Environmental Engineering Reference
In-Depth Information
A
B
0.01+0.01
0.15+0.15
R
em
=
(1-s) R
r
s
6
(1+0.01) 0.01
=
-0.01
~ -1
Figure 4.17
Equivalent circuit for Worked Example 4.3
Model answer
The circuit in Figure 4.17 brings to mind the synchronous generator equivalent circuit of
Figure 4.7. The reactance to resistance ratio of the series impedance in fi gure 4.17 is
0.3/0.02=15; hence, to a good approximation, Equations (4.8) and (4.9) can be used. The
mechanical power converted from the wind into electrical power per-phase is 450 000/3 =
150 000 W. This appears as a ' negative ' power dissipation in
R
em
therefore the voltage
V
A
across
R
em
is given by
2
V
R
A
150 000
=
em
and
V
A
=
387
V
Using Equation 4.8(a)
VV
X
387
03
V
AB
B
150 000
=
sin
δ
=
sin
δ
.
and
116 28
The reactive power at end
A
is zero, hence, from Equation (4.8b).
V
B
sin
δ =
.
V
X
387
03
A
(
)
=
(
)
0
=
VV
−
cos
δ
387
−
V
cos
δ
AB
B
.
and
V
B
cos
387
δ =
Hence
116 28
387
.
tan
δ
=
and
δ
=
16 7
.
°
giving
V
B
= 404 V, i.e.
404
3
≈
700
line volts
