Page 167 - Modern Control of DC-Based Power Systems

Control Approaches for Parallel Source Converter Systems 131

1
21
21
21
F 1 . 0- 1 A ð 1; 1Þa 12 1 A ð 1; 2Þa 12 1 A ð 1; 3Þa 12
R eq C eq
21 21 21
2; 3Þa 22
1 A ð 2; 1Þa 22 1 A ð 2; 2Þa 22 1 A ð
21 21 21
1 A ð 3; 1Þa 32 1 A ð 3; 2Þa 32 1 A ð 3; 3Þa 32 . 0
21 21 21 21
2; 1Þa 21
F 2 . 0-A ð 1; 1Þa 11 1 A ð 1; 2Þa 11 1 A ð 1; 3Þa 11 1 A ð
21 21 21 21
3; 2Þa 31
1 A ð 2; 2Þa 21 1 A ð 2; 3Þa 21 1 A ð 3; 1Þa 31 1 A ð
21
1 A ð 3; 3Þa 31 2 δ . 0 (5.61)
After fulfilling the stability conditions and the desired current sharing
methodology of the synergetic control law [25], the resulting duty cycles
(5.62) (5.64) are:

0 1
ψ
d 1 52 1 1 @ a 13 1 a 14 1 a 15 2 a 12 a 16 A
1
2 V 1 V c;ref
T 1 L 1 L 2 L 3 R eq C eq
V 1V c;ref R eq C eq
0 1
!
a 16 I 1 1I 2 1 I 3 P eq
2ηa 11 V 2 @ A
2 1δM 2
a 12 2
V 1V c;ref C eq V 1 V c;ref C eq
(5.62)
0 1
ψ a 23 a 24 a 25 a 22 a 26
d 2 52 2 1 @ 1 1 2 A
1
2 V 1V c;ref
T 2 L 1 L 2 L 3 R eq C eq
v1V c;ref R eq C eq
0 1
!
a 26 I 1 1 I 2 1I 3 P eq
2ηa 21 V 2 @ A
a 22 2
2 1δM 2
C eq v 1V c;ref C eq
V 1V c;ref
(5.63)
0 1
ψ a 33 a 34 a 35 a 32 a 36
d 3 52 2 1 @ 1 1 2 A V 1 V c;ref
2
1
T 2 L 1 L 2 L 3 R eq C eq
V 1V c;ref R eq C eq
0 1
!
a 36 I 1 1 I 2 1I 3 P eq
2ηa 31 V 2 @ A
a 32 2
2 1δM 2
V 1V c;ref C eq V 1V c;ref C eq
(5.64)