Chaos and Markov Based Approaches to Time Series Modeling of Power System Elements

本项目涉及电力系统负荷和组件建模的先进概念研究。拟议的项目包括两种不同的方法来建模不规则时变的电力系统负载和从测量（时间序列记录数据）中捕获信息的元素，以便这些元素可以准确地建模。目标是直接从操作系统数据开发模型，从而允许在没有专门测试和破坏性操作条件的情况下不断更新模型。该模型可用于控制系统的设计和精确的动态仿真。第一种建模方法是基于混沌动力学。目标是设计一个混沌过程动力学的局部线性近似系统，当更多的观测值可用时，或者当底层过程受到缓慢漂移时，该系统可以实时更新。第二种建模方法是基于随机迭代的概念。当噪声、近似误差或系统参数的快速时变使第一种方法不可靠时，它是一种统计方法，可以很好地工作。随机迭代很适合解释混沌序列在时间平均稳定性方面表现出统计规律性。它们可以用来以特定的准确度和信心水平预测未来的平均行为，并使基于大型数据集的预测更加可行。所提议的工作的教育组成部分是开发跨学科研究生课程的网络资源，涉及非线性动力学和统计学在当代工程问题中的应用。

This project relates to research in advanced concepts in power system load and component modeling. The proposed project encompasses two distinct approaches to the modeling of irregularly time varying power system loads and elements to capture information from measurements (time series recorded data) so that those elements can be modeled accurately. The goal is to develop models directly from operating system data, thereby permitting continuously updated models without specialized tests and disruptive operating conditions. The models shall be used in control system design and for accurate dynamic simulations.The first modeling approach is based chaotic dynamics. The objective is to design a system of local linear approximations to the dynamics of a chaotic process that can be updated in real time as more observations become available or when the underlying process is subject to a slow drift. The second modeling approach is based on the concept of random iterations. It is a statistical approach that can work well when noise, approximation errors, or rapid time variability of system parameters make the first approach unreliable. Random iterations are well suited to explain chaotic series exhibiting statistical regularity in terms of stability of time averages. They can be used to make predictions about average future behavior with specified levels of accuracy and confidence and make predictions based on large data sets more feasible.An educational component of the proposed work is the development of Web-based resources for interdisciplinary graduate courses involving applications of nonlinear dynamics and statistics to contemporary engineering problems.