Electrical Power Systems Technology

302 Electrical Power Systems Technology

phase voltages (VP). The line currents (IL) are equal to the phase currents
(IP) multiplied by 1.73. Thus:

VL = VP
IL = IP × 1.73

For a balanced three-phase wye system, the method used to find the
voltages and currents is similar. The voltage across the AC lines (VL) is
equal to the square root of 3 (1.73) multiplied by the voltage across the
phase windings (VP), or

VL = VP × 1.73.

The line currents (IL) are equal to the phase currents (IP), or

IL = IP

The power developed in each phase (PP), for either a wye or a delta
circuit, is expressed as:

PP = VP x IP × pf

where:
pf is the power factor (phase angle between voltage and current) of
the load.
The total power developed by all three phases of a three-phase gen-
erator (PT) is expressed as:

PT =3 × PP
= 3 × VP × IP × pf
= 1.73 × VL × IL × pf

As an example, we can calculate the phase current (IP), line current
(IL), and total power (PT) for a 240-volt, three-phase, delta-connected sys-
tem with 1000-watt load resistances connected across each power line. The
phase current is:

PP
IP = ——
VP