{"id":100191,"date":"2026-02-15T20:25:56","date_gmt":"2026-02-15T20:25:56","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100191"},"modified":"2026-07-13T03:35:23","modified_gmt":"2026-07-13T03:35:23","slug":"power-factor-correction","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/lt\/calculators\/power-factor-correction\/","title":{"rendered":"Fundamental Displacement-PF Compensation Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Fundamental Displacement-PF Compensation Arithmetic\",\"description\":\"Calculates ideal fundamental-frequency capacitive reactive power and element capacitance for controlled sinusoidal single-phase or balanced three-phase conditions. It does not size a safe capacitor bank.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/power-factor-correction\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Lagging fundamental displacement PF arithmetic\",\"Single-phase and balanced three-phase current\",\"Delta and wye element capacitance\",\"No utility-target recommendation\",\"No capacitor-bank safety verdict\"],\"keywords\":\"displacement power factor,reactive power arithmetic,capacitor delta wye,fundamental frequency\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Can I use measured true power factor with harmonics?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. The angle relation PF=cos phi is limited here to fundamental displacement power factor under the stated sinusoidal assumptions.\"}},{\"@type\":\"Question\",\"name\":\"Is the capacitance output a safe capacitor-bank selection?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Rated voltage, kvar steps, duty, switching, discharge, protection, harmonics, resonance, temperature and product standards require separate engineering.\"}},{\"@type\":\"Question\",\"name\":\"Why are delta and wye capacitances different?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Each delta element sees line-to-line voltage; each wye element sees line-to-neutral voltage in the ideal balanced system.\"}},{\"@type\":\"Question\",\"name\":\"What target power factor should I choose?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"This worksheet does not choose one. Use the applicable utility contract, measured load profile and controlled system study.\"}}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#66598b;--al:#f1eff8;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--f:'DM Sans',sans-serif;--m:'JetBrains Mono',monospace;--d:'Fraunces',serif}.vc-calculator{font-family:var(--f);font-size:15px;line-height:1.65;color:var(--i);max-width:960px;margin:auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 20px 40px;border-bottom:3px solid var(--a)}.vc-header-eyebrow{font:500 11px var(--m);letter-spacing:.15em;text-transform:uppercase;color:var(--a)}.vc-header-title{font:800 clamp(24px,4vw,36px)\/1.15 var(--d);margin:10px 0 14px}.vc-header-subtitle{max-width:760px;margin:auto;color:var(--is)}.vc-badges{display:flex;gap:8px;justify-content:center;flex-wrap:wrap;margin-top:18px}.vc-badge{font:500 11px var(--m);padding:4px 10px;border:1px solid var(--b);border-radius:4px}.vc-card,.vc-section{background:var(--s);border:1px solid var(--b);border-radius:12px;overflow:hidden;margin-top:28px}.vc-form{padding:24px}.vc-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px}.vc-field{display:flex;flex-direction:column}.vc-full{grid-column:1\/-1}.vc-label{font-size:12px;font-weight:600;letter-spacing:.04em;text-transform:uppercase;color:var(--is);margin-bottom:6px}.vc-hint{font-weight:400;text-transform:none;letter-spacing:0;color:var(--im)}.vc-input,.vc-select{width:100%;padding:10px 12px;border:1.5px solid var(--b);border-radius:6px;font:14px var(--f);background:var(--s)}.vc-check{display:flex;gap:10px;padding:12px;border:1px solid var(--bl);border-radius:6px;background:var(--sa);font-size:13px;color:var(--is)}.vc-check input{margin-top:4px}.vc-validation{min-height:22px;color:var(--r);font-size:13px;margin-top:10px}.vc-results{border-top:1px solid var(--bl);background:var(--sa);padding:0;max-height:0;overflow:hidden}.vc-results.vc-visible{max-height:1400px;padding:24px}.vc-result-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:12px}.vc-rcard{background:var(--s);border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--a);background:var(--al)}.vc-rcard-label{font:500 10px var(--m);letter-spacing:.1em;text-transform:uppercase;color:var(--im)}.vc-rcard-value{font:600 18px var(--m);overflow-wrap:anywhere}.vc-primary .vc-rcard-value{font-size:24px;color:var(--a)}.vc-status{grid-column:1\/-1;padding:12px;background:var(--yl);border-left:3px solid var(--y);font-size:13px;color:var(--is)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;padding:18px 24px;border:0;background:transparent;cursor:pointer;text-align:left}.vc-section-title{font:700 18px var(--d)}.vc-section-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-section-body{max-height:15000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--bl)}.vc-theory h3{font:700 17px var(--d);margin:24px 0 8px}.vc-theory p,.vc-theory li{font-size:14px;color:var(--is)}.vc-formula{padding:14px;border:2px solid var(--b);border-radius:6px;background:var(--sa);text-align:center;font:500 14px var(--m);margin:12px 0}.vc-warning{padding:14px;background:var(--yl);border-left:3px solid var(--y);color:var(--is)}.vc-faq-item{border:1px solid var(--bl);margin-top:8px}.vc-faq-q{width:100%;padding:14px;border:0;background:var(--sa);text-align:left;font-weight:600}.vc-faq-a{display:none;padding:14px;color:var(--is)}.vc-faq-item.vc-open .vc-faq-a{display:block}.vc-footer{text-align:center;padding:30px;color:var(--im);font-size:13px}@media(max-width:600px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-full,.vc-primary,.vc-status{grid-column:1}}<\/style>\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Ideal fundamental-frequency arithmetic \u2014 not bank sizing<\/p><h1 class=\"vc-header-title\">Fundamental Displacement-PF Compensation Arithmetic<\/h1><p class=\"vc-header-subtitle\">Calculate ideal capacitive kvar and ideal element capacitance for controlled sinusoidal single-phase or balanced three-phase conditions. The input is lagging fundamental displacement power factor, not unspecified true power factor.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Qc=P(tan\u03c61\u2212tan\u03c62)<\/span><span class=\"vc-badge\">1\u03c6 \/ 3\u03c6 \u0394 \/ 3\u03c6 Y<\/span><span class=\"vc-badge\">RMS voltage<\/span><span class=\"vc-badge\">No safe-bank verdict<\/span><\/div><\/header>\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\">\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-power\">Controlled constant active power P <span class=\"vc-hint\">kW<\/span><\/label><input class=\"vc-input\" id=\"vc-power\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-pf1\">Initial lagging fundamental displacement PF<\/label><input class=\"vc-input\" id=\"vc-pf1\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-pf2\">Target lagging\/unity fundamental displacement PF<\/label><input class=\"vc-input\" id=\"vc-pf2\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-system\">Ideal circuit \/ capacitor connection<\/label><select class=\"vc-select\" id=\"vc-system\"><option value=\"single\">Single phase \u2014 terminal RMS voltage<\/option><option value=\"delta\">Balanced 3 phase \u2014 delta elements<\/option><option value=\"wye\">Balanced 3 phase \u2014 wye elements<\/option><\/select><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-voltage\">Controlled RMS voltage <span class=\"vc-hint\">V; L-L for 3\u03c6<\/span><\/label><input class=\"vc-input\" id=\"vc-voltage\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-frequency\">Controlled fundamental frequency <span class=\"vc-hint\">Hz<\/span><\/label><input class=\"vc-input\" id=\"vc-frequency\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Controlled measurement\/design-basis source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"meter method\/location\/time aggregation;fundamental displacement PF;P\/V\/f operating point;phase balance;connection;load profile;revisions\"><\/div>\n<div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>PF1 and PF2 are positive lagging\/unity fundamental displacement power factors for the same sinusoidal steady-state load with constant active power, RMS voltage and frequency. For 3\u03c6 the system is balanced and voltage is line-to-line. The capacitance is ideal at the fundamental frequency. True PF under distortion, unbalance, changing loads, capacitor tolerances\/losses and harmonic currents are excluded.<\/span><\/label><\/div>\n<\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Ideal capacitive reactive-power change<\/div><div class=\"vc-rcard-value\" id=\"vc-r-qc\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Ideal capacitance per element<\/div><div class=\"vc-rcard-value\" id=\"vc-r-cap\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Apparent power before \/ after<\/div><div class=\"vc-rcard-value\" id=\"vc-r-apparent\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Ideal line current before \/ after<\/div><div class=\"vc-rcard-value\" id=\"vc-r-current\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Ideal current change<\/div><div class=\"vc-rcard-value\" id=\"vc-r-change\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Fundamental arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equations, units and boundaries<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula\">\u03c6i=acos(DPFi);&nbsp; Qc=P\u00b7(tan\u03c61\u2212tan\u03c62)<br>S=P\/DPF;&nbsp; I1\u03c6=P\/(V\u00b7DPF);&nbsp; I3\u03c6=P\/(\u221a3\u00b7VLL\u00b7DPF)<br>C1\u03c6=Qc\/(\u03c9V\u00b2);&nbsp; C\u0394,element=Qc\/(3\u03c9VLL\u00b2);&nbsp; CY,element=Qc\/(\u03c9VLL\u00b2)<\/div><p>P is kW, Qc is kvar, S is kVA, DPF is lagging fundamental displacement power factor, V is RMS volts, I is amperes, \u03c9=2\u03c0f, and C is converted from farads to microfarads. The wye relation uses ideal Vphase=VLL\/\u221a3.<\/p><p>Qc is a positive ideal capacitive change only when 0&lt;DPF1&lt;DPF2\u22641. No leading target is represented. Current\/apparent-power values assume unchanged P and V and exclude distortion\/unbalance.<\/p><div class=\"vc-warning\"><strong>Not a capacitor-bank selection.<\/strong> Do not purchase, connect or switch equipment from this arithmetic alone. System short-circuit impedance, harmonic spectrum\/resonance, load profile, voltage rise, inrush, switching transients, discharge, protection, detuning\/reactors, capacitor current\/voltage duty, tolerances, temperature, enclosure and applicable installation rules are not modeled.<\/div><h3>Power-factor definition<\/h3><p>IEC TR61000-1-7:2016 explicitly separates fundamental power factor caused by fundamental phase displacement from non-fundamental power factor caused by distortion in non-sinusoidal single-phase systems. Therefore `acos(PF)` is not applied here to an unspecified true PF reading.<\/p><h3>Equipment and harmonic boundaries<\/h3><p><strong>IEC61921:2017 edition2<\/strong> applies to low-voltage AC shunt capacitor banks for power-factor correction and includes assembly verification context.It is not replaced by this worksheet.<strong>IEEE519-2022<\/strong> is active and sets harmonic-control goals at the point of common coupling;exact limits and study procedures remain licensed.The US Department of Energy warns that capacitors and system inductance can create damaging harmonic resonance.<\/p><div class=\"vc-warning\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> applicable utility contract\/target and billing interval;meter definition;harmonic and resonance study;selected equipment rating\/steps\/duty;IEC61921 verification;IEEE519 limits;protection,switching,discharge,installation and commissioning rules.<\/div><h3>Sources<\/h3><p><a href=\"https:\/\/webstore.iec.ch\/en\/publication\/24199\" target=\"_blank\" rel=\"noopener\">IEC TR61000-1-7:2016<\/a>; <a href=\"https:\/\/webstore.iec.ch\/en\/publication\/60937\" target=\"_blank\" rel=\"noopener\">IEC61921:2017<\/a>; <a href=\"https:\/\/standards.ieee.org\/ieee\/519\/10677\/\" target=\"_blank\" rel=\"noopener\">IEEE519-2022<\/a>; <a href=\"https:\/\/www.energy.gov\/sites\/prod\/files\/2014\/04\/f15\/NN0116.pdf\" target=\"_blank\" rel=\"noopener\">US DOE motor-driven systems guide<\/a>; <a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST SI guidance<\/a>.<\/p><\/div><\/div><\/div>\n<div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 Vibromera \u2014 reviewed 13 July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function read(raw){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)&&v>0?v:null}function fmt(v){if(Math.abs(v)>=1e9||(Math.abs(v)>0&&Math.abs(v)<1e-7))return v.toExponential(8);return Number(v.toPrecision(12)).toString()}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){var source=$('vc-source').value.trim();if(!source)return hide('Enter the controlled measurement\/design-basis source.');if(!$('vc-gate').checked)return hide('Confirm the displacement-PF,steady-state and circuit assumptions.');var P=read($('vc-power').value),pf1=read($('vc-pf1').value),pf2=read($('vc-pf2').value),V=read($('vc-voltage').value),f=read($('vc-frequency').value);if([P,pf1,pf2,V,f].some(function(x){return x===null}))return hide('Enter complete positive P,DPF,voltage and frequency values.');if(pf1>=1||pf2>1||pf2<=pf1)return hide('Require 0 < initial DPF < target DPF \u2264 1 for lagging compensation.');var phi1=Math.acos(pf1),phi2=Math.acos(pf2),Qc=P*(Math.tan(phi1)-Math.tan(phi2)),omega=2*Math.PI*f,sys=$('vc-system').value,C=Qc*1e9\/(omega*V*V);if(sys==='delta')C\/=3;var S1=P\/pf1,S2=P\/pf2,I1,I2;if(sys==='single'){I1=P*1000\/(V*pf1);I2=P*1000\/(V*pf2)}else{I1=P*1000\/(Math.sqrt(3)*V*pf1);I2=P*1000\/(Math.sqrt(3)*V*pf2)}var change=(1-I2\/I1)*100;if(![Qc,C,S1,S2,I1,I2,change].every(function(x){return Number.isFinite(x)&&x>=0}))return hide('Arithmetic did not produce finite non-negative results.');$('vc-r-qc').textContent=fmt(Qc)+' kvar';$('vc-r-cap').textContent=fmt(C)+' \u00b5F per '+(sys==='single'?'single element':sys==='delta'?'delta branch':'wye phase');$('vc-r-apparent').textContent=fmt(S1)+' kVA | '+fmt(S2)+' kVA';$('vc-r-current').textContent=fmt(I1)+' A | '+fmt(I2)+' A';$('vc-r-change').textContent=fmt(change)+' %';$('vc-r-note').textContent='Ideal sinusoidal fundamental displacement-PF arithmetic only.No true-PF,harmonic,resonance,utility-target,equipment-rating,step,protection,switching or safe-installation verdict.';$('vc-validation').textContent='';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',String(s.classList.contains('vc-open')))})});var faq=[['Can I enter a meter total PF value?','Only if the controlled meter definition proves it is the lagging fundamental displacement PF required by this model.Unspecified true PF is rejected conceptually.'],['Why is there no recommended0.95 target?','Tariffs,penalties,voltage control and leading\/reactive-energy rules differ.Use the applicable contract and measured load profile.'],['Can I round kvar to the next bank step?','Not automatically.A step plan must account for load variability,overcorrection,voltage,harmonics,switching duty and the selected equipment.'],['Does lower ideal line current guarantee lower bill?','No.Billing rules,demand intervals,energy charges,loss location and operating profile must be evaluated separately.']];var l=$('vc-faq-list');faq.forEach(function(x){var w=document.createElement('div');w.className='vc-faq-item';var b=document.createElement('button');b.type='button';b.className='vc-faq-q';b.textContent=x[0];var 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sizing.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100191","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/calculator\/100191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/calculator\/100191\/revisions"}],"predecessor-version":[{"id":102529,"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/calculator\/100191\/revisions\/102529"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/media?parent=100191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/categories?post=100191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/lt\/wp-json\/wp\/v2\/tags?post=100191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}