Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis
Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis
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DOI：
10.1109/tcsi.2013.2246233
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发表时间：
2013-09-01
影响因子：
5.1
通讯作者：
Papachristodoulou, Antonis
中科院分区：
文献类型：
--
作者：
Anghel, Marian;Milano, Federico;Papachristodoulou, Antonis
提出了一种用于经典电力系统模型暂态稳定分析的Lyapunov函数的算法构造方法。所提出的方法利用了正多项式理论、半定规划和平方和分解的最新进展，这些理论已经成为分析具有多项式向量场的系统的有力工具。为了将这些技术应用到由三角非线性描述的电网系统中，我们使用了一种代数重构技术，将系统的动力学重塑为一组多项式微分代数方程。我们通过估计稳定运行点的吸引区，展示了这些技术在电力系统暂态稳定分析中的应用。描述了一种计算局部稳定性Lyapunov函数的算法，并设计了一种优化算法来改进这一估计。
We present a methodology for the algorithmic construction of Lyapunov functions for the transient stability analysis of classical power system models. The proposed methodology uses recent advances in the theory of positive polynomials, semidefinite programming, and sum of squares decomposition, which have been powerful tools for the analysis of systems with polynomial vector fields. In order to apply these techniques to power grid systems described by trigonometric nonlinearities we use an algebraic reformulation technique to recast the system's dynamics into a set of polynomial differential algebraic equations. We demonstrate the application of these techniques to the transient stability analysis of power systems by estimating the region of attraction of the stable operating point. An algorithm to compute the local stability Lyapunov function is described together with an optimization algorithm designed to improve this estimate.