1896 1920 1987 2006 Power System Transient Stability --Direct Method of Transient Stability Analysis Li Guo-Jie (李国杰) Dept. of Electrical Engineering ******@, ********** 2011. Sep. 1896 1920 1987 2006 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 ( )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 Vx 0 The system is asymptotically stable. If V(()x) > 0 and Vx 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 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 . The area i nsid e th e b owl represent s th e regi o