电力系统时滞依赖型鲁棒稳定判据及其应用

A Delay-dependent Robust Stability Criterion for Power System and Its Application

给出了一种改进的含不确定性时滞环节的电力系统稳定性Lyapunov鲁棒稳定判据。首先基于Krasovskii理论列解时滞系统的Lyapunov泛函,接着将泛函对系统轨迹的导函数用一组线性矩阵不等式表达,在泛函导数推导过程中,通过引入一些必要的松散项以减少该判据的保守性,然后利用Schur补对含不确定性的扰动项进行变换,最后借助单机无穷大系统和WSCC3机9节点系统,对含不确定性扰动的单一和双时滞情况下的系统保持鲁棒稳定时可承受的最大时滞进行分析,验证了所给方法的有效性。

An improved delay-dependent robust stability criterion for.power system with uncertain time-delay is presented. In the method, a Lyapunov function is constructed based on Lyapunov-Krasovskii theory, and the derivative function is then expressed as a set of linear matrix inequalities （LMI） which can he solved by the LMI toolboxes. Some necessary slack variables are introduced to its derivative function so as to reduce its conservativeness. The presented method is finally validated on a single-machine-infinite-bus system and the WSCC 3-generator 9 bus system. Cases of one time-delay and two time-delays with uncertainties are discussed. Numerical studies reveal that the presented method is correct and effective. This work is supported by National Natural Science Foundation of China （No. 50707019）, Special Fund of the National Basic Research Program of China （No. 2009CB219701）, Foundation for the Author of National Excellent Doctoral Dissertation of PR China （No. 200439）, Tianjin Municipal Science and Technology Development Program （No. 09JCZDJC25000）, National Major Project of Scientific and Technical Supporting Programs of China During the 11th Five-year Plan Period （No. 2006BAJ03A06）, Doctoral Fund of the State Education Ministry of China （No. 20090032110064）.