Editing Power factor (section)

== 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 lamp]]s, electric [[welding]] machines, or [[arc furnace]]s. 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.
[[File:Power factor 75 2.png|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.]]

=== 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''.<ref name="FuchsMasoum2015">{{cite book|author1=Ewald Fuchs|author2=Mohammad A. S. Masoum|title=Power Quality in Power Systems and Electrical Machines|url=https://books.google.com/books?id=wuGcBAAAQBAJ&pg=PA432|date=14 July 2015|publisher=Elsevier Science|isbn=978-0-12-800988-8|pages=432–|quote=The DPF is the cosine of the angle between these two quantities}}</ref>

Non-linear loads change the shape of the current waveform from a [[sine wave]] to some other form. Non-linear loads create [[harmonic]] currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain [[non-linear]] loads such as [[rectifiers]], some forms of electric lighting, [[electric arc furnace]]s, welding equipment, [[Switched-mode power supply|switched-mode power supplies]], 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]] 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.
:<math>
\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}
</math>

<math>\mbox{THD}_i</math> is the [[total harmonic distortion]] of the load current. 
:<math>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}</math>

<math>I_1</math> is the fundamental component of the current, <math>I_{rms}</math> is the total current, and <math>I_h</math> is the current on the h<sup>th</sup> harmonic; all are [[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.<ref>{{Citation |url=http://ecmweb.com/power-quality/effects-harmonics-power-systems |title=Effects of Harmonics on Power Systems |first=C. |last=Sankaran |year=1999 |publisher=Electro-Test |quote=...and voltage-time relationship deviates from the pure sine function. The distortion at the point of generation is very small (about 1% to 2%), but nonetheless it exists.}}</ref>

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

=== Distortion in three-phase networks ===
In practice, the local effects of distortion current on devices in a [[Three-phase electric power|three-phase distribution network]] rely on the magnitude of certain order harmonics rather than the total harmonic distortion.

For example, the [[Harmonics_(electrical_power)#Even%2C_odd%2C_triplen_and_non-triplen_odd_harmonics|triplen]], 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]], these harmonics can result in circulating currents in the delta windings and result in greater [[Joule heating|resistive 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 [[Ground and neutral|neutral wire]]. This could overload the neutral wire in some cases
and create error in kilowatt-hour metering systems and billing revenue.<ref>{{Citation | chapter-url = http://www.pge.com/includes/docs/pdfs/mybusiness/customerservice/energystatus/powerquality/harmonics.pdf | title = Power System Harmonics | publisher = Pacific Gas and Electric | chapter = Single-phase load harmonics vs. three-phase load harmonics | access-date = 2013-11-26 | archive-date = 2015-09-24 | archive-url = https://web.archive.org/web/20150924072113/http://www.pge.com/includes/docs/pdfs/mybusiness/customerservice/energystatus/powerquality/harmonics.pdf | url-status = dead }}</ref><ref>{{Citation | chapter-url = http://energylogix.ca/harmonics_and_ieee.pdf | title = Harmonics and IEEE 519 | publisher = EnergyLogix Solutions | chapter = Harmonic Effects | place = [[Canada|CA]] }}</ref>  The presence of current harmonics in a transformer also result in larger [[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.<ref>{{Citation |url=http://ecmweb.com/power-quality/effects-harmonics-power-systems |title=Effects of Harmonics on Power Systems |first=C. |last=Sankaran |year=1999 |publisher = Electro-Test |section=Transformers}}</ref>

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.<ref>{{Citation |url=http://ecmweb.com/power-quality/effects-harmonics-power-systems |title=Effects of Harmonics on Power Systems |first=C. |last=Sankaran |year=1999 |publisher=Electro-Test |section=Motors |quote=The interaction between the positive and negative sequence magnetic fields and currents produces torsional oscillations of the motor shaft. These oscillations result in shaft vibrations.}}</ref>

=== Power factor correction (PFC) in non-linear loads ===

==== Passive PFC ====
The simplest way to control the [[Harmonics (electrical power)|harmonic]] current is to use a [[electronic filter|filter]] that passes current only at [[utility frequency|line frequency]] (50 or 60&nbsp;Hz). The filter consists of capacitors or inductors and makes a non-linear device look more like a [[linear]] load. An example of passive PFC is a [[valley-fill circuit]].

A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit.<ref>{{Citation |url=http://www.nuvation.com/corporate/news/newsletter/fall2006/powersupply.html |publisher=Nuvation |date=Fall 2006 |title=Power Supply Design Principles: Techniques and Solutions, Part 3 |newspaper=Newsletter |first=Ben |last=Schramm |url-status=dead |archive-url=https://web.archive.org/web/20070309134617/http://www.nuvation.com/corporate/news/newsletter/fall2006/powersupply.html |archive-date=2007-03-09 }}</ref><ref>{{Citation | newspaper = Xplore | title = Quasi-active power factor correction with a variable inductive filter: theory, design and practice | volume = 18 | issue = 1 | pages = 248–255 | publisher = IEEE| doi = 10.1109/TPEL.2002.807135 | bibcode = 2003ITPE...18..248W | year = 2003 | last1 = Wolfle | first1 = W.H. | last2 = Hurley | first2 = W.G. }}</ref><ref>{{Citation |publisher=Nuigalway |type=project |url=http://www.nuigalway.ie/power_electronics/projects/quasi_active.html |place=[[Ireland|IE]] |title=Power electronics |contribution=Quasi-active Power Factor Correction: The Role of Variable Inductance |last1=Wölfle |first1=W. H. |last2=Hurley |first2=W. G. |access-date=2008-11-05 |archive-date=2020-08-06 |archive-url=https://web.archive.org/web/20200806105647/http://www.nuigalway.ie/power_electronics/projects/quasi_active.html |url-status=dead }}</ref> Also, in practice, passive PFC is often less effective at improving the power factor.<ref name="effi">{{Citation | url = http://www.xbitlabs.com/articles/coolers/display/atx-psu5_3.html | title = ATX Power Supply Units Roundup | publisher = xBit labs | quote = The power factor is the measure of reactive power. It is the ratio of active power to the total of active and reactive power. It is about 0.65 with an ordinary PSU, but PSUs with active PFC have a power factor of 0.97–0.99. […] hardware reviewers sometimes make no difference between the power factor and the efficiency factor. Although both these terms describe the effectiveness of a power supply, it is a gross mistake to confuse them. […] There is a very small effect from passive PFC – the power factor grows only from 0.65 to 0.7–0.75. | url-status = dead | archive-url = https://web.archive.org/web/20081120040707/http://www.xbitlabs.com/articles/coolers/display/atx-psu5_3.html | archive-date = 2008-11-20 }}</ref><ref>{{Citation|date=Mar 16, 2006 |publisher=Find articles |url=http://findarticles.com/p/articles/mi_m0EIN/is_2006_March_16/ai_n26797888 |archive-url=https://web.archive.org/web/20090901140721/http://findarticles.com/p/articles/mi_m0EIN/is_2006_March_16/ai_n26797888/ |url-status=dead |archive-date=September 1, 2009 |title=The Active PFC Market is Expected to Grow at an Annually Rate of 12.3% Till 2011 |quote=Higher-powered products are also likely to use active PFC, since it would be the most cost effective way to bring products into compliance with the EN standard. }}</ref><ref>{{Citation | url = http://www.techarp.com/showarticle.aspx?artno=81&pgno=1 | publisher = TECHarp | title = Power Factor Correction | quote = Passive PFC […] the power factor is low at 60–80%. […] Active PFC ... a power factor of up to 95%}}</ref><ref>{{Citation | publisher = Silverstone Technology | url = http://www.silverstonetek.com/tech/wh_pfc.php?area= | title = Why we need PFC in PSU | quote = Normally, the power factor value of electronic device without power factor correction is approximately 0.5. […] Passive PFC […] 70~80% […] Active PFC […] 90~99.9% | url-status = dead | archive-url = https://web.archive.org/web/20081222085515/http://www.silverstonetek.com/tech/wh_pfc.php?area= | archive-date = 2008-12-22 }}</ref><ref>{{Citation | publisher = Electronic products | newspaper = Taiyo | url = http://www2.electronicproducts.com/PFC_options_for_power_supplies-article-taiyo-mar2004-html.aspx | title = PFC options for power supplies | first = Tom | last = Brooks | date = Mar 2004 | quote = The disadvantages of passive PFC techniques are that they typically yield a power factor of only 0.60 to 0.70 […] Dual-stage active PFC technology [yields] a power factor typically greater than 0.98 | url-status = dead | archive-url = https://web.archive.org/web/20081202100831/http://www2.electronicproducts.com/PFC_options_for_power_supplies-article-taiyo-mar2004-html.aspx | archive-date = 2008-12-02 }}</ref>

==== Active PFC ====
[[File:Active pfc PSU packaging.svg|right|thumb|Specifications taken from the packaging of a 610 W [[Power supply unit (computer)|PC power supply]] showing active PFC rating]]

Active PFC is the use of [[power electronics]] to change the waveform of current drawn by a load to improve the power factor.<ref>{{Citation | publisher = Fairchild Semiconductor | year = 2004 | type = application note | number = 42047 | title = Power Factor Correction (PFC) Basics | url = http://www.fairchildsemi.com/an/AN/AN-42047.pdf | access-date = 2009-11-29 | archive-url = https://web.archive.org/web/20140611063712/http://www.fairchildsemi.com/an/AN/AN-42047.pdf | archive-date = 2014-06-11 | url-status = dead }}</ref>  Some types of the active PFC are [[Buck converter|buck]], [[Boost converter|boost]], [[Buck-boost converter|buck-boost]] and [[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]] 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]] configuration may be used to substantially improve the power factor.

[[Switched-mode power supply|SMPSs]] 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.<ref>{{Citation |last1=Sugawara |first1=I. |last2=Suzuki |first2=Y. |last3=Takeuchi |first3=A. |last4=Teshima |first4=T. |contribution=Experimental studies on active and passive PFC circuits |title=INTELEC 97, 19th International Telecommunications Energy Conference |date=19–23 Oct 1997 |pages=571–78 |doi=10.1109/INTLEC.1997.646051|isbn=978-0-7803-3996-5 |s2cid=109885369 }}</ref>

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&nbsp;V (Japan) to 240&nbsp;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.<ref>{{Cite conference|last1=Chavez |first1=C. |last2=Houdek |first2=J. A. |title=Dynamic Harmonic Mitigation and power factor correction |publisher=IEEE |book-title= EPQU'07 |conference=9th International Conference Electrical Power Quality and Utilisation: October 9–11, 2007, Barcelona, Spain |pages=1–5 |doi=10.1109/EPQU.2007.4424144 |isbn=978-84-690-9441-9 }}</ref>  DPFC uses semiconductor switches, typically [[thyristor]]s, to quickly connect and disconnect capacitors or inductors to improve power factor.