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id="toc-Linear_circuits-sublist" class="vector-toc-list"> <li id="toc-Definition_and_calculation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Definition_and_calculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Definition and calculation</span> </div> </a> <ul id="toc-Definition_and_calculation-sublist" class="vector-toc-list"> <li id="toc-Power_triangle" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Power_triangle"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Power triangle</span> </div> </a> <ul id="toc-Power_triangle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lagging,_leading_and_unity_power_factors" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Lagging,_leading_and_unity_power_factors"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2</span> <span>Lagging, leading and unity power factors</span> </div> </a> <ul id="toc-Lagging,_leading_and_unity_power_factors-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Power_factor_correction_of_linear_loads" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Power_factor_correction_of_linear_loads"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Power factor correction of linear loads</span> </div> </a> <ul id="toc-Power_factor_correction_of_linear_loads-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Non-linear_loads" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Non-linear_loads"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Non-linear loads</span> </div> </a> <button aria-controls="toc-Non-linear_loads-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Non-linear loads subsection</span> </button> <ul id="toc-Non-linear_loads-sublist" class="vector-toc-list"> <li id="toc-Non-sinusoidal_components" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-sinusoidal_components"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Non-sinusoidal components</span> </div> </a> <ul id="toc-Non-sinusoidal_components-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distortion_power_factor" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distortion_power_factor"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Distortion power factor</span> </div> </a> <ul id="toc-Distortion_power_factor-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distortion_in_three-phase_networks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distortion_in_three-phase_networks"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Distortion in three-phase networks</span> </div> </a> <ul id="toc-Distortion_in_three-phase_networks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Power_factor_correction_(PFC)_in_non-linear_loads" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Power_factor_correction_(PFC)_in_non-linear_loads"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Power factor correction (PFC) in non-linear loads</span> </div> </a> <ul id="toc-Power_factor_correction_(PFC)_in_non-linear_loads-sublist" class="vector-toc-list"> <li id="toc-Passive_PFC" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Passive_PFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.1</span> <span>Passive PFC</span> </div> </a> <ul id="toc-Passive_PFC-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Active_PFC" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Active_PFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.2</span> <span>Active PFC</span> </div> </a> <ul id="toc-Active_PFC-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dynamic_PFC" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Dynamic_PFC"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4.3</span> <span>Dynamic PFC</span> </div> </a> <ul id="toc-Dynamic_PFC-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Importance_in_distribution_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Importance_in_distribution_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Importance in distribution systems</span> </div> </a> <ul id="toc-Importance_in_distribution_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measurement_techniques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measurement_techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Measurement techniques</span> </div> </a> <ul id="toc-Measurement_techniques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mnemonics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mnemonics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mnemonics</span> </div> </a> <ul id="toc-Mnemonics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Power factor</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 39 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">39 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%85%D9%84_%D8%A7%D9%84%D9%82%D8%AF%D8%B1%D8%A9" title="معامل القدرة – Arabic" lang="ar" hreflang="ar" data-title="معامل القدرة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%93%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%B0_%E0%A6%AB%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%95%E0%A7%8D%E0%A6%9F%E0%A6%B0" title="পাওয়ার ফ্যাক্টর – Bangla" lang="bn" hreflang="bn" data-title="পাওয়ার ফ্যাক্টর" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80_%D0%BD%D0%B0_%D0%BC%D0%BE%D1%89%D0%BD%D0%BE%D1%81%D1%82%D1%82%D0%B0" title="Фактор на мощността – Bulgarian" lang="bg" hreflang="bg" data-title="Фактор на мощността" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Factor_de_pot%C3%A8ncia" title="Factor de potència – Catalan" lang="ca" hreflang="ca" data-title="Factor de potència" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C3%9A%C4%8Din%C3%ADk" title="Účiník – Czech" lang="cs" hreflang="cs" data-title="Účiník" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Leistungsfaktor" title="Leistungsfaktor – German" lang="de" hreflang="de" data-title="Leistungsfaktor" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/V%C3%B5imsustegur" title="Võimsustegur – Estonian" lang="et" hreflang="et" data-title="Võimsustegur" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Factor_de_potencia" title="Factor de potencia – Spanish" lang="es" hreflang="es" data-title="Factor de potencia" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Faktoro_de_povumo" title="Faktoro de povumo – Esperanto" lang="eo" hreflang="eo" data-title="Faktoro de povumo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B6%D8%B1%DB%8C%D8%A8_%D8%AA%D9%88%D8%A7%D9%86" title="ضریب توان – Persian" lang="fa" hreflang="fa" data-title="ضریب توان" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Facteur_de_puissance" title="Facteur de puissance – French" lang="fr" hreflang="fr" data-title="Facteur de puissance" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Factor_de_potencia" title="Factor de potencia – Galician" lang="gl" hreflang="gl" data-title="Factor de potencia" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%AD%EB%A5%A0" title="역률 – Korean" lang="ko" hreflang="ko" data-title="역률" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A4%95%E0%A5%8D%E0%A4%A4%E0%A4%BF_%E0%A4%97%E0%A5%81%E0%A4%A3%E0%A4%BE%E0%A4%82%E0%A4%95" title="शक्ति गुणांक – Hindi" lang="hi" hreflang="hi" data-title="शक्ति गुणांक" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Faktor_daya_listrik" title="Faktor daya listrik – Indonesian" lang="id" hreflang="id" data-title="Faktor daya listrik" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fattore_di_potenza" title="Fattore di potenza – Italian" lang="it" hreflang="it" data-title="Fattore di potenza" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A7%D7%93%D7%9D_%D7%94%D7%A1%D7%A4%D7%A7" title="מקדם הספק – Hebrew" lang="he" hreflang="he" data-title="מקדם הספק" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%9B%E1%83%AB%E1%83%9A%E1%83%90%E1%83%95%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%99%E1%83%9D%E1%83%94%E1%83%A4%E1%83%98%E1%83%AA%E1%83%98%E1%83%94%E1%83%9C%E1%83%A2%E1%83%98" title="სიმძლავრის კოეფიციენტი – Georgian" lang="ka" hreflang="ka" data-title="სიმძლავრის კოეფიციენტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Jaudas_koeficients" title="Jaudas koeficients – Latvian" lang="lv" hreflang="lv" data-title="Jaudas koeficients" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Fator_de_potenza" title="Fator de potenza – Lombard" lang="lmo" hreflang="lmo" data-title="Fator de potenza" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Faktor_kuasa" title="Faktor kuasa – Malay" lang="ms" hreflang="ms" data-title="Faktor kuasa" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%95%E1%80%AB%E1%80%9D%E1%80%AB%E1%80%8A%E1%80%BD%E1%80%BE%E1%80%94%E1%80%BA%E1%80%B8%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8" title="ပါဝါညွှန်းကိန်း – Burmese" lang="my" hreflang="my" data-title="ပါဝါညွှန်းကိန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Arbeidsfactor" title="Arbeidsfactor – Dutch" lang="nl" hreflang="nl" data-title="Arbeidsfactor" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8A%9B%E7%8E%87" title="力率 – Japanese" lang="ja" hreflang="ja" data-title="力率" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A8%BE%E0%A8%B5%E0%A8%B0_%E0%A8%AB%E0%A8%BC%E0%A9%88%E0%A8%95%E0%A8%9F%E0%A8%B0" title="ਪਾਵਰ ਫ਼ੈਕਟਰ – Punjabi" lang="pa" hreflang="pa" data-title="ਪਾਵਰ ਫ਼ੈਕਟਰ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%BE%D8%A7%D9%88%D8%B1_%D9%81%DB%8C%DA%A9%D9%B9%D8%B1" title="پاور فیکٹر – Western Punjabi" lang="pnb" hreflang="pnb" data-title="پاور فیکٹر" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wsp%C3%B3%C5%82czynnik_mocy" title="Współczynnik mocy – Polish" lang="pl" hreflang="pl" data-title="Współczynnik mocy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Fator_de_pot%C3%AAncia" title="Fator de potência – Portuguese" lang="pt" hreflang="pt" data-title="Fator de potência" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Factor_de_putere" title="Factor de putere – Romanian" lang="ro" hreflang="ro" data-title="Factor de putere" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%BE%D1%8D%D1%84%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82_%D0%BC%D0%BE%D1%89%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Коэффициент мощности – Russian" lang="ru" hreflang="ru" data-title="Коэффициент мощности" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Power_factor" title="Power factor – Simple English" lang="en-simple" hreflang="en-simple" data-title="Power factor" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%9A%C4%8Dinn%C3%ADk" title="Účinník – Slovak" lang="sk" hreflang="sk" data-title="Účinník" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B0%D0%BA%D1%82%D0%BE%D1%80_%D1%81%D0%BD%D0%B0%D0%B3%D0%B5" title="Фактор снаге – Serbian" lang="sr" hreflang="sr" data-title="Фактор снаге" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Faktor_daya" title="Faktor daya – Sundanese" lang="su" hreflang="su" data-title="Faktor daya" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tehokerroin" title="Tehokerroin – Finnish" lang="fi" hreflang="fi" data-title="Tehokerroin" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/G%C3%BC%C3%A7_fakt%C3%B6r%C3%BC" title="Güç faktörü – Turkish" lang="tr" hreflang="tr" data-title="Güç faktörü" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B5%D1%84%D1%96%D1%86%D1%96%D1%94%D0%BD%D1%82_%D0%BF%D0%BE%D1%82%D1%83%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D1%96" title="Коефіцієнт потужності – Ukrainian" lang="uk" hreflang="uk" data-title="Коефіцієнт потужності" data-language-autonym="Українська" 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div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the firearms cartridge ranking system, see <a href="/wiki/Power_factor_(shooting_sports)" title="Power factor (shooting sports)">Power factor (shooting sports)</a>.</div> <p>In <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a>, the <b>power factor</b> of an <a href="/wiki/AC_power" title="AC power">AC power</a> system is defined as the <a href="/wiki/Ratio" title="Ratio">ratio</a> of the <i><a href="/wiki/Real_power" class="mw-redirect" title="Real power">real power</a></i> absorbed by the <a href="/wiki/Electrical_load" title="Electrical load">load</a> to the <i><a href="/wiki/Apparent_power" class="mw-redirect" title="Apparent power">apparent power</a></i> flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> (RMS) current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average <a href="/wiki/Product_(mathematics)" title="Product (mathematics)">product</a> of the two. A negative power factor occurs when the device (normally the load) generates real power, which then flows back towards the source. </p><p>In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The larger currents increase the energy lost in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers with a low power factor. </p><p><b>Power-factor correction</b> increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with a low power factor (such as <a href="/wiki/Induction_motor" title="Induction motor">induction motors</a>) can be corrected with a passive network of <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> or <a href="/wiki/Inductor" title="Inductor">inductors</a>. Non-linear loads, such as <a href="/wiki/Rectifier" title="Rectifier">rectifiers</a>, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central <a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">substation</a>, spread out over a distribution system, or built into power-consuming equipment. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Linear_circuits">Linear circuits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=1" title="Edit section: Linear circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Power_factor_0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Power_factor_0.svg/300px-Power_factor_0.svg.png" decoding="async" width="300" height="247" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Power_factor_0.svg/450px-Power_factor_0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Power_factor_0.svg/600px-Power_factor_0.svg.png 2x" data-file-width="619" data-file-height="510" /></a><figcaption>Power flow calculated from AC voltage and current entering a load having a zero power factor (<span class="texhtml mvar" style="font-style:italic;">ϕ</span> = 90°, cos(<span class="texhtml mvar" style="font-style:italic;">ϕ</span>) = 0). The blue line shows the instantaneous power entering the load: all of the energy received during the first (or third) quarter cycle is returned to the grid during the second (or fourth) quarter cycle, resulting in an <i>average</i> power flow (light blue line) of zero.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Power_factor_0.7.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Power_factor_0.7.svg/300px-Power_factor_0.7.svg.png" decoding="async" width="300" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Power_factor_0.7.svg/450px-Power_factor_0.7.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Power_factor_0.7.svg/600px-Power_factor_0.7.svg.png 2x" data-file-width="669" data-file-height="559" /></a><figcaption>Instantaneous and average power calculated from AC voltage and current for a load with a lagging power factor (<span class="texhtml mvar" style="font-style:italic;">ϕ</span> = 45°, cos(<span class="texhtml mvar" style="font-style:italic;">ϕ</span>) ≈ 0.71). The blue line (instantaneous power) shows that a portion of the energy received by the load is returned to the grid during the part of the cycle labeled <span class="texhtml mvar" style="font-style:italic;">ϕ</span>.</figcaption></figure> <p>In a <a href="/wiki/Linear_time-invariant_system" title="Linear time-invariant system">linear circuit</a>, consisting of combinations of resistors, inductors, and capacitors, current flow has a sinusoidal response to the sinusoidal line voltage.<sup id="cite_ref-Das_2015_1-0" class="reference"><a href="#cite_note-Das_2015-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A linear load does not change the shape of the input waveform but may change the relative timing (phase) between voltage and current, due to its inductance or capacitance. </p><p>In a purely resistive AC circuit, voltage and current waveforms are in step (or <a href="/wiki/Phase_(waves)" title="Phase (waves)">in phase</a>), changing polarity at the same instant in each cycle. All the power entering the load is consumed (or dissipated). </p><p>Where <a href="/wiki/Reactance_(electronics)" class="mw-redirect" title="Reactance (electronics)">reactive</a> loads are present, such as with <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> or <a href="/wiki/Inductor" title="Inductor">inductors</a>, energy storage in the loads results in a phase difference between the current and voltage waveforms. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in <a href="/wiki/Electric_field" title="Electric field">electric</a> or <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic fields</a> then returned to the power grid a fraction of the period later. </p><p>Electrical circuits containing predominantly resistive loads (<a href="/wiki/Incandescent_lamps" class="mw-redirect" title="Incandescent lamps">incandescent lamps</a>, devices using <a href="/wiki/Heating_element" title="Heating element">heating elements</a> like <a href="/wiki/Electric_toaster" class="mw-redirect" title="Electric toaster">electric toasters</a> and <a href="/wiki/Electric_oven" class="mw-redirect" title="Electric oven">ovens</a>) have a power factor of almost 1, but circuits containing inductive or capacitive loads (electric motors, <a href="/wiki/Solenoid" title="Solenoid">solenoid</a> valves, transformers, <a href="/wiki/Electrical_ballast" title="Electrical ballast">fluorescent lamp ballasts</a>, and others) can have a power factor well below 1. </p><p>A circuit with a low power factor will use a greater amount of current to transfer a given quantity of real power than a circuit with a high power factor thus causing increased losses due to <a href="/wiki/Joule_heating" title="Joule heating">resistive heating</a> in power lines, and requiring the use of higher-rated conductors and transformers. </p> <div class="mw-heading mw-heading3"><h3 id="Definition_and_calculation">Definition and calculation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=2" title="Edit section: Definition and calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/AC_power#Instantaneous_power,_instantaneous_active_power_and_instantaneous_reactive_power_in_sinusoidal_steady-state" title="AC power">AC power</a> has two components: </p> <ul><li><a href="/wiki/AC_power#Active_power_in_sinusoidal_steady-state" title="AC power">Real power or active power</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span>) (sometimes called average power<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>), expressed in <a href="/wiki/Watt" title="Watt">watts</a> (W)</li> <li><a href="/wiki/AC_power#Reactive_power_in_sinusoidal_steady-state" title="AC power">Reactive power</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span>), usually expressed in <a href="/wiki/Volt-ampere_reactive" class="mw-redirect" title="Volt-ampere reactive">reactive volt-amperes</a> (var)<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li></ul> <p>Together, they form the <a href="/wiki/AC_power#Complex_power_in_sinusoidal_steady-state" title="AC power">complex power</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>) expressed as <a href="/wiki/Volt-amperes" class="mw-redirect" title="Volt-amperes">volt-amperes</a> (VA). The magnitude of the complex power is the apparent power (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |S|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |S|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28d901e98a035ff4c0e37fe6dd8e750ece6c1f0b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.793ex; height:2.843ex;" alt="{\displaystyle |S|}"></span>), also expressed in volt-amperes (VA). </p><p>The VA and var are non-SI units dimensionally similar to the watt but are used in engineering practice instead of the watt to state what <a href="/wiki/Physical_quantity" title="Physical quantity">quantity</a> is being expressed. The <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> explicitly disallows using units for this purpose or as the only source of information about a physical quantity as used.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The power factor can also be computed as the cosine of the angle θ by which the current waveform lags or leads the voltage waveform.<sup id="cite_ref-SureshKumar_2013_7-0" class="reference"><a href="#cite_note-SureshKumar_2013-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Power_triangle">Power triangle</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=3" title="Edit section: Power triangle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Power_triangle_diagram.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Power_triangle_diagram.jpg/370px-Power_triangle_diagram.jpg" decoding="async" width="370" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/b8/Power_triangle_diagram.jpg 1.5x" data-file-width="442" data-file-height="175" /></a></span> </p><p>One can relate the various components of AC power by using the power triangle in vector space. Real power extends horizontally in the real axis and reactive power extends in the direction of the imaginary axis. Complex power (and its magnitude, apparent power) represents a combination of both real and reactive power, and therefore can be calculated by using the vector sum of these two components. We can conclude that the mathematical relationship between these components is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}S&=P+jQ\\|S|&={\sqrt {P^{2}+Q^{2}}}\\{\text{pf}}&=\cos {\theta }={\frac {P}{|S|}}=\cos {\left(\arctan {\left({\frac {Q}{P}}\right)}\right)}\\Q&=P\,\tan(\arccos({\text{pf}}))\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>S</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>P</mi> <mo>+</mo> <mi>j</mi> <mi>Q</mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>pf</mtext> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>P</mi> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>Q</mi> <mi>P</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>Q</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>P</mi> <mspace width="thinmathspace" /> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>arccos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>pf</mtext> </mrow> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}S&=P+jQ\\|S|&={\sqrt {P^{2}+Q^{2}}}\\{\text{pf}}&=\cos {\theta }={\frac {P}{|S|}}=\cos {\left(\arctan {\left({\frac {Q}{P}}\right)}\right)}\\Q&=P\,\tan(\arccos({\text{pf}}))\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37992d4db007c5931353013d024c857c4dcdaafe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.171ex; width:40.926ex; height:17.509ex;" alt="{\displaystyle {\begin{aligned}S&=P+jQ\\|S|&={\sqrt {P^{2}+Q^{2}}}\\{\text{pf}}&=\cos {\theta }={\frac {P}{|S|}}=\cos {\left(\arctan {\left({\frac {Q}{P}}\right)}\right)}\\Q&=P\,\tan(\arccos({\text{pf}}))\end{aligned}}}"></span></dd></dl> <p>As the angle θ increases with fixed total apparent power, current and voltage are further out of phase with each other. Real power decreases, and reactive power increases. </p> <div class="mw-heading mw-heading4"><h4 id="Lagging,_leading_and_unity_power_factors"><span id="Lagging.2C_leading_and_unity_power_factors"></span>Lagging, leading and unity power factors</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=4" title="Edit section: Lagging, leading and unity power factors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Power factor is described as <i>leading</i> if the current waveform is advanced in phase concerning voltage, or <i>lagging</i> when the current waveform is behind the voltage waveform. A lagging power factor signifies that the load is inductive, as the load will <i>consume</i> reactive power. The reactive component <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> is positive as reactive power travels through the circuit and is <i>consumed</i> by the inductive load. A leading power factor signifies that the load is capacitive, as the load <i>supplies</i> reactive power, and therefore the reactive component <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8752c7023b4b3286800fe3238271bbca681219ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}"></span> is negative as reactive power is being supplied to the circuit. </p><p><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Lagging-Leading.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Lagging-Leading.jpg/590px-Lagging-Leading.jpg" decoding="async" width="590" height="224" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/40/Lagging-Leading.jpg 1.5x" data-file-width="737" data-file-height="280" /></a></span> </p><p>If θ is the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase angle</a> between the current and voltage, then the power factor is equal to the <a href="/wiki/Trigonometric_functions" title="Trigonometric functions">cosine</a> of the angle, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/611e5c70de1d1cf4ebc3b70d2b5467f45d17a483" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.589ex; height:2.176ex;" alt="{\displaystyle \cos \theta }"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |P|=|S|\cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |P|=|S|\cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d68e3a292318e732659831b37364d0bc2bfe6a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.906ex; height:2.843ex;" alt="{\displaystyle |P|=|S|\cos \theta }"></span></dd></dl> <p>Since the units are consistent, the power factor is by definition a <a href="/wiki/Dimensionless_number" class="mw-redirect" title="Dimensionless number">dimensionless number</a> between -1 and 1. When the power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, referred to as the <i>unity</i> power factor, all the energy supplied by the source is consumed by the load. Power factors are usually stated as <i>leading</i> or <i>lagging</i> to show the sign of the phase angle. Capacitive loads are leading (current leads voltage), and inductive loads are lagging (current lags voltage). </p><p>If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be 1, and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as induction motors (any type of wound coil) consume reactive power with the current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cables generate reactive power with the current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, which is stored in the device's magnetic or electric field, only to return this energy back to the source during the rest of the cycle. </p><p>For example, to get 1 kW of real power, if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kW ÷ 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor, 5 kVA of apparent power needs to be transferred (1 kW ÷ 0.2 = 5 kVA). This apparent power must be produced and transmitted to the load and is subject to losses in the production and transmission processes. </p><p>Electrical loads consuming <a href="/wiki/AC_power" title="AC power">alternating current power</a> consume both real power and reactive power. The vector sum of real and reactive power is the complex power, and its magnitude is the apparent power. The presence of reactive power causes the real power to be less than the apparent power, and so, the electric load has a power factor of less than 1. </p><p>A negative power factor (0 to −1) can result from returning active power to the source, such as in the case of a building fitted with solar panels when surplus power is fed back into the supply.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Power_factor_correction_of_linear_loads">Power factor correction of linear loads</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=5" title="Edit section: Power factor correction of linear loads"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Blindleistungskompensation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Blindleistungskompensation.svg/220px-Blindleistungskompensation.svg.png" decoding="async" width="220" height="118" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Blindleistungskompensation.svg/330px-Blindleistungskompensation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Blindleistungskompensation.svg/440px-Blindleistungskompensation.svg.png 2x" data-file-width="1860" data-file-height="1000" /></a><figcaption>Power factor correction of linear load</figcaption></figure> <p>A high power factor is generally desirable in a power delivery system to reduce losses and improve voltage regulation at the load. Compensating elements near an electrical load will reduce the apparent power demand on the supply system. Power factor correction may be applied by an <a href="/wiki/Electric_power_transmission" title="Electric power transmission">electric power transmission</a> utility to improve the stability and efficiency of the network. Individual electrical customers who are charged by their utility for low power factor may install correction equipment to increase their power factor to reduce costs. </p><p>Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying or absorbing reactive power, adding capacitors or inductors that act to cancel the inductive or capacitive effects of the load, respectively. In the case of offsetting the inductive effect of motor loads, capacitors can be locally connected. These capacitors help to generate reactive power to meet the demand of the inductive loads. This will keep that reactive power from having to flow from the utility generator to the load. In the electricity industry, inductors are said to consume reactive power, and capacitors are said to supply it, even though reactive power is just energy moving back and forth on each AC cycle. </p><p>The reactive elements in power factor correction devices can create voltage fluctuations and harmonic noise when switched on or off. They will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the system's no-load losses. In the worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe <a href="/wiki/Overvoltage" title="Overvoltage">overvoltage</a> fluctuations. As such, reactive elements cannot simply be applied without engineering analysis. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Condensatorenbatterij.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Condensatorenbatterij.jpg/220px-Condensatorenbatterij.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Condensatorenbatterij.jpg/330px-Condensatorenbatterij.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Condensatorenbatterij.jpg/440px-Condensatorenbatterij.jpg 2x" data-file-width="2272" data-file-height="1704" /></a><figcaption>1. <a href="/wiki/Static_VAR_compensator" title="Static VAR compensator">Reactive power control relay</a>; 2. Network connection points; 3. <a href="/wiki/Fuse_(electrical)" title="Fuse (electrical)">Slow-blow fuses</a>; 4. Inrush-limiting <a href="/wiki/Contactor" title="Contactor">contactors</a>; 5. <a href="/wiki/Capacitor" title="Capacitor">Capacitors</a> (single-phase or three-phase units, delta-connection); 6. <a href="/wiki/Transformer" title="Transformer">Transformer</a> (for controls and ventilation fans) </figcaption></figure> <p>An <b> automatic power factor correction unit</b> consists of some <a href="/wiki/Capacitor" title="Capacitor">capacitors</a> that are switched by means of <a href="/wiki/Contactor" title="Contactor">contactors</a>. These contactors are controlled by a regulator that measures power factor in an electrical network. Depending on the load and power factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value. </p><p>In place of a set of switched <a href="/wiki/Capacitor" title="Capacitor">capacitors</a>, an unloaded <a href="/wiki/Synchronous_motor" title="Synchronous motor">synchronous motor</a> can supply reactive power. The <a href="/wiki/Reactive_power" class="mw-redirect" title="Reactive power">reactive power</a> drawn by the synchronous motor is a function of its field excitation. It is referred to as a <b><a href="/wiki/Synchronous_condenser" title="Synchronous condenser">synchronous condenser</a></b>. It is started and connected to the <a href="/wiki/Electrical_network" title="Electrical network">electrical network</a>. It operates at a leading power factor and puts <a href="/wiki/Volt-ampere_reactive" class="mw-redirect" title="Volt-ampere reactive">vars</a> onto the network as required to support a system's <a href="/wiki/Voltage" title="Voltage">voltage</a> or to maintain the system power factor at a specified level. </p><p>The synchronous condenser's installation and operation are identical to those of large <a href="/wiki/Electric_motor" title="Electric motor">electric motors</a>. Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like a variable capacitor. Unlike with capacitors, the amount of reactive power furnished is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensers are often used in connection with <a href="/wiki/High-voltage_direct_current" title="High-voltage direct current">high-voltage direct-current</a> transmission projects or in large industrial plants such as <a href="/wiki/Steel_mill" title="Steel mill">steel mills</a>. </p><p>For power factor correction of high-voltage power systems or large, fluctuating industrial loads, power electronic devices such as the <a href="/wiki/Static_VAR_compensator" title="Static VAR compensator">static VAR compensator</a> or <a href="/wiki/STATCOM" class="mw-redirect" title="STATCOM">STATCOM</a> are increasingly used. These systems are able to compensate sudden changes of power factor much more rapidly than contactor-switched capacitor banks and, being solid-state, require less maintenance than synchronous condensers. </p> <div class="mw-heading mw-heading2"><h2 id="Non-linear_loads">Non-linear loads</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=6" title="Edit section: Non-linear loads"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Examples of non-linear loads on a power system are rectifiers (such as used in a power supply), and arc discharge devices such as <a href="/wiki/Fluorescent_lamp" title="Fluorescent lamp">fluorescent lamps</a>, electric <a href="/wiki/Welding" title="Welding">welding</a> machines, or <a href="/wiki/Arc_furnace" class="mw-redirect" title="Arc furnace">arc furnaces</a>. Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. <i>Distortion power factor</i> is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Power_factor_75_2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Power_factor_75_2.png/300px-Power_factor_75_2.png" decoding="async" width="300" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/94/Power_factor_75_2.png 1.5x" data-file-width="393" data-file-height="354" /></a><figcaption>Sinusoidal voltage and non-sinusoidal current give a distortion power factor of 0.75 for this computer power supply load.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Non-sinusoidal_components">Non-sinusoidal components</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=7" title="Edit section: Non-sinusoidal components"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 <i>displacement power factor</i>.<sup id="cite_ref-FuchsMasoum2015_11-0" class="reference"><a href="#cite_note-FuchsMasoum2015-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Non-linear loads change the shape of the current waveform from a <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a> to some other form. Non-linear loads create <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain <a href="/wiki/Non-linear" class="mw-redirect" title="Non-linear">non-linear</a> loads such as <a href="/wiki/Rectifiers" class="mw-redirect" title="Rectifiers">rectifiers</a>, some forms of electric lighting, <a href="/wiki/Electric_arc_furnace" title="Electric arc furnace">electric arc furnaces</a>, welding equipment, <a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">switched-mode power supplies</a>, variable speed drives and other devices. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system. </p><p>To measure the real power or reactive power, a <a href="/wiki/Wattmeter" title="Wattmeter">wattmeter</a> designed to work properly with non-sinusoidal currents must be used. </p> <div class="mw-heading mw-heading3"><h3 id="Distortion_power_factor">Distortion power factor</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=8" title="Edit section: Distortion power factor"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <b>distortion power factor</b> is the distortion component associated with the harmonic voltages and currents present in the system. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\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{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>distortion power factor</mtext> </mstyle> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msqrt> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> </msqrt> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> </mrow> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>+</mo> <mi>T</mi> <mi>H</mi> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\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{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9027a061193041b5732fec25cf4464f07cdd3a48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -15.171ex; width:53.142ex; height:31.509ex;" alt="{\displaystyle {\begin{aligned}{\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{aligned}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{THD}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>THD</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{THD}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e47a55ca3b41f55160baacd0b8cbe5dab3dfecc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.996ex; height:2.509ex;" alt="{\displaystyle {\mbox{THD}}_{i}}"></span> is the <a href="/wiki/Total_harmonic_distortion" title="Total harmonic distortion">total harmonic distortion</a> of the load current. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 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}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>H</mi> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </msqrt> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> </msqrt> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 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}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac832d1338f9e67b0db47335901a623fa4045c38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:43.01ex; height:10.676ex;" alt="{\displaystyle 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}}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03f18d041b2df30adef07164dbf285878893dedc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{1}}"></span> is the fundamental component of the current, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{rms}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{rms}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e397d267d8fb23b0fef967675b3169bca119b18b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.211ex; height:2.509ex;" alt="{\displaystyle I_{rms}}"></span> is the total current, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{h}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{h}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4c84ca7860f66cd4ed8ecb07b4c5691f73c7365" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.202ex; height:2.509ex;" alt="{\displaystyle I_{h}}"></span> is the current on the h<sup>th</sup> harmonic; all are <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> 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.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The result when multiplied with the displacement power factor is the overall, true power factor or just power factor (PF): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{PF}}={\frac {\cos {\varphi }}{\sqrt {1+THD_{i}^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>PF</mtext> </mstyle> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>φ</mi> </mrow> </mrow> <msqrt> <mn>1</mn> <mo>+</mo> <mi>T</mi> <mi>H</mi> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{PF}}={\frac {\cos {\varphi }}{\sqrt {1+THD_{i}^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/598c51e116683db75d9e5bb13fdb40b56ec1334b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:20.04ex; height:7.676ex;" alt="{\displaystyle {\mbox{PF}}={\frac {\cos {\varphi }}{\sqrt {1+THD_{i}^{2}}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Distortion_in_three-phase_networks">Distortion in three-phase networks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=9" title="Edit section: Distortion in three-phase networks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In practice, the local effects of distortion current on devices in a <a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">three-phase distribution network</a> rely on the magnitude of certain order harmonics rather than the total harmonic distortion. </p><p>For example, the <a href="/wiki/Harmonics_(electrical_power)#Even,_odd,_triplen_and_non-triplen_odd_harmonics" title="Harmonics (electrical power)">triplen</a>, or zero-sequence, harmonics (3rd, 9th, 15th, etc.) have the property of being in-phase when compared line-to-line. In a <a href="/wiki/Delta-wye_transformer" title="Delta-wye transformer">delta-wye transformer</a>, these harmonics can result in circulating currents in the delta windings and result in greater <a href="/wiki/Joule_heating" title="Joule heating">resistive heating</a>. 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 <a href="/wiki/Ground_and_neutral" title="Ground and neutral">neutral wire</a>. This could overload the neutral wire in some cases and create error in kilowatt-hour metering systems and billing revenue.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The presence of current harmonics in a transformer also result in larger <a href="/wiki/Eddy_currents" class="mw-redirect" title="Eddy currents">eddy currents</a> 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.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>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.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Power_factor_correction_(PFC)_in_non-linear_loads"><span id="Power_factor_correction_.28PFC.29_in_non-linear_loads"></span>Power factor correction (PFC) in non-linear loads</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=10" title="Edit section: Power factor correction (PFC) in non-linear loads"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Passive_PFC">Passive PFC</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=11" title="Edit section: Passive PFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The simplest way to control the <a href="/wiki/Harmonics_(electrical_power)" title="Harmonics (electrical power)">harmonic</a> current is to use a <a href="/wiki/Electronic_filter" title="Electronic filter">filter</a> that passes current only at <a href="/wiki/Utility_frequency" title="Utility frequency">line frequency</a> (50 or 60 Hz). The filter consists of capacitors or inductors and makes a non-linear device look more like a <a href="/wiki/Linear" class="mw-redirect" title="Linear">linear</a> load. An example of passive PFC is a <a href="/wiki/Valley-fill_circuit" title="Valley-fill circuit">valley-fill circuit</a>. </p><p>A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Also, in practice, passive PFC is often less effective at improving the power factor.<sup id="cite_ref-effi_20-0" class="reference"><a href="#cite_note-effi-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Active_PFC">Active PFC</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=12" title="Edit section: Active PFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Active_pfc_PSU_packaging.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Active_pfc_PSU_packaging.png/220px-Active_pfc_PSU_packaging.png" decoding="async" width="220" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e8/Active_pfc_PSU_packaging.png 1.5x" data-file-width="283" data-file-height="169" /></a><figcaption>Specifications taken from the packaging of a 610 W <a href="/wiki/Power_supply_unit_(computer)" title="Power supply unit (computer)">PC power supply</a> showing active PFC rating</figcaption></figure> <p>Active PFC is the use of <a href="/wiki/Power_electronics" title="Power electronics">power electronics</a> to change the waveform of current drawn by a load to improve the power factor.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Some types of the active PFC are <a href="/wiki/Buck_converter" title="Buck converter">buck</a>, <a href="/wiki/Boost_converter" title="Boost converter">boost</a>, <a href="/wiki/Buck-boost_converter" class="mw-redirect" title="Buck-boost converter">buck-boost</a> and <a href="/wiki/Synchronous_condenser" title="Synchronous condenser">synchronous condenser</a>. Active power factor correction can be single-stage or multi-stage. </p><p>In the case of a switched-mode power supply, a <a href="/wiki/Boost_converter" title="Boost converter">boost converter</a> 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. </p><p>For a three-phase SMPS, the <a href="/wiki/Vienna_rectifier" title="Vienna rectifier">Vienna rectifier</a> configuration may be used to substantially improve the power factor. </p><p><a href="/wiki/Switched-mode_power_supply" title="Switched-mode power supply">SMPSs</a> 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.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>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. </p> <div class="mw-heading mw-heading4"><h4 id="Dynamic_PFC">Dynamic PFC</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=13" title="Edit section: Dynamic PFC"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> DPFC uses semiconductor switches, typically <a href="/wiki/Thyristor" title="Thyristor">thyristors</a>, to quickly connect and disconnect capacitors or inductors to improve power factor. </p> <div class="mw-heading mw-heading2"><h2 id="Importance_in_distribution_systems">Importance in distribution systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=14" title="Edit section: Importance in distribution systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Condensor_bank_150kV_-_75MVAR.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/170px-Condensor_bank_150kV_-_75MVAR.jpg" decoding="async" width="170" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/255px-Condensor_bank_150kV_-_75MVAR.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Condensor_bank_150kV_-_75MVAR.jpg/340px-Condensor_bank_150kV_-_75MVAR.jpg 2x" data-file-width="926" data-file-height="1382" /></a><figcaption>75 MVAr capacitor bank in a 150 kV substation</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg/220px-Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg/330px-Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg/440px-Condenser_bank_on_utility_pole_with_fuses_disconnected.jpg 2x" data-file-width="965" data-file-height="965" /></a><figcaption>Capacitor bank on a utility pole in San Jose, CA, USA</figcaption></figure> <p>Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively, all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current. When the power factor is close to unity, for the same kVA rating of the transformer more load current can be supplied.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission. </p><p>With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Current <a href="/wiki/Energy_Star" title="Energy Star">Energy Star</a> guidelines for computers<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> call for a power factor of ≥ 0.9 at 100% of rated output in the <a href="/wiki/Power_supply_unit_(computer)" title="Power supply unit (computer)">PC's power supply</a>. According to a white paper authored by Intel and the <a href="/wiki/United_States_Environmental_Protection_Agency" title="United States Environmental Protection Agency">U.S. Environmental Protection Agency</a>, PCs with internal power supplies will require the use of active power factor correction to meet the ENERGY STAR 5.0 Program Requirements for Computers.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>In Europe, <a href="/wiki/IEC_EN_61000-3-2" class="mw-redirect" title="IEC EN 61000-3-2">EN 61000-3-2</a> requires power factor correction be incorporated into consumer products. </p><p>Small customers, such as households, are not usually charged for reactive power and so power factor metering equipment for such customers will not be installed. </p> <div class="mw-heading mw-heading2"><h2 id="Measurement_techniques">Measurement techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=15" title="Edit section: Measurement techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The power factor in a single-phase circuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced <a href="/wiki/Polyphase_system" title="Polyphase system">polyphase circuit</a> is the same as that of any phase. The power factor of an unbalanced polyphase circuit is not uniquely defined. </p><p>A direct reading power factor meter can be made with a <a href="/wiki/Moving_coil_meter" class="mw-redirect" title="Moving coil meter">moving coil meter</a> of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque, driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>Another electromechanical instrument is the polarized-vane type.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes that are magnetized by the current coil. In operation, the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a four-quadrant display of power factor or phase angle. </p><p>Digital instruments exist that directly measure the time lag between voltage and current waveforms. Low-cost instruments of this type measure the peak of the waveforms. More sophisticated versions measure the peak of the fundamental harmonic only, thus giving a more accurate reading for phase angle on distorted waveforms. Calculating power factor from voltage and current phases is only accurate if both waveforms are sinusoidal.<sup id="cite_ref-ni_white_paper_34-0" class="reference"><a href="#cite_note-ni_white_paper-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Power Quality Analyzers, often referred to as Power Analyzers, make a digital recording of the voltage and current waveform (typically either one phase or three phase) and accurately calculate true power (watts), apparent power (VA) power factor, AC voltage, AC current, DC voltage, DC current, frequency, IEC61000-3-2/3-12 Harmonic measurement, IEC61000-3-3/3-11 flicker measurement, individual phase voltages in delta applications where there is no neutral line, total harmonic distortion, phase and amplitude of individual voltage or current harmonics, etc.<sup id="cite_ref-Yokogawa_WT3000E_35-0" class="reference"><a href="#cite_note-Yokogawa_WT3000E-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fluke_1760_36-0" class="reference"><a href="#cite_note-Fluke_1760-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mnemonics">Mnemonics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=16" title="Edit section: Mnemonics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Anglophone power engineering students are advised to remember: <i>ELI the ICE man</i> or <i>ELI on ICE</i> – the voltage E, leads the current I, in an inductor L. The current I leads the voltage E in a capacitor C. </p><p>Another common mnemonic is CIVIL – in a capacitor (C) the current (I) leads voltage (V), voltage (V) leads current (I) in an inductor (L). </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Das_2015-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Das_2015_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDas2015" class="citation book cs1">Das, J. C. (2015). <i>Power System Harmonics and Passive Filter Design</i>. Wiley, IEEE Press. p. 2. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-118-86162-2" title="Special:BookSources/978-1-118-86162-2"><bdi>978-1-118-86162-2</bdi></a>. <q>To distinguish between linear and nonlinear loads, we may say that linear time-invariant loads are characterized so that an application of a sinusoidal voltage results in a sinusoidal flow of current.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Power+System+Harmonics+and+Passive+Filter+Design&rft.pages=2&rft.pub=Wiley%2C+IEEE+Press&rft.date=2015&rft.isbn=978-1-118-86162-2&rft.aulast=Das&rft.aufirst=J.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoylestad2002" class="citation book cs1">Boylestad, Robert (2002-03-04). <i>Introductory Circuit Analysis</i> (10th ed.). p. 857. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-097417-4" title="Special:BookSources/978-0-13-097417-4"><bdi>978-0-13-097417-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Circuit+Analysis&rft.pages=857&rft.edition=10th&rft.date=2002-03-04&rft.isbn=978-0-13-097417-4&rft.aulast=Boylestad&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071211234311/http://www.iec.ch/zone/si/si_elecmag.htm#si_epo">"SI Units – Electricity and Magnetism"</a>. <a href="/wiki/Switzerland" title="Switzerland">CH</a>: International Electrotechnical Commission. Archived from <a rel="nofollow" class="external text" href="http://www.iec.ch/zone/si/si_elecmag.htm">the original</a> on 2007-12-11<span class="reference-accessdate">. Retrieved <span class="nowrap">14 June</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=SI+Units+%E2%80%93+Electricity+and+Magnetism&rft.place=CH&rft.pub=International+Electrotechnical+Commission&rft_id=http%3A%2F%2Fwww.iec.ch%2Fzone%2Fsi%2Fsi_elecmag.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://www.bipm.org/documents/20126/41483022/si_brochure_8.pdf"><i>The International System of Units (SI) [SI brochure]</i></a> <span class="cs1-format">(PDF)</span>. § 5.3.2 (p. 132, 40 in the <a href="/wiki/PDF" title="PDF">PDF</a> file): <a href="/wiki/BIPM" class="mw-redirect" title="BIPM">BIPM</a>. 2006. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220319080426/https://www.bipm.org/documents/20126/41483022/si_brochure_8.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-03-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+International+System+of+Units+%28SI%29+%5BSI+brochure%5D&rft.place=%C2%A7+5.3.2+%28p.+132%2C+40+in+the+PDF+file%29&rft.pub=BIPM&rft.date=2006&rft_id=https%3A%2F%2Fwww.bipm.org%2Fdocuments%2F20126%2F41483022%2Fsi_brochure_8.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location (<a href="/wiki/Category:CS1_maint:_location" title="Category:CS1 maint: location">link</a>)</span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><i>Authoritative Dictionary of Standards Terms</i> (7th ed.), <a href="/wiki/Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">IEEE</a>, 2000, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7381-2601-2" title="Special:BookSources/978-0-7381-2601-2"><bdi>978-0-7381-2601-2</bdi></a>, Std. 100</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Authoritative+Dictionary+of+Standards+Terms&rft.edition=7th&rft.pub=IEEE&rft.date=2000&rft.isbn=978-0-7381-2601-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><i>Trial-Use Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions</i>, IEEE, 2000, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7381-1963-2" title="Special:BookSources/978-0-7381-1963-2"><bdi>978-0-7381-1963-2</bdi></a>, Std. 1459–2000</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Trial-Use+Standard+Definitions+for+the+Measurement+of+Electric+Power+Quantities+Under+Sinusoidal%2C+Nonsinusoidal%2C+Balanced%2C+or+Unbalanced+Conditions&rft.pub=IEEE&rft.date=2000&rft.isbn=978-0-7381-1963-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span>. Note 1, section 3.1.1.1, when defining the quantities for power factor, asserts that real power only flows to the load and can never be negative. As of 2013, one of the authors acknowledged that this note was incorrect, and is being revised for the next edition. See <a rel="nofollow" class="external free" href="http://powerstandards.com/Shymanski/draft.pdf">http://powerstandards.com/Shymanski/draft.pdf</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304071333/http://powerstandards.com/Shymanski/draft.pdf">Archived</a> 2016-03-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-SureshKumar_2013-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-SureshKumar_2013_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSuresh_Kumar2013" class="citation book cs1">Suresh Kumar, K. S. (2013). <i>Electric Circuit Analysis</i>. Pearson. p. 8.10. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-8-13-179155-4" title="Special:BookSources/978-8-13-179155-4"><bdi>978-8-13-179155-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electric+Circuit+Analysis&rft.pages=8.10&rft.pub=Pearson&rft.date=2013&rft.isbn=978-8-13-179155-4&rft.aulast=Suresh+Kumar&rft.aufirst=K.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDuddell1901" class="citation cs2">Duddell, W. (1901), "On the resistance and electromotive forces of the electric arc", <i>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, <b>203</b> (359–371): 512–15, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.1904.0022">10.1098/rsta.1904.0022</a></span>, <q>The fact that the solid arc has, at low frequencies, a negative power factor, indicates that the arc is supplying power to the alternator…</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+A%3A+Mathematical%2C+Physical+and+Engineering+Sciences&rft.atitle=On+the+resistance+and+electromotive+forces+of+the+electric+arc&rft.volume=203&rft.issue=359%E2%80%93371&rft.pages=512-15&rft.date=1901&rft_id=info%3Adoi%2F10.1098%2Frsta.1904.0022&rft.aulast=Duddell&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhang2006" class="citation cs2">Zhang, S. (July 2006), "Analysis of some measurement issues in bushing power factor tests in the field", <i>IEEE Transactions on Power Delivery</i>, <b>21</b> (3): 1350–56, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Ftpwrd.2006.874616">10.1109/tpwrd.2006.874616</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:39895367">39895367</a>, <q>…(the measurement) gives both negative power factor and negative resistive current (power loss)</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Power+Delivery&rft.atitle=Analysis+of+some+measurement+issues+in+bushing+power+factor+tests+in+the+field&rft.volume=21&rft.issue=3&rft.pages=1350-56&rft.date=2006-07&rft_id=info%3Adoi%2F10.1109%2Ftpwrd.2006.874616&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A39895367%23id-name%3DS2CID&rft.aulast=Zhang&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlmarshoud2004" class="citation cs2">Almarshoud, A. F.; et al. (2004), "Performance of Grid-Connected Induction Generator under Naturally Commutated AC Voltage Controller", <i>Electric Power Components and Systems</i>, <b>32</b> (7): 691–700, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F15325000490461064">10.1080/15325000490461064</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:110279940">110279940</a>, <q>Accordingly, the generator will consume active power from the grid, which leads to negative power factor.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Electric+Power+Components+and+Systems&rft.atitle=Performance+of+Grid-Connected+Induction+Generator+under+Naturally+Commutated+AC+Voltage+Controller&rft.volume=32&rft.issue=7&rft.pages=691-700&rft.date=2004&rft_id=info%3Adoi%2F10.1080%2F15325000490461064&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A110279940%23id-name%3DS2CID&rft.aulast=Almarshoud&rft.aufirst=A.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-FuchsMasoum2015-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FuchsMasoum2015_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEwald_FuchsMohammad_A._S._Masoum2015" class="citation book cs1">Ewald Fuchs; Mohammad A. S. Masoum (14 July 2015). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=wuGcBAAAQBAJ&pg=PA432"><i>Power Quality in Power Systems and Electrical Machines</i></a>. Elsevier Science. pp. 432–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-800988-8" title="Special:BookSources/978-0-12-800988-8"><bdi>978-0-12-800988-8</bdi></a>. <q>The DPF is the cosine of the angle between these two quantities</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Power+Quality+in+Power+Systems+and+Electrical+Machines&rft.pages=432-&rft.pub=Elsevier+Science&rft.date=2015-07-14&rft.isbn=978-0-12-800988-8&rft.au=Ewald+Fuchs&rft.au=Mohammad+A.+S.+Masoum&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DwuGcBAAAQBAJ%26pg%3DPA432&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSankaran1999" class="citation cs2">Sankaran, C. (1999), <a rel="nofollow" class="external text" href="http://ecmweb.com/power-quality/effects-harmonics-power-systems"><i>Effects of Harmonics on Power Systems</i></a>, Electro-Test, <q>...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.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Effects+of+Harmonics+on+Power+Systems&rft.pub=Electro-Test&rft.date=1999&rft.aulast=Sankaran&rft.aufirst=C.&rft_id=http%3A%2F%2Fecmweb.com%2Fpower-quality%2Feffects-harmonics-power-systems&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150924072113/http://www.pge.com/includes/docs/pdfs/mybusiness/customerservice/energystatus/powerquality/harmonics.pdf">"Single-phase load harmonics vs. three-phase load harmonics"</a> <span class="cs1-format">(PDF)</span>, <i>Power System Harmonics</i>, Pacific Gas and Electric, archived from <a rel="nofollow" class="external text" href="http://www.pge.com/includes/docs/pdfs/mybusiness/customerservice/energystatus/powerquality/harmonics.pdf">the original</a> <span class="cs1-format">(<a href="/wiki/PDF" title="PDF">PDF</a>)</span> on 2015-09-24<span class="reference-accessdate">, retrieved <span class="nowrap">2013-11-26</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Single-phase+load+harmonics+vs.+three-phase+load+harmonics&rft.btitle=Power+System+Harmonics&rft.pub=Pacific+Gas+and+Electric&rft_id=http%3A%2F%2Fwww.pge.com%2Fincludes%2Fdocs%2Fpdfs%2Fmybusiness%2Fcustomerservice%2Fenergystatus%2Fpowerquality%2Fharmonics.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://energylogix.ca/harmonics_and_ieee.pdf">"Harmonic Effects"</a> <span class="cs1-format">(<a href="/wiki/PDF" title="PDF">PDF</a>)</span>, <i>Harmonics and IEEE 519</i>, <a href="/wiki/Canada" title="Canada">CA</a>: EnergyLogix Solutions</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Harmonic+Effects&rft.btitle=Harmonics+and+IEEE+519&rft.place=CA&rft.pub=EnergyLogix+Solutions&rft_id=http%3A%2F%2Fenergylogix.ca%2Fharmonics_and_ieee.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSankaran1999" class="citation cs2">Sankaran, C. (1999), "Transformers", <a rel="nofollow" class="external text" href="http://ecmweb.com/power-quality/effects-harmonics-power-systems"><i>Effects of Harmonics on Power Systems</i></a>, Electro-Test</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Transformers&rft.btitle=Effects+of+Harmonics+on+Power+Systems&rft.pub=Electro-Test&rft.date=1999&rft.aulast=Sankaran&rft.aufirst=C.&rft_id=http%3A%2F%2Fecmweb.com%2Fpower-quality%2Feffects-harmonics-power-systems&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSankaran1999" class="citation cs2">Sankaran, C. 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H.; Hurley, W. G., "Quasi-active Power Factor Correction: The Role of Variable Inductance", <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200806105647/http://www.nuigalway.ie/power_electronics/projects/quasi_active.html"><i>Power electronics</i></a> (project), <a href="/wiki/Ireland" title="Ireland">IE</a>: Nuigalway, archived from <a rel="nofollow" class="external text" href="http://www.nuigalway.ie/power_electronics/projects/quasi_active.html">the original</a> on 2020-08-06<span class="reference-accessdate">, retrieved <span class="nowrap">2008-11-05</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Quasi-active+Power+Factor+Correction%3A+The+Role+of+Variable+Inductance&rft.btitle=Power+electronics&rft.place=IE&rft.pub=Nuigalway&rft.aulast=W%C3%B6lfle&rft.aufirst=W.+H.&rft.au=Hurley%2C+W.+G.&rft_id=http%3A%2F%2Fwww.nuigalway.ie%2Fpower_electronics%2Fprojects%2Fquasi_active.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-effi-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-effi_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081120040707/http://www.xbitlabs.com/articles/coolers/display/atx-psu5_3.html"><i>ATX Power Supply Units Roundup</i></a>, xBit labs, archived from <a rel="nofollow" class="external text" href="http://www.xbitlabs.com/articles/coolers/display/atx-psu5_3.html">the original</a> on 2008-11-20, <q>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.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=ATX+Power+Supply+Units+Roundup&rft.pub=xBit+labs&rft_id=http%3A%2F%2Fwww.xbitlabs.com%2Farticles%2Fcoolers%2Fdisplay%2Fatx-psu5_3.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090901140721/http://findarticles.com/p/articles/mi_m0EIN/is_2006_March_16/ai_n26797888/"><i>The Active PFC Market is Expected to Grow at an Annually Rate of 12.3% Till 2011</i></a>, Find articles, Mar 16, 2006, archived from <a rel="nofollow" class="external text" href="http://findarticles.com/p/articles/mi_m0EIN/is_2006_March_16/ai_n26797888">the original</a> on September 1, 2009, <q>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.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Active+PFC+Market+is+Expected+to+Grow+at+an+Annually+Rate+of+12.3%25+Till+2011&rft.pub=Find+articles&rft.date=2006-03-16&rft_id=http%3A%2F%2Ffindarticles.com%2Fp%2Farticles%2Fmi_m0EIN%2Fis_2006_March_16%2Fai_n26797888&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="http://www.techarp.com/showarticle.aspx?artno=81&pgno=1"><i>Power Factor Correction</i></a>, TECHarp, <q>Passive PFC […] the power factor is low at 60–80%. […] Active PFC ... a power factor of up to 95%</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Power+Factor+Correction&rft.pub=TECHarp&rft_id=http%3A%2F%2Fwww.techarp.com%2Fshowarticle.aspx%3Fartno%3D81%26pgno%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081222085515/http://www.silverstonetek.com/tech/wh_pfc.php?area="><i>Why we need PFC in PSU</i></a>, Silverstone Technology, archived from <a rel="nofollow" class="external text" href="http://www.silverstonetek.com/tech/wh_pfc.php?area=">the original</a> on 2008-12-22, <q>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%</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Why+we+need+PFC+in+PSU&rft.pub=Silverstone+Technology&rft_id=http%3A%2F%2Fwww.silverstonetek.com%2Ftech%2Fwh_pfc.php%3Farea%3D&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrooks2004" class="citation cs2">Brooks, Tom (Mar 2004), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081202100831/http://www2.electronicproducts.com/PFC_options_for_power_supplies-article-taiyo-mar2004-html.aspx">"PFC options for power supplies"</a>, <i>Taiyo</i>, Electronic products, archived from <a rel="nofollow" class="external text" href="http://www2.electronicproducts.com/PFC_options_for_power_supplies-article-taiyo-mar2004-html.aspx">the original</a> on 2008-12-02, <q>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</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Taiyo&rft.atitle=PFC+options+for+power+supplies&rft.date=2004-03&rft.aulast=Brooks&rft.aufirst=Tom&rft_id=http%3A%2F%2Fwww2.electronicproducts.com%2FPFC_options_for_power_supplies-article-taiyo-mar2004-html.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140611063712/http://www.fairchildsemi.com/an/AN/AN-42047.pdf"><i>Power Factor Correction (PFC) Basics</i></a> <span class="cs1-format">(PDF)</span> (application note), Fairchild Semiconductor, 2004, archived from <a rel="nofollow" class="external text" href="http://www.fairchildsemi.com/an/AN/AN-42047.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2014-06-11<span class="reference-accessdate">, retrieved <span class="nowrap">2009-11-29</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Power+Factor+Correction+%28PFC%29+Basics&rft.pub=Fairchild+Semiconductor&rft.date=2004&rft_id=http%3A%2F%2Fwww.fairchildsemi.com%2Fan%2FAN%2FAN-42047.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSugawaraSuzukiTakeuchiTeshima1997" class="citation cs2">Sugawara, I.; Suzuki, Y.; Takeuchi, A.; Teshima, T. 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Wayne (1978), <i>Standard Handbook for Electrical Engineers</i> (11 ed.), New York: McGraw-Hill, p. 3‐29 paragraph 80, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-020974-9" title="Special:BookSources/978-0-07-020974-9"><bdi>978-0-07-020974-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Standard+Handbook+for+Electrical+Engineers&rft.place=New+York&rft.pages=3%E2%80%9029+paragraph+80&rft.edition=11&rft.pub=McGraw-Hill&rft.date=1978&rft.isbn=978-0-07-020974-9&rft.aulast=Fink&rft.aufirst=Donald+G.&rft.au=Beaty%2C+H.+Wayne&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><i>Manual of Electric Instruments Construction and Operating Principles</i>, Schenectady, New York: General Electric, Meter and Instrument Department, 1949, pp. 66–68, GET-1087A</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Manual+of+Electric+Instruments+Construction+and+Operating+Principles&rft.place=Schenectady%2C+New+York&rft.pages=66-68&rft.pub=General+Electric%2C+Meter+and+Instrument+Department&rft.date=1949&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-ni_white_paper-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-ni_white_paper_34-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.ni.com/white-paper/4278/en/">"The Fundamentals of FFT-Based Signal Analysis and Measurement in LabVIEW and LabWindows/CVI"</a>. <i>National Instruments Corporation</i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 November</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=National+Instruments+Corporation&rft.atitle=The+Fundamentals+of+FFT-Based+Signal+Analysis+and+Measurement+in+LabVIEW+and+LabWindows%2FCVI&rft_id=http%3A%2F%2Fwww.ni.com%2Fwhite-paper%2F4278%2Fen%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-Yokogawa_WT3000E-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-Yokogawa_WT3000E_35-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20171107112155/http://www.yokogawa.co.jp/ftp/dist/ks/catalog/en/BUWT3000E-01EN_020.pdf">"WT3000E Series Precision Power Analyzers"</a> <span class="cs1-format">(PDF)</span>. <i>Yokogawa Corporation</i>. Archived from <a rel="nofollow" class="external text" href="http://www.yokogawa.co.jp/ftp/dist/ks/catalog/en/BUWT3000E-01EN_020.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 7 November 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">6 November</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Yokogawa+Corporation&rft.atitle=WT3000E+Series+Precision+Power+Analyzers&rft_id=http%3A%2F%2Fwww.yokogawa.co.jp%2Fftp%2Fdist%2Fks%2Fcatalog%2Fen%2FBUWT3000E-01EN_020.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> <li id="cite_note-Fluke_1760-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fluke_1760_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://cdn.testequity.com/documents/pdf/1760-ds.pdf">"Fluke 1760 Three-Phase Power Quality Recorder"</a> <span class="cs1-format">(PDF)</span>. <i>Fluke Corporation</i>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/https://cdn.testequity.com/documents/pdf/1760-ds.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09<span class="reference-accessdate">. Retrieved <span class="nowrap">6 November</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Fluke+Corporation&rft.atitle=Fluke+1760+Three-Phase+Power+Quality+Recorder&rft_id=https%3A%2F%2Fcdn.testequity.com%2Fdocuments%2Fpdf%2F1760-ds.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Power_factor&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110927074032/http://www.ece.utexas.edu/~grady/POWERFAC.pdf"><i>Harmonics and how they relate to power factor</i></a> <span class="cs1-format">(PDF)</span>, U Texas, archived from <a rel="nofollow" class="external text" href="http://www.ece.utexas.edu/~grady/POWERFAC.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2011-09-27<span class="reference-accessdate">, retrieved <span class="nowrap">2010-09-20</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Harmonics+and+how+they+relate+to+power+factor&rft.pub=U+Texas&rft_id=http%3A%2F%2Fwww.ece.utexas.edu%2F~grady%2FPOWERFAC.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3APower+factor" class="Z3988"></span>.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output 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href="/wiki/Backfeeding" title="Backfeeding">Backfeeding</a></li> <li><a href="/wiki/Base_load" title="Base load">Base load</a></li> <li><a href="/wiki/Demand_factor" title="Demand factor">Demand factor</a></li> <li><a href="/wiki/Droop_speed_control" title="Droop speed control">Droop speed control</a></li> <li><a href="/wiki/Electric_power" title="Electric power">Electric power</a></li> <li><a href="/wiki/Electric_power_quality" title="Electric power quality">Electric power quality</a></li> <li><a href="/wiki/Electrical_fault" title="Electrical fault">Electrical fault</a></li> <li><a href="/wiki/Energy_demand_management" title="Energy demand management">Energy demand management</a></li> <li><a href="/wiki/Energy_return_on_investment" title="Energy return on investment">Energy return on investment</a></li> <li><a href="/wiki/Grid_code" title="Grid code">Grid code</a></li> <li><a href="/wiki/Grid_energy_storage" title="Grid energy storage">Grid energy storage</a></li> <li><a href="/wiki/Grid_strength" class="mw-redirect" title="Grid strength">Grid strength</a></li> <li><a href="/wiki/Home_energy_storage" title="Home energy storage">Home energy storage</a></li> <li><a href="/wiki/Load-following_power_plant" title="Load-following power plant">Load-following</a></li> <li><a href="/wiki/Merit_order" title="Merit order">Merit order</a></li> <li><a href="/wiki/Nameplate_capacity" title="Nameplate capacity">Nameplate capacity</a></li> <li><a href="/wiki/Peak_demand" title="Peak demand">Peak demand</a></li> <li><a class="mw-selflink selflink">Power factor</a></li> <li><a href="/wiki/Power-flow_study" title="Power-flow study">Power-flow study</a></li> <li><a href="/wiki/Repowering" title="Repowering">Repowering</a></li> <li><a href="/wiki/Utility_frequency" title="Utility frequency">Utility frequency</a></li> <li><a href="/wiki/Variable_renewable_energy" title="Variable renewable energy">Variability</a></li> <li><a href="/wiki/Vehicle-to-grid" title="Vehicle-to-grid">Vehicle-to-grid</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="8" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Abspannportal.jpg" class="mw-file-description" title="Portal pylons of Kriftel substation near Frankfurt"><img alt="Portal pylons of Kriftel substation near Frankfurt" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/120px-Abspannportal.jpg" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/180px-Abspannportal.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Abspannportal.jpg/240px-Abspannportal.jpg 2x" data-file-width="2048" data-file-height="1536" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sources</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7em"><a href="/wiki/Non-renewable_resource" title="Non-renewable resource">Non-renewable</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fossil_fuel_power_station" title="Fossil fuel power station">Fossil fuel power station</a> <ul><li><a href="/wiki/Coal" title="Coal">Coal</a></li> <li><a href="/wiki/Natural_gas" title="Natural gas">Natural gas</a></li> <li><a href="/wiki/Oil_shale" title="Oil shale">Oil shale</a></li> <li><a href="/wiki/Petroleum" title="Petroleum">Petroleum</a></li></ul></li> <li><a href="/wiki/Nuclear_power" title="Nuclear power">Nuclear</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7em"><a href="/wiki/Renewable_energy" title="Renewable energy">Renewable</a></th><td class="navbox-list-with-group 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href="/wiki/Sustainable_biofuel" title="Sustainable biofuel">Sustainable biofuel</a></li> <li><a href="/wiki/Wind_power" title="Wind power">Wind</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Power_station_technology" title="Category:Power station technology">Generation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AC_power" title="AC power">AC power</a></li> <li><a href="/wiki/Cogeneration" title="Cogeneration">Cogeneration</a></li> <li><a href="/wiki/Combined_cycle_power_plant" title="Combined cycle power plant">Combined cycle</a></li> <li><a href="/wiki/Cooling_tower" title="Cooling tower">Cooling tower</a></li> <li><a href="/wiki/Induction_generator" title="Induction generator">Induction generator</a></li> <li><a href="/wiki/Micro_combined_heat_and_power" title="Micro combined heat and power">Micro CHP</a></li> <li><a href="/wiki/Microgeneration" title="Microgeneration">Microgeneration</a></li> <li><a href="/wiki/Rankine_cycle" title="Rankine cycle">Rankine cycle</a></li> <li><a href="/wiki/Three-phase_electric_power" title="Three-phase electric power">Three-phase electric power</a></li> <li><a href="/wiki/Virtual_power_plant" title="Virtual power plant">Virtual power plant</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Electric_power_transmission" title="Electric power transmission">Transmission</a><br />and <a href="/wiki/Electric_power_distribution" title="Electric power distribution">distribution</a></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Demand_response" title="Demand response">Demand response</a></li> <li><a href="/wiki/Distributed_generation" title="Distributed generation">Distributed generation</a></li> <li><a href="/wiki/Dynamic_demand_(electric_power)" title="Dynamic demand (electric power)">Dynamic demand</a></li> <li><a href="/wiki/Electric_power_distribution" title="Electric power distribution">Electric power distribution</a></li> <li><a href="/wiki/Electric_power_system" title="Electric power system">Electric power system</a></li> <li><a href="/wiki/Electric_power_transmission" title="Electric power transmission">Electric power transmission</a></li> <li><a href="/wiki/Electrical_busbar_system" title="Electrical busbar system">Electrical busbar system</a></li> <li><a href="/wiki/Electrical_grid" title="Electrical grid">Electrical grid</a></li> <li><a href="/wiki/Electrical_substation" class="mw-redirect" title="Electrical substation">Electrical substation</a></li> <li><a href="/wiki/Electricity_retailing" title="Electricity retailing">Electricity retailing</a></li> <li><a href="/wiki/High-voltage_direct_current" title="High-voltage direct current">High-voltage direct current</a></li> <li><a href="/wiki/High-voltage_shore_connection" title="High-voltage shore connection">High-voltage shore connection</a></li> <li><a href="/wiki/Interconnector" title="Interconnector">Interconnector</a></li> <li><a href="/wiki/Load_management" title="Load management">Load management</a></li> <li><a href="/wiki/Mains_electricity_by_country" title="Mains electricity by country">Mains electricity by country</a></li> <li><a href="/wiki/Overhead_power_line" title="Overhead power line">Overhead power line</a></li> <li><a href="/wiki/Power_station" title="Power station">Power station</a></li> <li><a href="/wiki/Pumped-storage_hydroelectricity" title="Pumped-storage hydroelectricity">Pumped hydro</a></li> <li><a href="/wiki/Single-wire_earth_return" title="Single-wire earth return">Single-wire earth return</a></li> <li><a href="/wiki/Smart_grid" title="Smart grid">Smart grid</a></li> <li><a href="/wiki/Super_grid" title="Super grid">Super grid</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li> <li><a href="/wiki/Transmission_system_operator" title="Transmission system operator">Transmission system operator</a> (TSO)</li> <li><a href="/wiki/Transmission_tower" title="Transmission tower">Transmission tower</a></li> <li><a href="/wiki/Utility_pole" title="Utility pole">Utility pole</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Failure modes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Black_start" title="Black start">Black start</a></li> <li><a href="/wiki/Brownout_(electricity)" title="Brownout (electricity)">Brownout</a></li> <li><a href="/wiki/Cascading_failure" title="Cascading failure">Cascading failure</a></li> <li><a href="/wiki/Power_outage" title="Power outage">Power outage</a> <ul><li><a href="/wiki/Rolling_blackout" title="Rolling blackout">Rolling blackout</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Protective<br />devices</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arc-fault_circuit_interrupter" title="Arc-fault circuit interrupter">Arc-fault circuit interrupter</a></li> <li><a href="/wiki/Circuit_breaker" title="Circuit breaker">Circuit breaker</a> <ul><li><a href="/wiki/Earth-leakage_circuit_breaker" title="Earth-leakage circuit breaker">Earth-leakage</a></li> <li><a href="/wiki/Sulfur_hexafluoride_circuit_breaker" title="Sulfur hexafluoride circuit breaker">Sulfur hexafluoride</a></li></ul></li> <li><a href="/wiki/Generator_interlock_kit" title="Generator interlock kit">Generator interlock kit</a></li> <li><a href="/wiki/Numerical_relay" title="Numerical relay">Numerical relay</a></li> <li><a href="/wiki/Power_system_protection" title="Power system protection">Power system protection</a></li> <li><a href="/wiki/Protective_relay" title="Protective relay">Protective relay</a></li> <li><a href="/wiki/Residual-current_device" title="Residual-current device">Residual-current device</a> (GFI)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Economics<br />and policies</div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Availability_factor" title="Availability factor">Availability factor</a></li> <li><a href="/wiki/Capacity_factor" title="Capacity factor">Capacity factor</a></li> <li><a href="/wiki/Carbon_offsets_and_credits" title="Carbon offsets and credits">Carbon offsets and credits</a></li> <li><a href="/wiki/Cost_of_electricity_by_source" title="Cost of electricity by source">Cost of electricity by source</a></li> <li><a href="/wiki/Energy_subsidy" title="Energy subsidy">Energy subsidies</a></li> <li><a href="/wiki/Environmental_tax" title="Environmental tax">Environmental tax</a></li> <li><a href="/wiki/Feed-in_tariff" title="Feed-in tariff">Feed-in tariff</a></li> <li><a href="/wiki/Fossil_fuel_phase-out" title="Fossil fuel phase-out">Fossil fuel phase-out</a></li> <li><a href="/wiki/Load_factor_(electrical)" title="Load factor (electrical)">Load factor</a></li> <li><a href="/wiki/Net_metering" title="Net metering">Net metering</a></li> <li><a href="/wiki/Pigouvian_tax" title="Pigouvian tax">Pigouvian tax</a></li> <li><a href="/wiki/Renewable_Energy_Certificate_(United_States)" title="Renewable Energy Certificate (United States)">Renewable Energy Certificates</a></li> <li><a href="/wiki/Renewable_energy_commercialization" title="Renewable energy commercialization">Renewable energy commercialization</a></li> <li><a href="/wiki/Renewable_Energy_Payments" title="Renewable Energy Payments">Renewable Energy Payments</a></li> <li><a href="/wiki/Spark_spread" title="Spark spread">Spark/Dark/Quark/Bark spread</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Statistics and<br />production</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electric_energy_consumption" title="Electric energy consumption">Electric energy consumption</a></li> <li><a href="/wiki/List_of_electricity_sectors" title="List of electricity sectors">List of electricity sectors</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" 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