Page 287 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 279

Substitute it into Eq. (7.77):

2 3
lnλ 1
7 1
lnλ 2 ln λ 1 5T
6 0
ðÞ
A ¼ T4
lnλ 2
2 3
1 10
6 7
¼ 4 4 30 5
10 2
(2) Using the logarithmic matrix method to obtain A:

2 3
1 1 0
A ¼ 4 4 3 0 5
13 10 8 2+3 10 9

(3) Using the successive approximation method to obtain A.
After obtaining ϕ(0.01), use the Eq. (7.106) to solve A:

2 3
0:995 1 0
A ¼ 4 4 3:005 0 5
1 0:006 2:001

7.8.6.3 Results of Example 3
If the transfer function for hydro turbine governor and prime mover is known:

ð 5S +1Þ 1 SÞ
ð
GSðÞ ¼
ð
ð
ð 0:53S 1Þ 45:2698S +1Þ 0:5S +1Þ
To be solved is the difference transfer function with difference time of T¼1s.
(1) Solve the transfer function by the Direct Z transform method.
With Eq. (7.108):
TS
ð 1 e Þ
GZðÞ ¼ ZG SðÞ
S
1
First, expand GZðÞ ¼ into the form of partial fractions
S