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

9314453福阿德今天的重载和压力的电力传输网络在受到小的或大的干扰时，表现出非常复杂的动态系统行为。这种复杂行为的几个方面令电力系统分析师感到震惊，因为它们可能反映出电力网络的结构性弱点。当受到小扰动时，主要考虑的是电力系统条件导致的区域间振荡模式现象。当受到大扰动时，压力大、负荷重的互联电网可能会经历系统分裂，涉及远离扰动位置的发电机。电力系统基本振荡模式的分析对电力系统的动态性能起着至关重要的作用。对控制进行了调整，以缓解轻微衰减的模式。分析通常使用线性化的系统模型来完成。如果基模由于非线性而相互作用，那么了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很重要。作者打算利用向量场的正规形式来研究在压力(例如，重负荷)运行条件下的动态电力系统行为。所采用的方法是通过范式分析，即通过加入高阶项(多项式)来获得对线性行为的非线性修正。其目的是通过多项式逼近、不变流形(稳定流形、不稳定流形和中心流形)、通过分支参数展开、灵敏度分析和加入随机扰动来更精确地了解系统的局部和几乎全局行为。这种方法是动力系统理论中的一种标准方法，但尚未被用于大型电力网络的分析。我们建议对这类系统的规范型分析进行系统的研究，以评估高阶非线性分析对电力系统运行的信息利用。***

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. ***