What is the Fortescue transformation?

The Fortescue (symmetrical component) transformation decomposes any set of three unbalanced phasors into three balanced sets called the positive, negative, and zero sequence components. This simplifies analysis of unbalanced power systems.

What units should I use for magnitude?

You can use any consistent unit — volts, kilovolts, amps, or per-unit. The tool outputs results in the same unit you enter. Angles must be in degrees.

What does the negative sequence component represent?

The negative sequence component (V2) represents the degree of unbalance and rotates in the opposite direction to the positive sequence. A large V2 indicates significant unbalance, which can cause overheating in motors and generators.

What does the zero sequence component represent?

The zero sequence component (V0) is equal in magnitude and phase in all three phases. It only flows through paths that allow ground or neutral current, and its presence typically indicates a ground fault.

Can I use this for currents instead of voltages?

Yes. The Fortescue transformation applies identically to three-phase current phasors. Simply enter your Ia, Ib, Ic values as the magnitudes and angles and interpret the results as sequence currents.

What is the operator "a" used in the transformation?

The operator a = 1∠120° = e^(j2π/3). It is a unit phasor that introduces a 120-degree phase shift. The transformation matrix uses powers of a to encode the balanced symmetry of the three sequences.

What is a symmetrical component?

A symmetrical component is one of three balanced phasor sets — positive, negative, or zero sequence — that together reconstruct any unbalanced three-phase system. To find them, multiply the phase phasors Va, Vb, Vc by the inverse Fortescue matrix (1/3 × A⁻¹).

Symmetrical Components Calculator

Name: Symmetrical Components Calculator
Availability: InStock
Author: Nham Vu

Convert unbalanced three-phase phasors (Va, Vb, Vc) into positive, negative, and zero sequence components using the Fortescue transformation.

Input Phasors

Enter magnitude and angle (degrees) for each phase.

Phase A (Va)

Magnitude

Angle (°)

Phase B (Vb)

Magnitude

Angle (°)

Phase C (Vc)

Magnitude

Angle (°)

Enter phasor values and click Calculate to see sequence components.

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Summary

Convert unbalanced three-phase phasors (Va, Vb, Vc) into positive, negative, and zero sequence components using the Fortescue transformation.

How it works

Enter the magnitude and phase angle (in degrees) for each of the three phasors Va, Vb, and Vc.
Click "Calculate" to apply the Fortescue transformation matrix.
The tool computes the complex product of the inverse symmetrical component matrix with the phasor vector.
Positive sequence (V1), negative sequence (V2), and zero sequence (V0) components are displayed in polar and rectangular form.
Use the "Copy Results" button to copy a formatted summary to your clipboard.

Use cases

Analyze fault conditions in power systems (single-line-to-ground, line-to-line, double-line-to-ground).
Verify protection relay settings by computing sequence components of measured phasors.
Teach or learn symmetrical component theory in electrical engineering courses.
Check power quality by quantifying voltage unbalance through negative sequence magnitude.
Design and validate sequence network models for asymmetrical fault studies.
Quickly transform field-measured voltage/current phasors for power system analysis.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu

Symmetrical Components Calculator

Input Phasors

Sequence Components

Summary

How it works

Use cases

Frequently Asked Questions

What is the Fortescue transformation?

What units should I use for magnitude?

What does the negative sequence component represent?

What does the zero sequence component represent?

Can I use this for currents instead of voltages?

What is the operator "a" used in the transformation?

What is a symmetrical component?

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