What Are Positive Sequence, Negative Sequence, and Zero Sequence in Three-Phase Circuits?

       In relay protection systems, we often encounter concepts such as zero-sequence current protection in microprocessor-based protection relay and inverse-time negative-sequence protection in transformer protection relays. Initially, I found these concepts quite confusing. However, to facilitate subsequent study and work, it is essential to understand these critical concepts of positive sequence, negative sequence, and zero sequence in three-phase circuits.

​Positive Sequence in Three-Phase Circuits​

Definition: Three-phase voltages or currents have equal magnitudes with phase angles successively lagging by 120°, following the sequence A→B→C (clockwise).
Characteristics:

• Represents the component under normal symmetrical operation.
• Positive sequence impedance determines symmetrical short-circuit currents (e.g., three-phase faults).

​Example:

• U A =U∠0°,
• U B =U∠−120°,
• U C =U∠120°.

​Negative Sequence in Three-Phase Circuits​

​Definition: Three-phase magnitudes are equal, but phase angles successively lead by 120°, following the sequence A→C→B (counterclockwise).
​Characteristics:

• Caused by asymmetrical faults (e.g., line-to-line faults, open-phase conditions) or load imbalance.
• Negative sequence currents can lead to motor overheating and vibration.

​Example:

• U A =U∠0°,
• U B =U∠120°,
• U C =U∠−120°.

​Zero Sequence in Three-Phase Circuits​

​Definition: Three-phase voltages or currents have identical magnitudes and phases (no phase difference).
​Characteristics:

• Generated by ground faults (e.g., single-line-to-ground) or asymmetrical three-phase conditions.
• Zero-sequence currents require a neutral wire or earth to form a closed loop.
• Zero-sequence protection in microprocessor-based protection devices is used to detect ground faults.

​Example:

• U A =U B =U C =U∠0°.

​Mathematical Representation of Positive, Negative, and Zero Sequences (Symmetrical Components Method)​​

Asymmetrical three-phase quantities (U A ,U B ,U C ) can be decomposed into:

• U 0 = ¹/₃ (U _A +U _B +U _C ) Zero Sequence
• U 1 =¹/₃ (U _A +aU _B +a ² U _C ) Positive Sequence
• U 2 =¹/₃(U _A +a ² U _B +aU _C )Negative Sequence

where a=e ^j120° is the phase rotation operator.

​Application Scenarios of Positive, Negative, and Zero Sequences​

• ​Fault Analysis: Distinguishing fault types (e.g., positive sequence dominates three-phase faults, zero sequence dominates ground faults).
• Protection Design: Negative sequence protection prevents motor damage; zero sequence protection detects ground faults.
• ​Imbalance Mitigation: Compensating negative/zero sequence components improves power quality.

​Summary of Positive, Negative, and Zero Sequences​

• ​Positive Sequence: Symmetrical component under normal operation.
• ​Negative Sequence: Asymmetrical or reverse-rotating component, harmful to equipment.
• ​Zero Sequence: In-phase component, indicating ground faults or neutral point displacement.