360
Electrical Power Systems
Fig. 14.3: Phasor diagram for balanced three phase system.
From Fig. 14.3, we can write Van = Van 0º
...(14.11)
Vab =
3 Van 30º
...(14.12)
Vac =
3 Van -30º
...(14.13)
Also, for a balanced three phase system qa + qb + qc = 0
\ 2p Î0 rGa + 2 p Î0 rGb + 2p Î0 rGc = 0 Ga + Gb + Gc = 0 \ For equilateral spacing, Dab = Dbc = Dca = D (say). Therefore eqn. (14.14) can be written as:
...(14.14)
LMb N
g FGH Dr IJK OPQ
...(14.15)
3 Van 30º = r Ga - Gb ln r
LMb N
g FGH D IJK OPQ
...(14.16)
LMb N
g FGH D IJK OPQ
... (14.17)
Vab = r Ga - Gb ln From eqns. (14.12) and (14.15), we get
Similarly,
3 Van -30º = r Ga - Gc ln r
Adding eqns. (14.16) and (14.17), we get 3Van = 3Gar ln \
Ga =
Van D r ln r
FG D IJ HrK
FG IJ H K
...(14.18)