{"id":3959,"date":"2022-06-01T07:59:17","date_gmt":"2022-06-01T07:59:17","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=3959"},"modified":"2022-06-01T07:59:17","modified_gmt":"2022-06-01T07:59:17","slug":"power-factor","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/01\/power-factor\/","title":{"rendered":"Power Factor"},"content":{"rendered":"\n<p>In AC circuits, the power factor is the ratio of the&nbsp;<a href=\"https:\/\/www.rapidtables.com\/electric\/electric_power.html\">real power<\/a>&nbsp;that is used to do work and the&nbsp;<a href=\"https:\/\/www.rapidtables.com\/electric\/electric_power.html\">apparent power<\/a>&nbsp;that is supplied to the circuit.<\/p>\n\n\n\n<p>The power factor can get values in the range from 0 to 1.<\/p>\n\n\n\n<p>When all the power is reactive power with no real power (usually inductive load) &#8211; the power factor is 0.<\/p>\n\n\n\n<p>When all the power is real power with no reactive power (resistive load) &#8211; the power factor is 1.<\/p>\n\n\n\n<ul><li><a href=\"https:\/\/www.rapidtables.com\/electric\/Power_Factor.html#power%20factor%20definition\">Power factor definition<\/a><\/li><li><a href=\"https:\/\/www.rapidtables.com\/electric\/Power_Factor.html#power%20factor%20calculation\">Power factor calculation<\/a><\/li><li><a href=\"https:\/\/www.rapidtables.com\/electric\/Power_Factor.html#power%20factor%20correction\">Power factor correction<\/a><\/li><li><a href=\"https:\/\/www.rapidtables.com\/calc\/electric\/power-factor-calculator.html\">Power factor calculator<\/a><\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><a><\/a>Power factor definition<\/h3>\n\n\n\n<p>The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA):<\/p>\n\n\n\n<p><em>PF<\/em>&nbsp;=&nbsp;<em>P<\/em><sub>(W)<\/sub>\/<em>&nbsp;|S<\/em><sub>(VA)<\/sub>|<\/p>\n\n\n\n<p><em>PF&nbsp;<\/em>&#8211; power factor.<\/p>\n\n\n\n<p><em>P&nbsp;&nbsp; &#8211;&nbsp;<\/em>real power in watts (W).<\/p>\n\n\n\n<p><em>|S|&nbsp;&nbsp; &#8211;&nbsp;<\/em>apparent power &#8211; the magnitude of the complex power in volt\u22c5amps (VA).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><a><\/a>Power factor calculations<\/h3>\n\n\n\n<p>For sinusuidal current, the power factor PF is equal to the absolute value of the cosine of the apparent power phase angle&nbsp;<em>\u03c6&nbsp;<\/em>(which is also is impedance phase angle):<\/p>\n\n\n\n<p><em>PF<\/em>&nbsp;= |cos<em>&nbsp;\u03c6|<\/em><\/p>\n\n\n\n<p><em>PF&nbsp;<\/em>is the power factor.<\/p>\n\n\n\n<p><em>\u03c6&nbsp;&nbsp;&nbsp;<\/em>is the apprent power phase angle.<\/p>\n\n\n\n<p>The real power P in watts (W) is equal to the apparent power |S| in volt-ampere (VA) times the power factor PF:<\/p>\n\n\n\n<p><em>P<\/em><sub>(W)<\/sub>&nbsp;=&nbsp;<em>|S<\/em><sub>(VA)<\/sub>| \u00d7&nbsp;<em>PF<\/em>&nbsp;=&nbsp;<em>|S<\/em><sub>(VA)<\/sub>| \u00d7 |cos&nbsp;<em>\u03c6|<\/em><\/p>\n\n\n\n<p>When the circuit has a resistive impedance load, the real power P is equal to the apparent power |S| and the power factor PF is equal to 1:<\/p>\n\n\n\n<p><em>PF<\/em><sub>(resistive load)<\/sub>&nbsp;=&nbsp;<em>P<\/em>&nbsp;\/&nbsp;<em>|S|<\/em>&nbsp;= 1<\/p>\n\n\n\n<p>The reactive power Q in volt-amps reactive (VAR) is equal to the apparent power |S| in volt-ampere (VA) times the sine of the phase angle&nbsp;<em>\u03c6<\/em>:<\/p>\n\n\n\n<p><em>Q<\/em><sub>(VAR)<\/sub>&nbsp;=&nbsp;<em>|S<\/em><sub>(VA)<\/sub>| \u00d7 |sin&nbsp;<em>\u03c6|<\/em><\/p>\n\n\n\n<p>Single phase circuit calculation from real power meter reading P in kilowatts (kW), voltage V in volts (V) and current I in amps (A):<\/p>\n\n\n\n<p><em>PF<\/em>&nbsp;= |cos&nbsp;<em>\u03c6|<\/em>&nbsp;= 1000 \u00d7&nbsp;<em>P<\/em><sub>(kW)<\/sub>&nbsp;\/ (<em>V<\/em><sub>(V)<\/sub>&nbsp;\u00d7&nbsp;<em>I<\/em><sub>(A)<\/sub>)<\/p>\n\n\n\n<p>Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line voltage&nbsp;<em>V<\/em><sub>L-L<\/sub>&nbsp;in volts (V) and current I in amps (A):<\/p>\n\n\n\n<p><em>PF<\/em>&nbsp;= |cos<em>&nbsp;\u03c6|<\/em>&nbsp;= 1000 \u00d7&nbsp;<em>P<\/em><sub>(kW)<\/sub>&nbsp;\/ (<em>\u221a<\/em>3<em>&nbsp;\u00d7 V<\/em><sub>L-L(V)<\/sub>&nbsp;\u00d7&nbsp;<em>I<\/em><sub>(A)<\/sub>)<\/p>\n\n\n\n<p>Three phase circuit calculation from real power meter reading P in kilowatts (kW), line to line neutral&nbsp;<em>V<\/em><sub>L-N<\/sub>&nbsp;in volts (V) and current I in amps (A):<\/p>\n\n\n\n<p><em>PF<\/em>&nbsp;= |cos<em>&nbsp;\u03c6|<\/em>&nbsp;= 1000 \u00d7&nbsp;<em>P<\/em><sub>(kW)<\/sub>&nbsp;\/ (3<em>&nbsp;\u00d7 V<\/em><sub>L-N(V)<\/sub>&nbsp;\u00d7&nbsp;<em>I<\/em><sub>(A)<\/sub>)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Power factor correction<\/h3>\n\n\n\n<p>Power factor correction is an adjustment of the electrical circuit in order to change the power factor near 1.<\/p>\n\n\n\n<p>Power factor near 1 will reduce the reactive power in the circuit and most of the power in the circuit will be real power. This will also reduce power lines losses.<\/p>\n\n\n\n<p>The power factor correction is usually done by adding capacitors to the load circuit, when the circuit has inductive components, like an electric motor.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Power factor correction calculation<\/h4>\n\n\n\n<p>The apparent power |S| in volt-amps (VA) is equal to the voltage V in volts (V) times the current I in amps (A):<\/p>\n\n\n\n<p><em>|S<\/em><sub>(VA)<\/sub>| =&nbsp;<em>V<\/em><sub>(V)<\/sub>&nbsp;\u00d7&nbsp;<em>I<\/em><sub>(A)<\/sub><\/p>\n\n\n\n<p>The reactive power Q in volt-amps reactive (VAR) is equal to the square root of the square of the apparent power |S| in volt-ampere (VA) minus the square of the real power P in watts (W) (pythagorean theorem):<\/p>\n\n\n\n<p><em>Q<\/em><sub>(VAR)<\/sub>&nbsp;= \u221a(<em>|S<\/em><sub>(VA)<\/sub>|<sup>2<\/sup>&nbsp;&#8211;&nbsp;<em>P<\/em><sub>(W)<\/sub><sup>2<\/sup>)<\/p>\n\n\n\n<p><em>Q<\/em><sub>c (kVAR)<\/sub>&nbsp;=&nbsp;<em>Q<\/em><sub>(kVAR)<\/sub>&nbsp;&#8211;&nbsp;<em>Q<\/em><sub>corrected (kVAR)<\/sub><\/p>\n\n\n\n<p><a><\/a>The reactive power Q in volt-amps reactive (VAR) is equal to the square of voltage V in volts (V) divided by the reactance Xc:<\/p>\n\n\n\n<p><em>Q<\/em><sub>c (VAR)<\/sub>&nbsp;=&nbsp;<em>V<\/em><sub>(V)<\/sub><sup>2<\/sup>&nbsp;\/&nbsp;<em>X<\/em><sub>c<\/sub>&nbsp;=&nbsp;<em>V<\/em><sub>(V)<\/sub><sup>2<\/sup>&nbsp;\/ (1 \/ (2\u03c0<em>f<\/em><sub>(Hz)<\/sub><em>\u00d7C<\/em><sub>(F)<\/sub>)) = 2\u03c0<em>f<\/em><sub>(Hz)<\/sub><em>\u00d7C<\/em><sub>(F)<\/sub><em>\u00d7V<\/em><sub>(V)<\/sub><sup>2<\/sup><\/p>\n\n\n\n<p><a><\/a>So the power factor correction capacitor in Farad (F) that should be added to the circuit in parallel is equal to the reactive power Q in volt-amps reactive (VAR) divided by 2\u03c0 times the frequency f in Hertz (Hz) times the squared voltage V in volts (V):<\/p>\n\n\n\n<p><em>C<\/em><sub>(F)<\/sub>&nbsp;=&nbsp;<em>Q<\/em><sub>c (VAR)<\/sub>&nbsp;\/ (2\u03c0<em>f<\/em><sub>(Hz)<\/sub><em>\u00b7<\/em><em>V<\/em><sub>(V)<\/sub><sup>2<\/sup>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In AC circuits, the power factor is the ratio of the&nbsp;real power&nbsp;that is used to do work and the&nbsp;apparent power&nbsp;that is supplied to the circuit. The power factor can get values in the range from 0 to 1. When all the power is reactive power with no real power (usually inductive load) &#8211; the power [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[258],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3959"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3959"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3959\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3959"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}