Sections: Positive | Negative | Zero | Formulas | Examples

Positive Symmetrical Components

Definition. The positive sequence consists of three phasors equal in magnitude displaced from each other by 120º in phase and having the same phase sequence as the original phasors.

The positive sequence is assummed as abc.
The positive sequence subscript is 1.

Phasor Relation. With Va1 taken as the reference phasor, the relationships are:

V_b1 = a² V_a1V_c1 = a V_a1

---

Sections: Positive | Negative | Zero | Formulas | Examples

Negative Symmetrical Components

Definition. The negative sequence consists of three phasors equal in magnitude displaced from each other by 120º in phase and having the phase sequence opposite to that of the original phasors.

The negative sequence is assummed as acb.
The negative sequence subscript is 2.

Phasor Relation. With Va2 taken as the reference phasor, the relationships are:

V_b2 = a V_a2V_c2 = a² V_a2

---

Sections: Positive | Negative | Zero | Formulas | Examples

Zero Symmetrical Components

Definition. The zero sequence consists of three phasors equal in magnitude and with zero phase displacement from each other.

The zero sequence subscript is 0.

Phasor Relation. With Va0 taken as the reference phasor, the relationships are:

V_b0 = V_a0V_c0 = V_a0

---

Sections: Positive | Negative | Zero | Formulas | Examples

Formula / Matrix

Formula. Thus, relating the preliminary equations with the above information, and substituting respective values, referred to V_awe have:

V_a = V_a1 + V_a2 + V_a0
V_b = V_b1 + V_b2 + V_b0 = a² V_a1 + a V_a2 + V_a0
V_c = V_c1 + V_c2 + V_c0 = a V_a1 + a² V_a2 + V_a0

Matrix.

Important Notes:
1. Although the discussion here is focussed on the derivation of the symmetrical components of the voltage, V, the equations should also be applicable to currents, I, by replacing all the V with I.

2. No zero sequence components exist if the sum of unbalanced phasors is zero. Since the sum of the line-to-line voltage phases in a three-phase system is always zero, zero-sequence components are never present in line voltages, regardless of imbalance. The summation of the three line-to-neutral phasors, however, is not equal to zero. Thus voltage-to-neutral may contain zero-sequence components.

3. In a three-phase four-wire system, the sum of line currents' components is equal to I_N, i.e., I_N = I_a + I_b + I_c. Thus I_N = 3I_a0. When machine is delta-connected, however, the current to neutral, I_N = 0.