Page 193 - Modern Control of DC-Based Power Systems

Control Approaches for Parallel Source Converter Systems 157

1 1
2 3
2
V 6 7
2 3 6 R L C f C f 7
6 7
x ext 5 4 I L 5 A ext 5 6 1 R f 7
2 2
6 7
6 7
I d L f
4 L f 5
0 2a d
(5.128)
0
2 3
6 E 7

C ext 5 1 0 0
6 7
B ext 5 6
7
4 L f 5
0
h 1 i T
N ext 5 2 C f 0 b d
The difference between the augmented version and the Kalman filter
from Section 5.4.1.2 is that the state-space matrices incorporate the addi-
tional state which will lead to the following augmented state:
_
^ x ext 5 A ext ^x ext 1 B ext d i 1 K KF ðx i 2 C ext ^x ext Þ (5.129)
where K KF corresponds to the steady-state Kalman gain which can be
determined by the equations of (5.100) and (5.101), while assuming that
the observability condition of the augmented system is kept valid.
As the observer estimates one additional state, the 2DOF structure is
augmented with L ext , a term expressing the online deviation of the system
set-point due to the virtual disturbance. This set-point trajectory genera-
tor is also used to mitigate the difference between the linearized model
values of the states and the actual nonlinear values. In steady-state the
derivatives of the differential equations of the system are equal to zero,
yielding at the equilibrium point of (5.118). The nominal set-point of the
system without the presence of I d ; thus based on the nonaugmented sys-
tem, results in a set-point only dependent on V nom ; adding the adaption
term corresponding to I d and substituting it by its estimate ^ I d leads to a
set-point dependent on ^ I d and V nom .
21
^

^ x AB 0 2nI d
5 1 (5.130)
^ u c 0 V nom 0
Correspondingly the estimate of ^ I d needs to be multiplied by the fac-
tor L ext (6) in order to correct the set-point variations induced by the
disturbance.