Environmental Engineering Reference
In-Depth Information
or in the simplified form as
i
(
k
+
1)
=
ai
(
k
)
+
bu
i
(
k
)
−
bu
g
(
k
)
.
(17.5)
Due to the one-step computation delay, the current
i
can be controlled to reach its reference
in a minimum of two steps.
By incrementing (17.5) with one step, then
i
(
k
+
2)
=
ai
(
k
+
1)
+
bu
i
(
k
+
1)
−
bu
g
(
k
+
1)
.
(17.6)
Substituting (17.5) into (17.6), then the output current
i
at step
k
+
2 is obtained as
a
2
i
(
k
)
i
(
k
+
2)
=
+
abu
i
(
k
)
−
abu
g
(
k
)
+
bu
i
(
k
+
1)
−
bu
g
(
k
+
1)
.
(17.7)
By rearranging (17.7), the required inverter command voltage is
a
2
b
i
(
k
)
1
b
i
(
k
u
i
(
k
+
1)
=
+
2)
−
−
au
i
(
k
)
+
au
g
(
k
)
+
u
g
(
k
+
1)
,
(17.8)
which requires the knowledge of the output current
i
(
k
+
2) and the grid voltage
u
g
(
k
+
1).
Here, the output current
i
(
k
+
2) can be predicted (expected) to be the reference current
i
ref
(
k
+
2) and estimated via the linear extrapolation (Holmes and Martin 1996) as
i
ref
(
k
+
2)
=
4
i
ref
(
k
−
1)
−
3
i
ref
(
k
−
2)
.
(17.9)
Similar to (17.9), the grid voltage can be estimated as
u
g
(
k
+
1)
=
2
u
g
(
k
)
−
u
g
(
k
−
1)
.
(17.10)
Substituting (17.9) and (17.10) into (17.8),
the control signal
u
i
(
k
+
1) can then be
obtained as
2
i
(
k
)
1
a
b
u
i
(
k
+
1)
=
b
(4
i
ref
(
k
−
1)
−
3
i
ref
(
k
−
2))
−
(17.11)
−
au
i
(
k
)
+
(2
+
a
)
u
g
(
k
)
−
u
g
(
k
−
1)
.
Hence, the inputs of the DB controller are
i
ref
,
i
and
u
g
.
17.3 Experimental Results
The control strategy was evaluated in the grid-connected mode under the same five different
scenarios tested in Chapters 15 and 16.
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