Page 307 - Mathematical Models and Algorithms for Power System Optimization

Local Decoupling Control Method for Transient Stability of a Power System 299

_
½
δ si ¼ ω i ω s ð i 2 1, NŠÞ (8.12)
also can be defined the second state variable, where ω s could be determined by the equation:
N
X
J j ω j
j¼1
ω s ¼ (8.13)
N
X
J j
j¼1
_

Then observation decoupled state space could be constructed with δ, δ s .
This shows that the observation decoupled state space is not unique in the form, and it could be
formulated according to different requirements and conditions. But it is important to emphasize
that, the form of δ i is the most fundamental and also unique, because of the local observation
decoupled characteristic, δ i is the only specific expression of the new state space, which is
called as observation decoupled state space.
8.3.3.3 Formulation of observation decoupled state space in the power system

The observation decoupled state space is constituted in the existence of a decoupling reference.
Follow the power system simplified model and the equations to derive the δ ei from
Eqs. (8.1)–(8.3) in line with the local power balance assumption, which are listed here:
0
E U ei
i
G ei ¼ P mi sin δ ei α ei Þ u i ¼ 0 i 2 1, NŠÞ (8.14)
ð
½
ð
X 0
di
N
0
E U ei X U ei U j °
i
G ePi ¼ sin δ ei α ei Þ C ij sin α ei α j + φ 90
ð
ij
X 0 Z ij
di
j ¼ 1
j 6¼ i
(8.15)
N cosφ
X ij
2
U C ij P Li ¼ 0
ei
Z ij
j ¼ 1
j 6¼ i
0 2 N
E U ei U ei X U ei U j °
i
ð
G eQi ¼ cos δ ei α ei Þ + C ij cos α ei α j + φ 90
ij
X 0 X 0 Z ij
di di j ¼ 1
j 6¼ i
N
X sinφ ij 1
2
U C ij Q Li ¼ 0 i 2 1, N½ð ŠÞ (8.16)
ei
Z ij X cij
j ¼ 1
j 6¼ i
π π

j
α ei α j + φ 90 < ε, δ ei α ei j < ε, 8ε > 0 (8.17)
°
ij
2 2