Environmental Engineering Reference
In-Depth Information
The phase currents
I
of the delta connection are split between the currents in
the windings. This reduces the rms currents
I
in the windings by a factor of
∆
√3
The result is:
(5.73)
Since the voltages
V
Y
at the windings of the star connection are reduced by the
factor
√3
, the currents
I
Y
in the windings are also reduced by the factor
√3
relative to the delta connection:
(5.74)
Thus, the phase currents
I
of a star and a delta connection with the same
windings and the same phase-to-phase voltages are not identical.
The total active power of a symmetrical three-phase system in a star
connection is given by the sum of the active powers of all three windings:
(5.75)
The total active power of a delta connection is calculated similarly:
(5.76)
The measurement of voltage and current of only one phase is therefore
sufficient to estimate the total power of a symmetrical connection. With
V
=
∆
√3
•
I
Y
, the correlation between the active power of a star and
a delta connection becomes:
•
V
Y
and
I
=
√3
∆
(5.77)
In other words, the power input of a delta connection is three times higher
than the associated star connection.
The
reactive power Q
and the
apparent power S
of delta and star
connections are calculated similarly to the active power. Hence, they are:
and
(5.78)
(5.79)
Synchronous machines
Design of synchronous machines
A synchronous machine consists of a
stator
and a rotor. The stator is the
stationary part of the machine with the three-phase windings to produce the
rotating field as described in the previous section. The casing is made of
