Page 155 - Modern Control of DC-Based Power Systems

Control Approaches for Parallel Source Converter Systems 119

The share of every generator to the linearizing function is determined
by the sharing coefficient S i : The sum of all sharing coefficients has to be
equal to one in order to ensure linearization. Because the system is sup-
posed to have a certain natural frequency ω 0 and damping ratio ξ, the
variables of (5.25) and (5.26) are chosen as follows:
a 0 5 ω 2
0
a 1 5 2ξω 0
(5.28)
E i
V i 5 5 L b L a c xðÞ i
C eq L fi
V i is chosen like this to be compatible to the controller designed in
[11]. Inserting the control law (5.27) in system (5.21) yields
€
2
V5 L c xðÞ 1 L b L a c xðÞUu
a
T
2
2
5 L c xðÞ 2 L c xðÞ 1 k z 1 w 1 E 1 1 w 2 E 2 1 w 3 E 3
a a
C eq L f 1 C eq L f 2 C eq L f 3
_
52 a 1 V 2 a 0 V 1 w 1 E 1 1 w 2 E 2 1 w 3 E 3 (5.29)
C eq L f 1 C eq L f 2 C eq L f 3
_
2
52 2ξω 0 V 2 ω V 1 w 1 E 1 1 w 2 E 2 1 w 3 E 3
0
C eq L f 1 C eq L f 2 C eq L f 3
The control input is calculated to be
C eq L fi 2 T
d i 52 L c xðÞ1k z 1w i
a
S i E i
!
_ V
_
_
C eq L fi P eq I V
52 2 1 V 2 2 2a 1 V 2a 0 V 1w i :
S i E i R L C eq C eq V 2 C eq T f C eq L eq
(5.30)
Using Kirchhoff’s law, the following representation of the overall cur-
rent is obtained:
V P eq
_
1 I CPL 5 C eq V 1 1 (5.31)
I 5 I C 1 I R L
R L V
Inserting (5.31) in (5.30), the control law can be transformed so that
the control law is not dependent on the currents anymore. This is done
to retrieve a representation that is equivalent to the one in [11].