Page 289 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 281

2 3 2 32 3 2 3
pΔM 2 1:88624 0 0 ΔM 2 1:88625
6 7 6 76 7 6 7
+ 0:208335 Δu
pΔN 2 ΔN 2
6
6 7 ¼ 0:18624 0:02209 0 76 7 6 7
4 5 4 54 5 4 5
0:3729 2:04418 2 0:4167
pΔP T ΔP T
2 3
ΔM 2
6 7
½
Z ¼ 0, 0, 1Š ΔN 2 7
6
4 5
ΔP T
1. Calculate the coefficient of difference equation (T ¼1):
ð
½
Xk +1Þ ¼ ϕτðÞXkðÞ + G τðÞukðÞ, ZkðÞ ¼ 0, 0, 1ŠXkðÞ
2 3 2 3
0:15164 0 0 0:84836
ϕτðÞ ¼ 0:08257 0:97815 0 5 , G τðÞ ¼ 4 0:10443 5
4
0:00436 0:87106 0:13534 0:00204
2. Normalize the difference equation:
∗
Yk +1Þ ¼ ϕ τ ðÞXk ðÞ + G ∗ τ ðÞuk ðÞ
ð
T
Zk ðÞ ¼ h ∗ Yk ðÞ
2 3 2 3
0 1 0 0:00204
∗ ∗
ϕ τðÞ ¼ 4 0 0 1 5 , G τðÞ ¼ 4 0:08698 5
0:02 0:31:265 0:03916
T
3. h ∗ ¼ 1, 0, 0½ Š｡
(3) Solve the transfer function by the normalized equation method.
ϕ∗(τ) has been solved, that is, the coefficients a 1 ,…,a n of difference transfer function
have been obtained:

a 1 ¼ 1:265, a 2 ¼ 0:3, a 3 ¼ 0:02
and the coefficient b can, by Eq. (7.119), be determined
2 3 2 32 3 2 3
b 1 1 0 0 0:00204 0:00204
4 b 2 ¼ 1:265 1 0 54 0:08698 5 ¼ 4 0:08956 5
4
5
0:3 1:265 1 0:03919 0:07148
b 3
Thus, finally we have
0:00204Z 1 +0:08956Z 2 0:07148Z 3
GZðÞ ¼
1 1:265Z 1 +0:3Z 2 0:02Z 3