads
-----------------

Examples of non\-linear loads on a power system are rectifiers (such as used in a power supply), and arc discharge devices such as [fluorescent lamps](/wiki/Fluorescent_lamp "Fluorescent lamp"), electric [welding](/wiki/Welding "Welding") machines, or [arc furnaces](/wiki/Arc_furnace "Arc furnace"). Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. *Distortion power factor* is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load.
[right\|thumb\|upright\=1\.36\|Sinusoidal voltage and non\-sinusoidal current give a distortion power factor of 0\.75 for this computer power supply load.](/wiki/File:Power_factor_75_2.png "Power factor 75 2.png")

### Non\-sinusoidal components

In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is *displacement power factor*.

Non\-linear loads change the shape of the current waveform from a [sine wave](/wiki/Sine_wave "Sine wave") to some other form. Non\-linear loads create [harmonic](/wiki/Harmonic "Harmonic") currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain [non\-linear](/wiki/Non-linear "Non-linear") loads such as [rectifiers](/wiki/Rectifiers "Rectifiers"), some forms of electric lighting, [electric arc furnaces](/wiki/Electric_arc_furnace "Electric arc furnace"), welding equipment, [switched\-mode power supplies](/wiki/Switched-mode_power_supply "Switched-mode power supply"), variable speed drives and other devices. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system.

To measure the real power or reactive power, a [wattmeter](/wiki/Wattmeter "Wattmeter") designed to work properly with non\-sinusoidal currents must be used.

### Distortion power factor

The **distortion power factor** is the distortion component associated with the harmonic voltages and currents present in the system.

\\begin{align}
\\mbox{distortion power factor}
\& \= \\frac{ I\_1}{I\_{rms \\\\
\& \= \\frac{I\_1} {\\sqrt{I\_1^2\+I\_2^2\+I\_3^2\+I\_4^2\+\\cdots \\\\
\& \= \\frac{1} { \\sqrt{1\+ \\frac{I\_2^2\+I\_3^2\+I\_4^2\+\\cdots}{I\_1^2} \\\\
\& \= \\frac{1} {\\sqrt{ 1\+THD\_i^2 \\\\
\\end{align}

\\mbox{THD}\_i is the [total harmonic distortion](/wiki/Total_harmonic_distortion "Total harmonic distortion") of the load current. 
THD\_i \= \\frac{\\sqrt{\\displaystyle\\sum\_{h\=2}^\\infty I\_h^2 {I\_1}\= \\frac{\\sqrt{I\_2^2\+I\_3^2\+I\_4^2\+\\cdots {I\_1}

I\_1 is the fundamental component of the current, I\_{rms} is the total current, and I\_h is the current on the hth harmonic; all are [root mean square](/wiki/Root_mean_square "Root mean square") values (distortion power factor can also be used to describe individual order harmonics, using the corresponding current in place of total current). This definition with respect to total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for stiff voltage sources (not being affected by changes in load downstream in the distribution network). Total harmonic distortion of typical generators from current distortion in the network is on the order of 1–2%, which can have larger scale implications but can be ignored in common practice.

The result when multiplied with the displacement power factor is the overall, true power factor or just power factor (PF):
\\mbox{PF} \= \\frac{\\cos{\\varphi {\\sqrt{ 1\+THD\_i^2

### Distortion in three\-phase networks

In practice, the local effects of distortion current on devices in a [three\-phase distribution network](/wiki/Three-phase_electric_power "Three-phase electric power") rely on the magnitude of certain order harmonics rather than the total harmonic distortion.

For example, the [triplen](/wiki/Harmonics_%28electrical_power%29%23Even%2C_odd%2C_triplen_and_non-triplen_odd_harmonics "Harmonics (electrical power)#Even, odd, triplen and non-triplen odd harmonics"), or zero\-sequence, harmonics (3rd, 9th, 15th, etc.) have the property of being in\-phase when compared line\-to\-line. In a [delta\-wye transformer](/wiki/Delta-wye_transformer "Delta-wye transformer"), these harmonics can result in circulating currents in the delta windings and result in greater [resistive heating](/wiki/Joule_heating "Joule heating"). In a wye\-configuration of a transformer, triplen harmonics will not create these currents, but they will result in a non\-zero current in the [neutral wire](/wiki/Ground_and_neutral "Ground and neutral"). This could overload the neutral wire in some cases
and create error in kilowatt\-hour metering systems and billing revenue. The presence of current harmonics in a transformer also result in larger [eddy currents](/wiki/Eddy_currents "Eddy currents") in the magnetic core of the transformer. Eddy current losses generally increase as the square of the frequency, lowering the transformer's efficiency, dissipating additional heat, and reducing its service life.

Negative\-sequence harmonics (5th, 11th, 17th, etc.) combine 120 degrees out of phase, similarly to the fundamental harmonic but in a reversed sequence. In generators and motors, these currents produce magnetic fields which oppose the rotation of the shaft and sometimes result in damaging mechanical vibrations.

### Power factor correction (PFC) in non\-linear loads

#### Passive PFC

The simplest way to control the [harmonic](/wiki/Harmonics_%28electrical_power%29 "Harmonics (electrical power)") current is to use a [filter](/wiki/Electronic_filter "Electronic filter") that passes current only at [line frequency](/wiki/Utility_frequency "Utility frequency") (50 or 60 Hz). The filter consists of capacitors or inductors and makes a non\-linear device look more like a [linear](/wiki/Linear "Linear") load. An example of passive PFC is a [valley\-fill circuit](/wiki/Valley-fill_circuit "Valley-fill circuit").

A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit. Also, in practice, passive PFC is often less effective at improving the power factor.

#### Active PFC

[right\|thumb\|Specifications taken from the packaging of a 610 W [PC power supply](/wiki/Power_supply_unit_%28computer%29 "Power supply unit (computer)") showing active PFC rating](/wiki/File:Active_pfc_PSU_packaging.png "Active pfc PSU packaging.png")

Active PFC is the use of [power electronics](/wiki/Power_electronics "Power electronics") to change the waveform of current drawn by a load to improve the power factor. Some types of the active PFC are [buck](/wiki/Buck_converter "Buck converter"), [boost](/wiki/Boost_converter "Boost converter"), [buck\-boost](/wiki/Buck-boost_converter "Buck-boost converter") and [synchronous condenser](/wiki/Synchronous_condenser "Synchronous condenser"). Active power factor correction can be single\-stage or multi\-stage.

In the case of a switched\-mode power supply, a [boost converter](/wiki/Boost_converter "Boost converter") is inserted between the bridge rectifier and the main input capacitors. The boost converter attempts to maintain a constant voltage at its output while drawing a current that is always in phase with and at the same frequency as the line voltage. Another switched\-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics but permits cheaper and smaller passive components. It is frequently used in practice.

For a three\-phase SMPS, the [Vienna rectifier](/wiki/Vienna_rectifier "Vienna rectifier") configuration may be used to substantially improve the power factor.

[SMPSs](/wiki/Switched-mode_power_supply "Switched-mode power supply") with passive PFC can achieve power factor of about 0\.7–0\.75, SMPSs with active PFC, up to 0\.99 power factor, while a SMPS without any power factor correction have a power factor of only about 0\.55–0\.65\.

Due to their very wide input voltage range, many power supplies with active PFC can automatically adjust to operate on AC power from about 100 V (Japan) to 240 V (Europe). That feature is particularly welcome in power supplies for laptops.

#### Dynamic PFC

Dynamic power factor correction (DPFC), sometimes referred to as real\-time power factor correction, is used for electrical stabilization in cases of rapid load changes (e.g. at large manufacturing sites). DPFC is useful when standard power factor correction would cause over or under correction. DPFC uses semiconductor switches, typically [thyristors](/wiki/Thyristor "Thyristor"), to quickly connect and disconnect capacitors or inductors to improve power factor.


Can SMPSs without any power factor correction have a power factor of 0.55-0.65?