Electrical Power Systems

360 Electrical Power Systems
rom ig. 14.3, we can write
ig. 14.3: Phasor diagram for balanced three phase system.
V an = V an 0º ...(14.11)
V ab = 3 V an 30º ...(14.12)
V ac = 3 V an -30º ...(14.13)
Also, for a balanced three phase system
q a + q b + q c = 0
\ 2pÎ0 rGa + 2pÎ0 rGb + 2pÎ0 rGc = 0
\ G a + G b + G c = 0 ...(14.14)
or equilateral spacing, D ab = D bc = D ca = D (say).
Therefore eqn. (14.14) can be written as:
L
HG I
KJ O
Vab = r Ga NMb
- Gbgln
D
r QP
...(14.15)
rom eqns. (14.12) and (14.15), we get
L DI
3 Van 30º = r Ga - Gb
NMb
O gln HG r KJ QP
...(14.16)
Similarly,
3 Van L -30º = r Ga NMb
- DIO
Gcgln
HG r KJ QP
... (14.17)
Adding eqns. (14.16) and (14.17), we get
3Van = 3Gar ln D I
HG r KJ
\ G a =
r
V
an
ln I
HG KJ
D
r
...(14.18)