Page 271 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 263
where d 1 , …, d n are:

3 1
1
2
2 3 2 3
d 1 b 1
1 7
⋮ ⋮
a 1
6
6 7 6 7 6 7
6 7 6 ⋱ 7 6 7
(7.114)
6 7 6 7 6 7
6 ⋮ 7 ¼ 6 7 6 ⋮ 7
a 2 a 1 1
6 7 6 7 6 7
4 ⋮ 5 6 7 4 ⋮ 5
⋮ ⋱
4 5
d n b n
a n 1 a n 2 ⋯ a 1 1
Rearrange Eq. (7.113) to get the state equation:
ð7:115Þ

or alternatively, the transfer function is represented the factorization form, or rewrite
Eq. (7.112) into the factorization form:

ð
ð
KS + b 1 Þ⋯ S + b m Þ
DSðÞ ¼
ð S + a 1 Þ S + a 2 Þ⋯ S + a n Þ
ð
ð
1 K
S + b 1 S + b 2 S + b m (7.116)
¼ ⋯ ⋯
S + a 1 S + a 2 S + a m S + a m +1 S + a n
¼ D 1 SðÞ D 2 SðÞ⋯D n SðÞ
D(S) can be depicted into the following block diagram:

where

S + b 1 S + b 2 K
D 1 SðÞ ¼ , D 2 SðÞ ¼ ,…,D n SðÞ ¼
S + a 1 S + a 2 S + a n
List the first-order differential equations of each block, and make them in a simultaneous
way to get the state equation of the whole system.