Environmental Engineering Reference
In-Depth Information
9.3.2 Compensation of Active and Reactive Power
In order to make the three-phase currents balanced and obtain the unity power factor at the
grid side, all the reactive power consumed by the load should be provided by the SPC. Since
there is no external power supply to maintain the DC-bus voltage of the SPC, the active power
consumed by the SPC should
b
e zero when the losses are ignored. In this case, the active power
consumed by the load, i.e.,
√
3
U
I
L
1
K
V
, should be provided by the grid currents in a bal-
anced way. Hence, the RMS value of the three-phase grid currents after compensation should be
√
3
U
I
L
1
K
V
×
cos
θ
cos
θ
θ
√
3
K
V
,
which means the three-phase grid currents should be
⎧
⎨
I
L
1
cos
=
3
U
I
L
1
c
os
θ
√
3
K
V
∠
I
A
=
0
,
I
L
1
cos
θ
√
3
K
V
∠
−
2
3
π,
I
B
=
(9.4)
⎩
I
L
1
c
os
θ
√
3
K
V
∠
2
3
π.
I
C
=
The corresponding phasor diagram is shown in Figure 9.2(b). Mapping the grid-side currents
to the track side, the corresponding three-phase currents are
⎧
⎨
I
L
1
cos
θ
√
3
∠
I
a
=
0
,
I
L
1
cos
θ
√
3
∠
−
2
3
π,
I
b
=
(9.5)
⎩
I
L
1
c
o
s
θ
√
3
∠
2
3
π.
I
c
=
Therefore, the Phase-A and Phase-B compensation currents provided by the three-phase
converter are
I
ra
=
I
a
−
I
L
,
I
rb
=
I
b
+
I
L
.
or
i
ra
=
i
a
−
i
L
,
(9.6)
i
rb
=
i
b
+
i
L
.
The Phase-C compensation current is
i
rc
=
i
c
=−
i
ra
−
i
rb
.
The phasor diagram of the system at the track side after compensation is shown in
Figure 9.2(c). It can be seen that
I
ra
and
I
rb
are not the same unless cos
1. Because of
the high voltage of the traction power system, two single-phase step-down transformers with
turns ratio of
K
D
can be used.
θ
=
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