Three-Phase Circuit

Balance Three-Phase Voltage

A balance 3-phase voltage can only be obtain if we have a 3-phase ac generator by converting potential energy to mechanical energy and to electrical energy in the hydro-power plant for example. A three-phase voltage may be arranged in delta (∆) or wye (Y) system. A wye system allows to provide two different voltages for example 173-300 volts, 173v is the line to neutral voltage and the 300v is the line-to-line voltage. In delta system can only provide one voltage magnitude however it has a greater redundancy as it may continue to operate normally with one of the three supply windings offline.

This is the graph of the balance three-phase voltage source connected into the loads by three to four wires and each voltage source has 120 degrees apart.

3-phase delta system

 3-phase wye system

Conversion of delta to wye and wye to delta source

V_p = V_L  /  sqr.(3)∠-30
V_L = V_p sqr.(3)∠30



Conversion of delta to wye and wye to delta loads

Z_Y=Z_D / 3

Z_D= Z_Y (3)

Balance Y-Y connection example problem

find the total current flowing in a single phase circuit (Ia)
Vy = 110∠0 V

since it is a balance single phase first we draw the single phase equivalent circuit

we know that
                                      Ia=Van / Zy
to obtain (Ia) we calculate the total impedance of the single phase circuit
                                      Ia=110∠0 / (5-j2)+(10+j8)
                                      Ia=6.81∠-21.8 A
the total current flowing in the 3-phase system is
                                     6.81A x 3 = 20.23 A

finding the delta equivalent of the source is
                                      V_{D =}V_p sqr.(3)∠30
                                      V_D = 110 sqr.(3) ∠(0+30)
                                      V_D =190.52∠30
delta equivalent of the load in the circuit
                                       Z_D= Z_Y (3)
                                       Z_D=10+j8 x (3)
                                       Z_D=30+j24 ohm
note: when the source is connected in delta it is much easier if we convert it in Y- connection to solve the problem.