Page 256 - Mathematical Models and Algorithms for Power System Optimization
P. 256
248 Chapter 7
7.5.2 Central Estimator
From the hierarchical estimator, it is possible to acquire the information of all power plants, and
accordingly, the central estimator can be used to estimate the whole system information.
First, discretize the system equivalent generator equation:
M e Δ _ ω e ¼ DΔω e + ΔP Te ΔP L
into difference equation, then combine it with the load model Eq. (7.31) to get:
^
Xk +1Þ ¼ ϕXkðÞ + GΔP T kðÞ + V (7.56)
ð
The measurement equation is expressed as:
X
M j Δω j kðÞ η
Δω m kðÞ ¼
M (7.57)
T
¼ Δω m kðÞ + η ¼ H XkðÞ + η
where
ð
X ¼ y 1 y 2 …y n Δωf g the number of y depends on the load modelÞ
^ P ^
In Eq. (7.56), ΔP T ¼ ΔP Tj is obtained by the local estimator. V and η are assumed to be white
noise; Kalman filtering equations corresponding to Eqs. (7.56) and (7.57) are:
^
ð
Xk +1Þ ¼ Xk +1ð Þ + kk +1Þ Δω m k +1Þ Xk +1Þ (7.58)
ð
ð
ð
^
ð
Xk +1Þ ¼ ϕXkðÞ + GΔP T kðÞ (7.59)
T T 1
Kk +1=kÞ ¼ Pk +1=kÞH HP k +1=kð ÞH + R (7.60)
ð
ð
T
Pk +1=kÞ ¼ ϕPkðÞϕ + Q (7.61)
ð
ð
½
ð
Pk +1Þ ¼ I Kk ðÞHPk +1=kÞ (7.62)
where R and Q mean the covariance matrix of η and V respectively.
7.5.3 Estimation and Forecasting of Load Disturbance ΔP L
From the second equation of load model Eq. (7.31), the estimation formula of ΔP L is
^ ∗ ^ ∗ T ^
T
ΔP L kðÞ ¼ H YkðÞ ¼ H WXkðÞ (7.63)
^
whereXkðÞisobtainedbythelocalestimator.WmeansthetransformationmatrixfromXtoY.Based
on Eq. (7.56), the load disturbance forecasting formula calculated from kth step is obtained as
follows:
^ ∗ T ∗ 1
ΔP L k +1ð Þ ¼ H ð ϕ Þ ^ ykðÞ (7.64)
