Page 315 - Mathematical Models and Algorithms for Power System Optimization

Local Decoupling Control Method for Transient Stability of a Power System 307

As the system is still in a steady-state during t 0 , then:

ðÞ
ω i t 0 ¼ ω 0 (8.53)
Therefore, Eq. (8.52) could be also written as:

1 1
2

ΔW i t p ¼ J i ω t p J i ω 2 (8.54)
2 i 2 0
(2) Absorbed energy during the brake:
1 2 1 2
ðÞ
ΔW bi t 1 ¼ J i ω t i ðÞ J i ω t p (8.55)
i
i
2 2
(3) Energy equilibrium control criterion at the first stage:

1 2 1 2 1 2 1 2
ðÞ
ΔW i + ΔW bi ¼ J i ω t p J i ω + J i ω t 1 J i ω t p
i
i
i
0
2 2 2 2 (8.56)
1 2 1 2
¼ J i ω t 1 J i ω ¼ 0
ðÞ
i
0
2 2
8.5 Formulation and Proof of the Second Stage Control Criterion
(Norm Reduction)
Section 8.5.1 describes the mathematical model of the critical power control for the second
stage control criterion; Section 8.5.2 gives the mathematic proof of the topological properties
of the observation decoupled state space; Section 8.5.3 shows the topological equivalence proof
of the observation decoupled state space and the original state space; Section 8.5.4 provides that
the origin of the observation decoupled state space is the only equilibrium point of the power
system; and Section 8.5.5 gives sufficient conditions for the norm reduction criterion.

8.5.1 Mathematical Model of the Observation Decoupled State Space

The second stage norm reduction control criterion followed by the local on-line stability control
is derived on the basis of introducing the observation decoupled state space. Whether the
derived norm reduction control criterion is reasonable and feasible can be determined only by
sufficiently explaining and studying the relations between the observation decoupled state
space and original system state space.

Therefore, to facilitate the discussion, it is required to first show the structure of the power
system mathematical model, present its general form in the original system state space, and then