Page 179 - Electrician - TT (Volume 1)

ELECTRICIAN - CITS

Fig 5 Fig 6

The phase voltages V and V are separated in phase by one third of a period, or 120° between the two
VN
UN
phasors. (Fig 7)
The phasor sum of the two phase voltages V and V can be obtained geometrically, and the resultant phasor
UN
NV
so obtained is the line voltage V through the relation V = V + V .
UV
UN
UV
NV
Note that to obtain the line voltage V the measurement is made from the U terminal through the common point
UV
N to the V terminal, for a star connection.
This fact is illustrated in Fig 8. Starting with the phasors V and V (Fig 7), the phasor V = V is produced
UN
VN
NV
VN
from the point N. The diagonal of the parallelogram with sides V and V is the phasor representing the resulting
NV
UN
line voltage V .
UV
It can be concluded, therefore, that in a generator the line voltage V is related to the phase voltage V by a
L
P
multiplying factor. This factor can be shown to be , so that
3
V = x V
3
L P
In a three-phase generating system, the line voltage is always times the phase-to-neutral voltage. The factor
relating the line voltage to the phase voltage is .
It was shown that the line voltage is greater than the phase voltage. Here is a numerical example.
The RMS phase voltage in a three-phase system is 240V. Since the ratio of line voltage to phase voltage is the
3
RMS line voltage is
V = x V = x 240
3
L
P
= 415.68V
or rounded down, V = 415V.
L
Fig 7 Fig 8

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CITS : Power - Electrician & Wireman - Lesson 26-29