论文标题
通过Lyapunov指数对动力系统应用的Lyapunov指数对随机差分 - 代数系统的稳定性评估
Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems
论文作者
论文摘要
在本文中，我们讨论了通过Lyapunov指数（LES）对此类系统的随机差异代数方程（SDAE）和渐近稳定性评估。我们专注于指数一个SDAE及其作为普通随机微分方程（SDE）的重新制定。然后，通过厄贡理论，可以通过基础SDE产生的随机动力学系统来分析LE。一旦确保了明确定义的LE的存在，我们就可以使用数值模拟技术来数值确定LES。实施了离散和连续$ QR $分解的数值方法来计算基本解决方案矩阵并将其用于LES的计算。通过数值测试说明了两种方法的重要计算特征。最后，将方法应用于电力系统工程的两个应用程序，包括单台无限型酒吧（SMIB）电源系统模型。
In this paper we discuss Stochastic Differential-Algebraic Equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-one SDAEs and their reformulation as ordinary stochastic differential equation (SDE). Via ergodic theory it is then feasible to analyze the LEs via the random dynamical system generated by the underlying SDE. Once the existence of well-defined LEs is guaranteed, we proceed to the use of numerical simulation techniques to determine the LEs numerically. Discrete and continuous $QR$ decomposition-based numerical methods are implemented to compute the fundamental solution matrix and to use it in the computation of the LEs. Important computational features of both methods are illustrated via numerical tests. Finally, the methods are applied to two applications from power systems engineering, including the single-machine infinite-bus (SMIB) power system model.
