Electrical Power Systems

has the following properties
R
S|
T|
2 j240 j120°
b = e = e = b
*
2 ej
3
– *
b = b
b = 1
2
1+ b+ b = 0
U
V|
W|
Symmetrical Components 227
...(9.1)
If the phase sequence is acb (negative sequence) then
V a = V a, V b = b V a, V c = b 2 V a
It is assumed that the subscript 1, 2, 0 refer to positive sequence, negative sequence and
zero sequence respectively.
If V a , V b and V c represent an unbalanced set of voltage phasors, the three balanced sets are
written as:
(V a1, V b1, V c1) positive sequence set
(V a2, V b2, V c2) negative sequence set
(V a0, V b0, V c0) zero sequence set
A set of (balanced) positive sequence phasors is written as
V a1, V b1 = b 2 V a1, V c1 = b 2 V a1 ...(9.2)
A set of (balanced) negative sequence phasors is written as
V a2, V b2 = bV a2, V c2 = b 2 V a2 ...(9.3)
A set of zero sequence phasors is written as
V a0 , V b0 = V a0 , V c0 = V a0 ...(9.4)
The three phasors (Va , Vb , Vc ) can be expressed as the sum of positive, negative and zero
sequence phasors defined above.
Thus we can write,
Va = Va1 + Va2 + Va0 ...(9.5)
Vb = Vb1 + Vb2 + Vb0 ...(9.6)
Vc = Vc1 + Vc2 + Vc0 ...(9.7)
igure 9.1 shows symmetrical components of the unbalanced phasors.
ig. 9.1: Symmetrical Components of Unbalanced Voltage Phasors.