System Development for on-Line Evaluation of Power Systems Through a Non-Lure Type Lyapunov Function

1.磁通衰减导致电功率输出方程呈现乘积型非线性，传统的诱饵型李雅普诺夫函数不能很好地适用于这种乘积型非线性系统。本文给出了一种构造乘积型非线性系统的扩展Lyapunov函数的方法。针对电力系统负荷连续变化引起的系统参数模糊性和系统辨识中的估计误差问题，提出了一种基于Lyapunov直接法的非线性系统鲁棒稳定性分析方法。影响电力系统稳定性的主要因素是同步电机。然后，在本报告中，提出了利用李亚普诺夫函数来分析同步电机的跳步和拉步现象以及改善同步的方法。利用阻尼器进行开关控制是提高电力系统稳定性的一种有效方法。该报告给出了一种利用李雅普诺夫函数确定电阻最优通断时序的方法。为了实现电力系统稳定在线评估系统，必须对发电机相角等状态变量进行测量。本研究试制了发电机相角测量装置。本文利用非诱导型李雅普诺夫函数，实现了基于微机的电力系统暂态稳定在线评估系统。Lyapunov函数由拉格朗日-夏皮特方法构造。开发了电力系统控制软件。实验结果表明，该评估系统能较好地实现电力系统的稳定控制。

1. The flux decay causes a product-type nonlinearity in the formulation of the electrical power output, and the conventional Lure-type Lyapunov function can not be well adapted for such a product-type nonlinear system. This report presents a way of constructing extended Lyapunov function for the product-type nonlinear system.2. The report proposes a method of analyzing robust stability of nonlinear system through the direct method of Lyapunov, in order to cope with both ambiguity of the system parameters due to successive variation of power system loads and estimation errors in the system identifications.3. The main factor which affects on the power system stability is synchronous machine. Then, in this report, methods are presented for analyzing hunting and pulling-into-step phenomena and improving the synchronization of synchronous machines, utilizing Lyapunov functions.4. A useful method for improving stability of power system is on-off control utilizing damping resistor. This report gives a way of deciding optimal on-off timing of the resistor, using Lyapunov function.5. In order to realize the on-line evaluating system for power system stability, the state variable such as phase angle of generator must be measured. This research has made a trial production of a measuring device of phase angle of generator.6. A microcomputer-based on-line transient stability evaluation system for power systems using a non-Lure type Lyapunov function has been accomplished in the report. The Lyapunov function is constructed by the Lagrange-Charpit method. A software for controlling power system has also been developed. The experimental results show that this evaluation system can act satisfactorily for controlling stability of power system.