Reactive Power Compensation

Compute compensation kvar, capacitor size, and resulting power factor

Calculation
Quick Introduction

Reactive power compensation reduces the reactive current share of inductive loads (e.g., motors). This typically lowers current, reduces losses, and improves the power factor.

Capacitor banks are commonly used. This calculator supports sizing of required \(Q_c\), conversion to branch capacitance, and verification of the resulting \(\cos\varphi\).

  • Input state: \(P\), \(\cos\varphi_1\)
  • Target: \(\cos\varphi_2\) or chosen \(Q_c\)
  • Output: \(Q_c\), \(C\), and new power factor
Formulas (MathJax)
\[Q_c = P\,(\tan\varphi_1-\tan\varphi_2),\quad \varphi_i=\arccos(\cos\varphi_i)\]
\[Q_1=P\tan\varphi_1,\quad Q_2=Q_1-Q_c,\quad \tan\varphi_2=\frac{Q_2}{P}\]
\[\cos\varphi_2=\frac{1}{\sqrt{1+\tan^2\varphi_2}}\]
\[C_{\Delta}=\frac{Q_c}{3\,\omega\,U_{LL}^2},\quad C_{Y}=\frac{Q_c}{\omega\,U_{LL}^2},\quad \omega=2\pi f\]
Symbol Legend
  • \(P\): active power [kW]
  • \(Q_c\): compensation reactive power [kvar]
  • \(\varphi_1,\varphi_2\): phase angle before/after compensation
  • \(\cos\varphi\): power factor
  • \(U_{LL}\): line-to-line voltage [V]
  • \(f\): frequency [Hz]
  • \(C\): capacitance per branch [F]


Examples
Example 1: \(P=45\,kW\), \(\cos\varphi_1=0.72\), \(\cos\varphi_2=0.95\) ⇒ \(Q_c\approx29.3\,kvar\).
Example 2: \(Q_c=29.3\,kvar\), \(U=400\,V\), \(f=50\,Hz\), delta ⇒ \(C_\Delta\approx194\,\mu F\) per branch.
Example 3: \(P=45\,kW\), \(\cos\varphi_1=0.72\), \(Q_c=20\,kvar\) ⇒ new \(\cos\varphi_2\approx0.85\).
Detailed Description & Summary

In installations with inductive loads, reactive power increases line current without increasing useful work. This can increase losses and voltage drop. Properly sized capacitor banks reduce reactive current and improve operating conditions.

In practice, avoid overcompensation. Typical target values are in the range of 0.90 to 0.98, depending on the installation and utility requirements. This calculator supports transparent planning and validation.

Summary
  • Computes required \(Q_c\) for a target power factor
  • Calculates capacitor branch value for star/delta connection
  • Checks resulting power factor for an installed compensation level

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