论文标题
在二阶动力系统中阻尼的影响以及用于电网稳定性的应用
The Impact of Damping in Second-Order Dynamical Systems with Applications to Power Grid Stability
论文作者
论文摘要
我们考虑了一系列二阶动力学系统，并研究阻尼作为系统参数对此类系统中稳定性，双曲线和分叉的影响。我们证明了阻尼对相应一阶系统平衡点的双波利度的单调效应。这为直观的观念提供了严格的表述和理论上的理由，即阻尼会提高稳定性。为了确定这一结果，我们证明了对具有阳性半芬矿摄动的复杂对称矩阵的矩阵扰动结果，这可能具有独立的兴趣。此外，我们建立了必要的条件，以在阻尼变化下崩溃的一对矩阵的可观察性，与阻尼，惯性和Jacobian矩阵有关，并提出足够的条件，以使Hopf分歧是由这种超级性能崩溃导致的。开发的理论在电力系统的稳定性中具有重要的应用，这是最复杂，最重要的工程系统之一。特别是，我们表征了阻尼对摇摆方程模型的双波利度的影响，该模型是功率系统的基本动力学模型，并证明了由阻尼变化引起的HOPF分叉。
We consider a broad class of second-order dynamical systems and study the impact of damping as a system parameter on the stability, hyperbolicity, and bifurcation in such systems. We prove a monotonic effect of damping on the hyperbolicity of the equilibrium points of the corresponding first-order system. This provides a rigorous formulation and theoretical justification for the intuitive notion that damping increases stability. To establish this result, we prove a matrix perturbation result for complex symmetric matrices with positive semidefinite perturbations to their imaginary parts, which may be of independent interest. Furthermore, we establish necessary and sufficient conditions for the breakdown of hyperbolicity of the first-order system under damping variations in terms of observability of a pair of matrices relating damping, inertia, and Jacobian matrices, and propose sufficient conditions for Hopf bifurcation resulting from such hyperbolicity breakdown. The developed theory has significant applications in the stability of electric power systems, which are one of the most complex and important engineering systems. In particular, we characterize the impact of damping on the hyperbolicity of the swing equation model which is the fundamental dynamical model of power systems, and demonstrate Hopf bifurcations resulting from damping variations.
