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

本计画系关于电力系统负荷与元件模型之先进概念研究。 拟议的项目包括两种不同的方法来建模不规则时变电力系统负载和元素，以捕获测量（时间序列记录数据）的信息，使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持续更新模型。 这些模型将用于控制系统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。 我们的目标是设计一个系统的局部线性近似的动态混沌过程，可以更新在真实的时间，因为更多的观察变得可用或当底层的过程是受到缓慢漂移。 第二种建模方法是基于随机迭代的概念。 这是一种统计方法，当噪声、近似误差或系统参数的快速时变性使第一种方法不可靠时，这种方法可以很好地工作。 随机迭代非常适合于解释混沌序列的时间平均值的稳定性方面表现出统计规律性。 它们可以用来预测平均未来的行为与指定的准确度和信心水平，并作出预测的基础上，大数据集更可行的建议工作的一个教育组成部分是基于Web的跨学科的研究生课程，涉及非线性动力学和统计的应用，以当代工程问题的发展资源。

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.