Combining Trajectory Data With Analytical Lyapunov Functions for Improved Region of Attraction Estimation
Combining Trajectory Data With Analytical Lyapunov Functions for Improved Region of Attraction Estimation
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DOI：
10.1109/lcsys.2022.3187651
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发表时间：
2021-11
影响因子：
3
通讯作者：
Lucas L. Fernandes;Morgan Jones;L. Alberto;M. Peet;D. Dotta
中科院分区：
文献类型：
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作者：
Lucas L. Fernandes;Morgan Jones;L. Alberto;M. Peet;D. Dotta
基于逆变器的资源（IBR）的不断增加给世界各地的电力系统运营商带来了许多新的挑战。IBR发电机的高度复杂性使得精确的经典基于模型的稳定性分析成为一项困难的任务。本文提出了一种新的方法来解决非线性系统的吸引域（罗阿）的估计问题，通过结合经典的基于模型的方法和现代数据驱动的方法。我们的方法产生可证明的内部近似的罗阿，典型的基于模型的方法，但也利用轨迹数据，以产生一个改进的准确的罗阿估计。该方法是通过使用分析李雅普诺夫函数，如能量函数，与数据相结合，是用来适应一个匡威李雅普诺夫函数。我们的方法是独立的函数拟合方法。在这封信中，为了实现的目的，我们使用伯恩斯坦多项式函数拟合。给出了单机无穷大系统、三机系统和Van-der-Pol系统的罗阿估计算例。
The increasing uptake of inverter based resources (IBRs) has resulted in many new challenges for power system operators around the world. The high level of complexity of IBR generators makes accurate classical model-based stability analysis a difficult task. This letter proposes a novel methodology for solving the problem of estimating the Region of Attraction (ROA) of a nonlinear system by combining classical model based methods with modern data driven methods. Our method yields certifiable inner approximations of the ROA, typical to that of model based methods, but also harnesses trajectory data to yield an improved accurate ROA estimation. The method is carried out by using analytical Lyapunov functions, such as energy functions, in combination with data that is used to fit a converse Lyapunov function. Our methodology is independent of the function fitting method used. In this letter, for implementation purposes, we use Bernstein polynomials to function fit. Several numerical examples of ROA estimation are provided, including the Single Machine Infinite Bus (SMIB) system, a three machine system and the Van-der-Pol system.