Introduction to Electric Circuits

5.4 Balanced three-phase systems 111

Three-wire star system

If the system is balanced the current in each phase can be represented by three
sine waveforms, each having the same maximum value and with a successive
phase displacement of 120 ~. At any instant therefore the sum of the currents is
zero. Because the current in the return wire at any instant (iA + iB + iC) = 0 it
carries no current and may be dispensed with entirely, giving the three-wire
system shown in Fig. 5.8.
The current flowing in the generator-phase winding or in the load-phase
impedance is called the phase current (IpH). The current flowing in the wires
connecting the generator to the load is called the line current (IL). Clearly in
this connection, the phase current and the line current are one and the same
SO

Ip. = IL (5.1)

The junction of the three-phase windings (or of the three-phase loads) is called
the star point. The voltage between any line and the star point is called the
phase voltage (EpH on the generator side; VpH on the load side). The voltage
between any two lines is called the line voltage (EL on the generator side; VL on
the load side). In order to obtain the relationship between the phase voltage
and the line voltage we note from Fig. 5.8 that the line voltage is
VAB = VAN -- VBN. This is shown phasorially in Fig. 5.9 where we have drawn
--VBN equal and opposite to VBN and added it to VAN to give VAB. A line is
drawn perpendicularly from the end of VAN to meet VAB at M, which, by the
geometry of the diagram, is its mid-point. Note also that the angle O is 30 ~

A

A r-I I

EA B = EL VAB -- VL VAN = VpH l" UZA

i I

N

Figure 5.8

Figure 5.9

VAB = V L

" >~ VAN = VpH

|

-VBN ~

VCN VBN