
26 Shipboard Electrical Power Systems
The line-to-line voltage is obviously the same as the phase voltages, that is, V
LL
= V
ph
Three-phase power P
3-ph
= 3 × P
1ϕ
= 3 × V
ph
× I
ph
× pf = 3 × V
LL
× (I
L
/√3) × pf
∴P
3-ph
= √3 V
LL
I
L
pf watts and S
3-ph
= √3 V
LL
I
L
volt-amperes (1.30)
Note that the expression for 3-phase power works out to be the same in both Y and ∆.
In a 3-phase, 4-wire, Y-connected system, the neutral current is the sum of three
line currents. In a balanced Y system, the current in the neutral wire (if used) is
always zero, because it is the phasor sum of three equal line currents out of phase by
120° from each other. For this