A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere

• Main Author: A. V. Stepanov
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2014-01-01
• Series: Nauka i Obrazovanie
• Subjects: transient stability; Lyapunov function; critical value; multidimensional sphere; synchronous generator
• Online Access: http://technomag.edu.ru/jour/article/view/608

<p>A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere.</p><p>We consider the problem of transient stability analysis for a system of synchronous generators under the action of strong perturbations. The aim of our work is to develop methods to analyze a transient stability of the system of synchronous generators, which allow getting trustworthy results on reserve transient stability under different perturbations. For the analysis of transient stability, we use the direct Lyapunov method.</p><p>One of the problems for this method application is to find the Lypunov function that well reflects the properties of a parallel system of synchronous generators. The most reliable results were obtained when the analysis of transient stability was performed with a Lyapunov function of energy type. Another problem for application of the direct Lyapunov method is to determine the critical value of the Lyapunov function, which requires finding the non-stable equilibria of the system. Determination of the non-stable equilibria requires studying the Lyapunov function in a multidimensional space in a neighborhood of a stable equilibrium for the post-breakdown system; this is a complicated non-linear problem.</p><p>In the paper, we propose a method for determination of the non-stable equilibria on a multidimensional sphere. The method is based on a search of a minimum of the Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. Our method allows, comparing with the other, e.g., gradient methods, reliable finding a non-stable equilibrium and calculating the critical value. The reliability of our method is proved by numerical experiments. The developed methods and a program realized in a MATLAB package can be recommended for design of a post-breakdown control system of synchronous generators or as a component of a real-time control system.</p>