Symmetrical Components Calculator

Symmetrical Components Calculator. In three-phase power systems, unbalanced voltages or currents during faults can be decomposed into three simpler sets — the Symmetrical Components Calculator does exactly that using the Fortescue method. Enter your Phase A, B, and C phasors in either rectangular (real + imaginary) or polar (magnitude and angle) format to get the positive, negative, and zero sequence components — each returned as a magnitude and phase angle. Also try the Three-Phase kVA Calculator.

Input Format *

Rectangular (Real + j Imaginary)Polar (Magnitude ∠ Angle)

Phase A Real Part *

Phase A Imaginary Part *

Phase A Magnitude *

Phase A Angle (degrees) *

Phase B Real Part *

Phase B Imaginary Part *

Phase B Magnitude *

Phase B Angle (degrees) *

Phase C Real Part *

Phase C Imaginary Part *

Phase C Magnitude *

Phase C Angle (degrees) *

Results

Positive Sequence Magnitude

Positive Sequence Angle

Negative Sequence Magnitude

Negative Sequence Angle

Zero Sequence Magnitude

Zero Sequence Angle

Results Table

What are symmetrical components in power systems?

Symmetrical components are a mathematical technique used to analyze unbalanced three-phase power systems by decomposing them into three balanced sets: positive sequence (normal operation), negative sequence (imbalance), and zero sequence (ground faults). See also our use the Phase Angle Calculator.

What is the difference between positive, negative, and zero sequence components?

Positive sequence represents normal balanced operation with ABC phase rotation, negative sequence represents unbalanced conditions with ACB rotation, and zero sequence represents ground fault conditions where all phases have the same magnitude and phase angle.

When should I use rectangular vs polar input format?

Use rectangular format when you have real and imaginary parts (like from phasor measurements), and use polar format when you have magnitude and angle measurements (common in field measurements and relay settings).

How do symmetrical components help in power system protection?

Symmetrical components allow protective relays to distinguish between different fault types. Zero sequence detects ground faults, negative sequence detects phase-to-phase faults, and positive sequence represents normal load current.

What does it mean when zero sequence is non-zero?

Non-zero zero sequence components indicate an unbalanced condition, typically a ground fault or single-phase load. In a balanced three-phase system, the zero sequence should be zero.

Why is negative sequence important for motor protection?

Negative sequence currents create reverse rotating magnetic fields that cause excessive heating in motors. Motor protection relays monitor negative sequence to prevent damage from unbalanced conditions. You might also find our Three Phase Calculator useful.