In a balanced 3-phase system, the magnitudes of line voltage VL, line current IL, and 3-phase power in terms of the magnitudes of phase voltage Vph and phase current Iph are derived as follows, where the term phase voltage (Vph) also means line-to-neutral voltage (VLN), and the term line voltage (VL) also means line-to-line voltage (VLL).
The Y-connected ship system gives the voltage of line a from line.
Balanced star connected three phase ship system
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 reason, a balanced 3-phase system performs exactly the same with or without the neutral wire, except in unbalanced load conditions.
Balanced delta connected three phase ship system
In a 3-phase, Δ-connected system, no wire exists for the return current, so the phasor sum of all line currents is forced to be zero regardless of a balanced or unbalanced load. With an unbalanced 3-phase load, however, this imposed-zero on the return current produces unbalanced line-to-line voltages.