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Control Approaches for Parallel Source Converter Systems 149

5.4.1.3 Augmented Kalman Filter
Typically ISPSs can be divided in local subsystems with local states x i
which are dynamically coupled such as in Fig. 5.7. In the context of a
decentralized control architecture which is able to accommodate sudden
changes in topology and operates without the need of additional measure-
ments, each subsystem assumes to lump the nonlocal part into an equiva-
lent virtual source. Additionally, this source is considered to be a
disturbance with unknown dynamics as it is illustrated in Fig. 5.23.
It is considered now that the ISPS can be represented by a LTI system
like (5.97). This allows expressing any subsystem as [32]:
m
X
_ x i 5 A i x i 1 B i u i 1 F i x j (5.102)
j5k;j6¼1
m
X
_ y 5 C i x i 1 (5.103)
i G i x j 1 H i v i
j5k;j6¼1
Where the local state vectors are x i and u i and y represent the local
i
measurements which are degraded by the noise v i . The remote j-th sub-
system is represented by its state x j . The interaction between subsystems
m m
P P
are represented by the terms F i x j , G i x j .
j5k;j6¼1 j5k;j6¼1
Incorporating now the concept of a virtual disturbance source, defined
in [32], into the Eqs. (5.117) and (5.118) and denoting it with x di permits
to define the following system model:

_ x i 5 A i x i 1 B i u i 1 D i x di (5.104)
(5.105)
_ y 5 C i x i 1 E i x di 1 H i v i
i
Where the terms related to x di have now substituted the interconnec-
tion terms, and therefore the local subsystem dynamics depend only on
these states and the dynamics of the virtual disturbance. As the virtual

R f L f I L PCC

I I
d·E C f V R L I d 1 k

Figure 5.23 Decentralized model including the virtual disturbance.