Nonlinear Power System Behavior Using Normal Forms: Extension of Linear System Analysis Via Higher Order Correction

小行星9314453 今天的重负荷和压力的电力传输网络表现出非常复杂的动态系统行为时，受到小或大的干扰。 这种复杂行为的几个方面是令人震惊的电力系统分析师，因为它们可能反映了电力网络的结构性弱点。 当受到小扰动时，主要关注的是导致称为区域间振荡模式的现象的电力系统条件。 当受到大的干扰时，压力和重负载的互联电力网络可能经历涉及远离干扰位置的发电机的系统分裂。 分析电力系统的基本振荡模式对电力系统的动态性能起着至关重要的作用。 控制被调整以减轻轻微阻尼模式。 通常使用线性化系统模型进行分析。 如果基本模式由于非线性而相互作用，那么理解这些相互作用的性质并将其纳入分析和设计过程就变得非常重要。 提出者打算研究在压力下的动态电力系统行为（例如，重负载）操作条件，使用向量场的正规形式。 所使用的方法是通过正规形式分析获得对线性行为的非线性校正，即，通过引入高阶（多项式）项。 目标是通过多项式近似、不变流形（稳定、不稳定和中心流形）、通过分叉参数展开、灵敏度分析和随机扰动的结合，更精确地理解系统的局部和“几乎全局”行为。 这种方法，这是一个标准的方法，在动力系统理论，还没有被用于大型电力网络的分析，我们提出了一个系统的研究，这些系统的正规形分析，以评估使用的信息，从高阶非线性分析电力系统运行。 ***

9314453 Fouad Today's heavily loaded and stressed power transmission networks exhibit very complex dynamic system behavior, when subjected to small or large disturbances. Several aspects of this complex behavior are alarming to the power system analyst, since they are likely to reflect structural weakness in the power network. When subjected to small disturbances, the main concern is the power system conditions which lead to the phenomenon known as the interarea mode of oscillation. When subjected to a large disturbance, a stressed and heavily loaded interconnected power network may experience a system split involving generators far away from the location of the disturbance. Analysis of the fundamental modes of oscillation play a crucial role in power system dynamic performance. Controls are tuned to mitigate lightly damped modes. The analysis is usually done using a linearized system model. If fundamental modes interact due to nonlinearities, then it becomes important to understand the nature of these interactions and to incorporate them in the analysis and design procedure. The proposers intend to study the dynamic power system behavior under stressed (e.g., heavy load) operating conditions, using normal forms of vector fields. The approach to be used is to obtain nonlinear corrections to the linear behavior through normal form analysis, i.e., through incorporating higher order (polynomial) terms. The objective is to obtain a more precise understanding of the local and "almost global" behavior of a system via polynomial approximation, invariant manifolds (stable, unstable and center manifolds), unfolding via bifurcation parameters, sensitivity analysis and incorporation of random perturbations. This approach, which is a standard approach in the theory of dynamical systems, has not been used for the analysis of large electrical power networks, and we propose a systematic study of normal form analysis for these systems to assess the us e of information from higher order nonlinear analysis for power systems operation. ***