Three-Phase Calculator (3~)

Active, reactive and apparent power plus line current in 3-phase systems

Calculation
Quick Introduction

Three-phase power (3~) uses three sinusoidal voltages shifted by 120°. This improves power transfer smoothness and motor performance compared with single-phase systems.

In practice, many industrial networks use \(U_{LL}=400\,V\). For design and checks, the key quantities are \(P\), \(Q\), \(S\), \(I\), and power factor \(\cos\varphi\).

  • Active power \(P\): useful converted power
  • Reactive power \(Q\): oscillating field energy
  • Apparent power \(S\): total electrical loading
Formulas (MathJax)
\[S = \sqrt{3}\,U_{LL}\,I_L\]
\[P = \sqrt{3}\,U_{LL}\,I_L\cos\varphi\]
\[Q = \sqrt{3}\,U_{LL}\,I_L\sin\varphi\]
\[I_L = \frac{P}{\sqrt{3}\,U_{LL}\cos\varphi}\]
\[V_{ph,star}=\frac{V_{LL}}{\sqrt{3}},\quad I_{ph,delta}=\frac{I_L}{\sqrt{3}}\]
Symbol Legend
  • \(U_{LL}\): line-to-line voltage [V]
  • \(U_{ph}\): phase voltage [V]
  • \(I_L\): line current [A]
  • \(I_{ph}\): phase current [A]
  • \(P\): active power [W]
  • \(Q\): reactive power [var]
  • \(S\): apparent power [VA]
  • \(\varphi\): phase angle
  • \(\cos\varphi\): power factor


Examples
Example 1: \(U_{LL}=400\,V\), \(I=16\,A\), \(\cos\varphi=0.85\) ⇒ \(S\approx11.09\,kVA\), \(P\approx9.43\,kW\), \(Q\approx5.83\,kvar\).
Example 2: \(P=7.5\,kW\), \(U_{LL}=400\,V\), \(\cos\varphi=0.85\) ⇒ \(I\approx12.73\,A\).
Example 3 (star/delta): For \(U_{LL}=400\,V\), star gives \(U_{ph}\approx230.94\,V\). For \(I_L=16\,A\), delta gives \(I_{ph}\approx9.24\,A\).
Detailed Description & Summary

This three-phase calculator supports typical sizing and verification tasks in electrical installation, industrial commissioning, and maintenance. It connects direct measurements with design quantities using the standard balanced-load relations.

The star/delta helper provides fast consistency checks when datasheets provide phase values but measurements are made on line values. This prevents common conversion mistakes during troubleshooting.

Summary
  • Fast calculation of \(P\), \(Q\), \(S\), and \(I\) in 3-phase systems
  • Power-factor-aware estimation for realistic loading
  • Integrated star/delta conversion for practical checks

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