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# Power-System-Transient-Stability201109-EN6-[兼容模式].pdf

Power-System-Transient-Stability201109-EN6-[兼容模式].pdf

1896 1920 1987 2006

Power System Transient Stability

--Direct Method of Transient Stability Analysis

Li Guo-Jie (李国杰)
Dept. of Electrical Engineering
******@sjtu.edu.cn, **********
2011. Sep.
1896 1920 1987 2006
13.7 DIRECT METHOD OF
TRANSIENT STABILITY ANALYSIS
Simulation in time-domain: slow computation speed, no
stability degree, cannot meet transient stability analysis under
predicted events.
PresThe direct methods determine stability without explicitly
solving the system differential equations, which was presented by
Lyapunov ( А.М.Ляпнов )in 1892. The energy-based methods are
aspecilial case of the more general L'Lyapunov'ssecond method or the
direct method, the energy function being one possible Lyapunov
function.
1896 1920 1987 2006
What is a Lyapunov Function?
The second method attempts to determine stability
directly by using suitable function which are
defined in the state space.
 If t here ex ists a posi ti ve-defi ni te (lik e energy)
function and its derivative is not positive. Then, the
system is stable.
V(()x) > 0 and Vx 0
 The system is asymptotically stable.
If V(()x) > 0 and Vx 0

3
1896 1920 1987 2006
Energy: forms
Kine tic energy ithis the energy of moti on
1
E  mv2
K 2
Potential energy is energy stored – by position,
within a spring , within a chemical bond , within the
particles of a nucleus

EP  mgh

4
13.7.1 Description of the Transient Energy Function (TEF)
Approach 1896 1920 1987 2006

Rollingggy ball analogy
The transient energy approach can be described by considering a
ball rolling on the inner surface of a bowl as depicted in Figure 13.59.
The area i nsid e th e b owl represent s th e regi on o

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