基于积分不等式多时滞电力系统的改进稳定判据

针对互联的广域电力系统,考虑多条回路存在传输时滞,建立多时滞电力系统模型,然后构造更优的Lyapunov-Krasovskii泛函,利用辅助函数积分不等式界定泛函导数中的积分项,推导得出多时滞系统的稳定判据。新构造的泛函和辅助函数积分不等式引入了多时滞系统更多的边界信息,获得了更加自由的求解空间,减小了积分界定过程中带来的误差。最后,借助MATLAB软件中的线性矩阵不等式工具箱,应用多种稳定判据分别仿真计算典型二阶时滞系统、单机无穷大系统以及WSCC 3机9节点系统的时滞稳定性。仿真结果表明,文中所提出的稳定判据能得到比已有文献保守性更小的结果,并揭示了系统多个时滞稳定区间,能够更加准确地反映多时滞电力系统的稳定性。

Integral Inequality Based Improved Stability Criterion for Power System with Multiple Time Delays

For the wide-area interconnected power system, considering there exist transmission delays in multiple loops, a power system model with multiple time delays is established. Then a Lyapunov-Krasovskii functional with higher accuracy is constructed, using the integral inequality of auxiliary function to define the integral term in the functional derivative, the stability criterion of the system with with multiple time delays is derived. The newly constructed functional and integral inequality of auxiliary function introduce more boundary information for the system with multiple time delays, and obtains more free solution space, the error caused by the integral definition process is reduced. Finally, by using the linear matrix inequality toolbox in MATLAB software, the stability of typical second-order time-delay system, single-machine infinite bus system and WSCC three-machine nine-node system are simulated and computed by multiple stability criteria. The simulation results show that the stability criterion proposed in this paper can produce more tighter time delay bounds than those in the existing literatures, several delay stability intervals of the system are also revealed, and can more accurately reflect the stability of power system with multiple time delays.