This paper introduces an alternative description of autonomous dynamical systems as a sum of individual vector fields. This structure of a dynamical system gives us the opportunity to construct individual Lyapunov-like functions to certify stability of an equilibrium point. A theorem on individual functions is developed in a quadratic form to maintain computational efficiency. As a corollary to the developed theory, we conclude that regions of attraction can be estimated by sub-level sets of individual quadratic functions, and through geometric programs they can easily be maximized efficiently. Theoretical findings in this paper are examined on transient stability problem in power systems for both single machine to infinite bus and multi-machine systems with promising results for critical clearing time estimation compared to the values obtained from time domain simulations.

中文翻译：

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电力系统暂态稳定性评估的个别函数法

本文介绍了作为单个矢量场的总和的自主动力系统的替代描述。动力系统的这种结构使我们有机会构建单独的类李雅普诺夫函数来证明平衡点的稳定性。以二次形式开发关于单个函数的定理以保持计算效率。作为发展理论的推论，我们得出结论，吸引力区域可以通过各个二次函数的子级集来估计，并且通过几何程序可以很容易地有效地最大化它们。