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Control Approaches for Parallel Source Converter Systems 151

Therefore, the white noise is transformed by a linear filter which is
proposed in [48]. The disturbance model is then:
_ u d 52 a d u d 1 b d w (5.111)

With the filter parameters according to [33], τ c is the correlation time
and σ w is the variance of the noise that has to be estimated:

s ffiffiffiffiffiffiffiffi
1 2σ 2
a d 5 ;b d 5 w (5.112)
τ c τ c

5.4.2 Application to Decentralized Controlled MVDC System
(LQG 1 Virtual Disturbance)
The LQG design is composed of a LQR and a linear Kalman filter and is
applied to the decentralized system which is depicted in Fig. 5.22. The
LQR is implemented with static feedback of the estimated state variables
of the controlled system and the feed-forward of the control variables and
estimated. The Kalman filter is an optimal linear observer which estimates
the state and disturbance from the measured variables. The achievable
control performance is dependent on the speed of the estimation of the
disturbance. The LQR guarantees optimal state feedback given that the
state estimation by the Kalman filter is sufficiently accurate. This structure
is shown in Fig. 5.24. The modifications are explained in the following.
In order to facilitate the understanding the overall system model is
presented again in Fig. 5.25 while the decentralized system model is
depicted in Fig. 5.26.
In [36] the authors introduced a concept to handle those unknown
disturbances on the bus. They proposed to sum up all unknown currents

LQR + setpoint
V bus Augmented Estimates: trajectory
kalman filter ^ ^ ^
Vbus; I ; I generation
L
d
Measurement Control signal
Plant:
generators and loads

Figure 5.24 LQG controller structure using an augmented Kalman filter and a LQR
with set-point trajectory generation.