Page 311 - Mathematical Models and Algorithms for Power System Optimization

Local Decoupling Control Method for Transient Stability of a Power System 303

0
i
E _ _ €
ð
u i J i δ i + P mi U i + U ei sin δ i + δ ei α i + α ei Þ P Di δ i + δ ei J i δ ei (8.34)
X 0
di
_ _
(3) When δ i < 0, divide both sides of Eq. (8.33) with δ i , and derive:
0
E _ _ €
i
u i J i δ i + P mi U i + U ei sin δ i + δ ei α i + α ei Þ P Di δ i + δ ei J i δ ei (8.35)
ð
X 0
di
For the sake of convenience, rewrite Eqs. (8.34), (8.35) into the following equivalents:
8 0
E U i € _
i
u i J i δ i + P mi sin δ i α i Þ P Di ω i ω 0 Þ J i δ ei , δ i > 0
ð
ð
>
>
X
< 0
di < 0 (8.36)
0
E U i _
> i €
>
ð
ð
: u i J i δ i + P mi sin δ i α i Þ P Di ω i ω 0 Þ J i δ ei , δ i
X 0
di

When the control power u i satisfies Eq. (8.36), it is obvious that the norm V i will monotonously
decrease. Therefore, the system stability could be restored through satisfying Eq. (8.36)
showing control power u i . Eq. (8.36) shows that u i is time-varying. However, u i in the actual
system normally joins in a discrete stage-wise manner, which is caused by the specific device
_
itself for the stability measures. In addition, in line with the difference of symbols for δ i , the
control mode of u i should proceed from increasing or decreasing the electromagnetic power
(such as imposing brake and shedding load).
Eq. (8.36) is the norm reduction control criterion to be followed by the local control power u i
during the second control period.
8.3.3.6 Formulation of norm reduction control criterion in other observation decoupled state space

(1) The form of the norm reduction control criterion in the space δ, δ 50ð Þ . Let
_
ðÞ
W 1i ¼ δ i ¼ δ i δ ei , W 2i ¼ δ 50 ¼ ω i ω 0 , U i ¼ U i U ei , α i ¼ α i α ei (8.37)
i

Then the dynamic equation follows the following form in the space δ, δ 50ð Þ :
8 _
_ _
< W 1i ¼ δ i ¼ W 2i δ ei

1 0 ð i 2 1, NŠÞ
½
_ € E
i
W 2i ¼ δ 50ð Þ ¼ P mi ½ ð
i 0
: U i + U ei sin W Li + δ ei α i + α ei ފ P Di W 2i u i
J i X
di
(8.38)
Define the norm as:
1
(
X X
_
2 2
V ¼ V δ, δ 50ðÞ ¼ V i ¼ δ + δ _ 50 > 0
i
2 ðÞ i (8.39)
V 0, 0Þ ¼ 0
ð