Collaborative Research: Dynamic Data Analytics for the Power Grid via Koopman and Perron-Frobenius Operators

合作研究：通过 Koopman 和 Perron-Frobenius 算子对电网进行动态数据分析

• 批准号: 2031570
• 负责人: Subhonmesh Bose
• 金额: $ 20.39万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-15 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2031570&HistoricalAwards=false
• 关键词: Collaborative; Research; Dynamic; Data; Analytics

The modern power grid is becoming increasingly complex. Ensuring stable grid operation is becoming more and more challenging. Classical tools for stability assessment for power systems largely rely on accurate system models. Such models are becoming less reliable as the grid continues to aggressively integrate new renewable, and often distributed, energy resources. Efficient computational tools are necessary to ensure reliable operation. This proposal seeks to develop such tools for stability monitoring, combining both coarse model information and real-time data streams from the power grid. Existing relationships with the power industry will play a crucial role in disseminating the research findings. Students working on this project will learn to utilize powerful techniques from modern data science that have applications in power systems. Research outcomes will be seamlessly integrated in multiple existing courses at both universities. The proposed work leverages a linear transfer operator-based framework to build computational tools for stability monitoring, involving the Koopman and Perron-Frobenius operators. These operators are used to lift the nonlinear dynamics from state space to linear dynamics in the space of functions of the states. The eigenvalues and eigenfunctions of these operators are rich in information that is relevant to stability monitoring for a power grid. This work builds a framework to combine measurements of a subset of the states of a power system and a potentially coarse power system model to adaptively compute eigenvalues and eigenfunctions using kernel methods from machine learning. The eigenfunctions are then leveraged to estimate region of attraction of power system dynamics and propagate uncertainties in initial condition and model parameters. Special attention is paid to scalability of the approach to viably evaluate power system stability, in (almost) real-time. The proposed methods are fundamentally different from techniques that rely on local linearization that cannot capture the complex nonlinear behavior of power system dynamics. These methods are deeply rooted in dynamical systems theory and offer a natural mechanism to harness both model information and measurements from sensors within a unified framework.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

现代电网变得越来越复杂。确保电网稳定运行变得越来越具有挑战性。电力系统稳定性评估的经典工具在很大程度上依赖于精确的系统模型。随着电网继续积极整合新的可再生能源（通常是分布式能源），这种模式变得越来越不可靠。有效的计算工具是必要的，以确保可靠的操作。该提案旨在开发用于稳定性监测的此类工具，将粗略的模型信息和来自电网的实时数据流相结合。与电力行业的现有关系将在传播研究成果方面发挥关键作用。从事该项目的学生将学习利用现代数据科学中应用于电力系统的强大技术。研究成果将无缝集成到两所大学的多个现有课程中。所提出的工作利用基于线性传递算子的框架来构建用于稳定性监测的计算工具，涉及Koopman和Perron-Frobenius算子。这些算子用于将非线性动力学从状态空间提升到状态函数空间中的线性动力学。这些操作员的特征值和特征函数是丰富的信息，是相关的稳定性监测的电网。这项工作建立了一个框架，结合联合收割机测量的一个子集的状态的电力系统和一个潜在的粗糙的电力系统模型，自适应地计算特征值和特征函数使用核方法从机器学习。然后利用特征函数估计电力系统动态的吸引域，并传播初始条件和模型参数的不确定性。特别注意的是可行的方法来评估电力系统的稳定性，在（几乎）实时的可扩展性。所提出的方法是从根本上不同的技术，依赖于局部线性化，不能捕捉复杂的非线性行为的电力系统动态。这些方法深深植根于动力系统理论，并提供了一种在统一框架内利用模型信息和传感器测量结果的自然机制。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估而被认为值得支持。审查标准。

项目成果

Sparse Learning of Dynamical Systems in RKHS: An Operator-Theoretic Approach

RKHS 中动力系统的稀疏学习：算子理论方法

• 发表时间: 2023
• 期刊: Proceedings of Machine Learning Research
• 作者: Hou, Boya;Sanjari, Sina;Dahlin, Nathan;Bose, Subhonmesh;Vaidya, Umesh
• 通讯作者: Vaidya, Umesh