Page 192 - Modern Control of DC-Based Power Systems

156 Modern Control of DC-Based Power Systems

the disturbance current estimation as a state based on a model of white
noise as input to a linear filter.
The disturbance estimation is handled by the augmented Kalman fil-
ter. The design of the augmented Kalman filter for decentralized con-
trolled MVDC systems is performed in two consecutive steps.
1. The disturbance I d in the system is simply included as noise rather
than a state and the Kalman filter is introduced to estimate the induc-
tor current of the buck converter.
2. This Kalman filter is augmented to include the disturbance current esti-
mation as a state based on a model of white noise as input to a linear
shaping filter for representing nonstationary colored noise [47] and [34].
At first, the system model looks exactly like the one for the LQR
controller:

_ x 5 Ax 1 Bd 1 NI d
(5.123)
y 5 Cx
1 1
2 3
2

V 6 R L C f C f 7
x 5 6 7
7
I L A 5 6 1 R f 5
4 2 2
(5.124)
L f L f
h E i T

B 5 0 L f C 5 1 0
h 1 i T
N 5 2 C f 0
According to Section 5.4.1.4, the disturbance current model for non-
white noise is given in (5.125):
_ _ I d 52 a d I d 1 b d w (5.125)

with the filter parameters:

s ffiffiffiffiffiffiffiffi
1 2σ 2
a d 5 ;b d 5 w (5.126)
τ c τ c
where τ c is the correlation time and σ w is the variance of the noise that
has to be estimated. Extending the system (5.115) by the linear filter leads
to, with v being the measurement noise in the local available measure-
ment (e.g., the bus voltage):

_ x ext 5 A ext x ext 1 B ext d 1 N ext w
(5.127)
y 5 C ext x ext 1 v