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Construction of Lyapunov function for power system based on solving linear matrix inequality
Author(s) -
Ishigame Atsushi,
Sakaguchi Hiromu,
Takashima Jun,
Suzaki Shirou
Publication year - 2007
Publication title -
electrical engineering in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.136
H-Index - 28
eISSN - 1520-6416
pISSN - 0424-7760
DOI - 10.1002/eej.20328
Subject(s) - lyapunov function , lyapunov redesign , lyapunov equation , control theory (sociology) , mathematics , lyapunov optimization , control lyapunov function , linear matrix inequality , quadratic equation , electric power system , mathematical optimization , power (physics) , computer science , nonlinear system , control (management) , physics , geometry , quantum mechanics , artificial intelligence
Abstract This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One‐machine one‐load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42– 50, 2007; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20328