Page 273 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 265

As:
1
XkðÞ ¼ F YkðÞ (7.120)

Substitute Eq. (7.120) into Eq. (7.118), then we have:
1
ð
Yk +1Þ ¼ FϕF YkðÞ + FGu kðÞ
∗ ∗
¼ ϕ YkðÞ + G ukðÞ
T 1 T
∗
ZkðÞ ¼ h F YkðÞ ¼ h YkðÞ
where
2 T 3
h
T
h ϕ
6 7
F ¼ 6 7
4 ⋮ 5
T
h ϕ n 1
Now, the coefficients a 1 , …, a n of transfer function have been determined, which are used
together with G*¼[d 1 , …, d n ]T to obtain the coefficients b 1 , …, b n of the transfer function.
Step 3: Obtain the system’s transfer function based on the normalized equation.

According to Eq. (7.119), the calculation formula is as follows:

2 3 2 32 3
1
b 1 d 1
⋮ ⋮
6 7 6 a 1 1 76 7
⋮ ⋮
6 7 6 76 7
6 7 ¼ 6 a 2 a 1 1 76 7 (7.121)
⋮ ⋮ ⋮ ⋱ ⋱ ⋮
6 7 6 76 7
4 5 4 54 5
b n a n 1 a n 2 ⋯ a 1 1 d n
From this, the coefficients a 1 , …, a n , b 1 , …, b n of transfer function have been determined; in other
words, the state equations of difference transfer function from differential transfer function have
beensolved,whichisanadvisablemethodsuitableforallcomplexconditions.Inparticulartohigh-
order models, such a method only needs to obtain the inverse of transformation matrix without
having to iteratively solve the root of the model, which greatly speeds up the calculation and
facilitates the programming, thereby demonstrating great superiority. As for low-order models, it
can be solved by the direct solution and thus can be solved in any of the two solutions.

7.8 Implementation

7.8.1 Parameters From Figs. 7.4 and 7.7

The model of Figs. 7.6 and 7.10 is chosen in the simulation test of which the parameters
are as follows: