Page 245 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 237

^ ρ 0 ^ ρ 1 ⋯ ^ ρ p 1 ϕ 1 ^ ρ 1
^
2 32 3 2 3
⋮ ⋯ ⋯
4 ⋯ 54 ⋮ 5 ¼ 4 ⋮ 5 (7.33)
^ ρ p 1 ⋯⋯ ^ ρ 0 ϕ n ^ ρ p
^
^
^
Solve the equation to get autoregressive parameters ϕ ,…,ϕ .
1 n
^
Estimation of constant θ 00 by:
8 !
p
X
^
>
< ϕ
^ μ 1 i ð p > 0Þ
θ 00 ¼ (7.34)
i¼1
>
μ ð p ¼ 0Þ
:
where μ is the mean value of the given time series.
2
Estimation of white noise variance σ a by:
p
X
2 ^
σ ¼ γ ϕ γ (7.35)
a
0
i i
i¼1
These estimation methods are approximated estimations, and there are more exact estimation
methods. In the case of AR models, based on Reference [78], the approximated and exact
estimation values are of little difference; in this section, the AR model is selected, and the exact
estimation is not discussed herein.
7.4 Model for a Typical Power System
The power generation system is a typical large system consisting of all power plants, each of
which is made up of a governor block, excitation block, prime mover block, and generator
block. As previous discussed, this chapter only considers the changes of load frequency under
small disturbances, taking no account of the excitation block of the unit. The mathematical
models for various blocks of the units will be discussed respectively as follows.

7.4.1 Generator Model

Under small disturbance, the motion equation of generator rotor is:
dΔω
M + DΔω ¼ Δp T Δp L (7.36)
dt
This power balance equation is suitable for all units.
All power values in Eq. (7.36) are the per-unit value of rated powers; M is inertia constant,
M¼2H, H is generally 2–8s, and this chapter takes 5s.

The transfer function of generator model can be obtained by Laplace transform of Eq. (7.36):