Page 255 - Mathematical Models and Algorithms for Power System Optimization

Optimization Method for Load Frequency Feed Forward Control 247

7.5.1 Local Estimator

From Eqs. (7.39) to (7.41), motion equations of the steam turbine and hydro turbine have the
following structures:
_
X Tj ¼ A Tj X Tj + B Tj Δu j + C Tj ΔP Lj (7.44)

The difference between the above mentioned equations is that the elements in A Tj , B Tj , and C Tj
are different,
where

T
X ¼ ΔM j ΔN j ΔP Tj Δω j
Xj
Local measurement includes:
Δω mj ¼ Δω j + η ¼ H X Tj + η (7.45)
T
j j j
Δu mj ¼ Δu j + η (7.46)
mj
ΔP mLj ¼ ΔP Lj + η j (7.47)

From Eqs. (7.44)–(7.47), we know
_
X Tj ¼ A Tj X Tj + B Tj Δu mj + C Tj ΔP mLj + V Tj
(7.48)
T
Δω mj ¼ H X Tj + η
Tj Tj
η and V in Eq. (7.45)–(7.48) are white noise. Transform the Eq. (7.44) into equivalent discrete
state equation:
X Tj k +1ð (7.49)
Þ ¼ ϕ X Tj kðÞ + G Tj Δu mj kðÞ + T Tj ΔP mLj kðÞ + V Tj
Tj
Δω mj kðÞ ¼ H X Tj + η (7.50)
T
Tj Tj
Transformation methods are shown in Section 7.6.

V Tj and η Tj are white noise. Kalman filtering equations corresponding to Eqs. (7.49) and
(7.50) are:

^
X Tj k +1Þ ¼ X Tj k +1Þ + Kk +1Þ Δω mj k +1Þ X Tj k +1Þ (7.51)
ð
ð
ð
ð
ð
^
ð
X Tj kðÞ ¼ ϕ X Tj k 1Þ + G Tj Δu mj k 1Þ + T Tj ΔP mLj k 1Þ (7.52)
ð
ð
Tj
h i 1
T
K Tj k +1ð ð ð (7.53)
Þ ¼ P Tj k +1=kÞH Tj + H Tj P Tj k +1=kÞH + R Tj
Tj
T
P Tj k +1=kð Þ ¼ ϕ P Tj kðÞϕ + Q Tj (7.54)
Tj
Tj

ð
P Tj k +1ð Þ ¼ 1 KkðÞH Tj P Tj k +1=kÞ (7.55)
where R Tj and Q Tj mean the covariance matrix of η Tj and V Tj , respectively.