Symmetrical Components Calculator
Compute positive, negative and zero sequence components from three-phase currents or voltages (balanced or unbalanced), then reconstruct phase phasors back.
Overview
Symmetrical components (Fortescue transform) decompose any unbalanced three-phase system into three balanced systems: the positive, negative and zero sequence networks. They are the standard way engineers analyse unbalanced faults, motor negative-sequence heating and protective relay settings.
Positive sequence V1 is the healthy rotating set (direct). Negative sequence V2 rotates backwards and heats rotor iron in motors. Zero sequence V0 only exists if there is a return path for common-mode current — i.e. a grounded neutral.
This calculator computes both directions: phase phasors → sequences, and sequences → reconstructed phases. Use it with the complex calculator when combining impedances in the sequence domain.
How it works
- 1. Input phasorsEnter magnitude and angle for all three phases or sequences.
- 2. Apply FortescueThe tool rotates with a = 1∠120° and builds V0, V1, V2.
- 3. Inspect negative and zeroLarge V2 indicates unbalanced faults; V0 implies a neutral return path.
- 4. Reconstruct (reverse mode)Feed sequences back to obtain the original phase phasors.
FAQ
When do I need symmetrical components?+
Any unbalanced three-phase analysis: SLG, LL, LLG faults, motor negative-sequence heating, relay settings.
Why is zero sequence zero in a delta system?+
Because delta windings trap homopolar currents and provide no neutral return.
What is Fortescue’s theorem?+
Any system of N unbalanced phasors decomposes into N balanced N-phase systems plus a zero-sequence set when applicable.