Decomposes unbalanced three-phase phasors into three symmetrical balanced components: positive-sequence (fundamental forward rotation), negative-sequence (reverse rotation, motor heating), and zero-sequence (in-phase neutral current). Also synthesizes phase quantities from sequence components and calculates Voltage Unbalance Factor (VUF %).
Governing Formulas & Standards
Standards Basis: IEC 61000-4-30 / Fortescue Method (1918)
\begin{bmatrix} V_0 \\ V_1 \\ V_2 \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{bmatrix} \begin{bmatrix} V_a \\ V_b \\ V_c \end{bmatrix}, \quad a = 1\angle 120^\circ
Applies the Fortescue transformation matrix using the complex 120-degree phase rotation operator a.
Worked Engineering Example: Unbalance Analysis of 230V Feeder with Sagged Phase B
- Calculate Zero-Sequence Component (V0): V0 = (Va + Vb + Vc) / 3 → 8.65 V ∠35.4°
- Calculate Positive-Sequence Component (V1): V1 = (Va + a·Vb + a²·Vc) / 3 → 226.54 V ∠-3.2°
- Calculate Negative-Sequence Component (V2): V2 = (Va + a²·Vb + a·Vc) / 3 → 11.82 V ∠84.7°
- Compute Voltage Unbalance Factor (VUF %): VUF = (|V2| / |V1|) × 100% = (11.82 / 226.54) × 100% → 5.22%
Final Solution: V1: 226.5V ∠-3.2° | V2: 11.8V ∠84.7° | V0: 8.7V ∠35.4° | VUF: 5.22% (Severe)
Frequently Asked Questions
- What does the zero-sequence component indicate in a power system?
- Zero-sequence current flows through neutral conductors, earth paths, or ground return paths during unbalanced phase-to-ground faults or load unbalance. In delta connections, zero-sequence current circulates within the closed loop.
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