0195136047.pdf

4.1 THREE-PHASE SOURCE VOLTAGES AND PHASE SEQUENCE 201

VL−L

Vph

(a)

(b)

b

b′

IL

A

C

B

a

a′

c′

c

Iph

n N

c′

c

b

b′

A

a

a′

Iph

B

C

IL

VL−L = 3 Vph

IL = Iph

VL−L

VL−L = Vph

IL = 3 Iph

Figure 4.1.3Schematic representation of generator windings.(a)Balanced wye connection.(b)Balanced
delta connection.

as a reference with a phase angle of zero for convenience. This procedure yields the equivalent
single-phase circuit in which all quantities correspond to those of one phase in the three-phase
circuit. Except for the 120° phase displacements in the currents and voltages, the conditions in
the other two phases are the same, and there is no need to investigate them individually. Line
currents in the three-phase system are the same as in the single-phase circuit, and total three-phase
real power, reactive power, and volt-amperes are three times the corresponding quantities in the
single-phase circuit. Line-to-line voltages, in magnitude, can be obtained by multiplying voltages
in the single-phase circuit by

√
3.
When a system of sources is so large that its voltage and frequency remain constant regardless
of the power delivered or absorbed, it is known as aninfinite bus. Such a bus has a voltage and
a frequency that are unaffected by external disturbances. The infinite bus is treated as an ideal
voltage source.

Phase Sequence

It is standard practice in the United States to designate the phaseA–B–Csuch that under balanced
conditions the voltage and current in theA-phase lead in time the voltage and current in the
B-phase by 120° and in theC-phase by 240°. This is known aspositive phase sequence A–B–C.
The phase sequence should be observed either from the waveforms in the time domain shown in
Figure 4.1.2(a) or from the phasor diagrams shown in Figure 4.1.2(b) or 4.1.4(b), and not from
space or schematic diagrams, such as Figures 4.1.3 and 4.1.4(a). If the rotation of the generator
of Figure 4.1.1 is reversed, or if any two of the three leads from the armature (not counting the
neutral) to the generator terminals are reversed, the phase sequence becomesA–C–B(orC–B–A
orB–A–C), which is known asnegative phase sequence.
Only the balanced three-phase sources are considered in this chapter. Selection of one
voltage as the reference with a phase angle of zero determines the phase angle of all the other
voltages in the system for a given phase sequence. As indicated before, the reference phasor
is chosen arbitrarily for convenience. In Figure 4.1.4(b),V ̄BCis the reference phasor, and with
the counterclockwise rotation (assumed positive) of all the phasors at the same frequency, the