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

现代电网日趋复杂。电网的稳定运行越来越具有挑战性。传统的电力系统稳定性评估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），这种模式正变得越来越不可靠。高效的计算工具是保证可靠运行的必要条件。本提案旨在开发这样的稳定监测工具，将粗模型信息和来自电网的实时数据流结合起来。与电力工业的现有关系将在传播研究成果方面发挥关键作用。参与本项目的学生将学习如何利用现代数据科学中应用于电力系统的强大技术。研究成果将无缝整合到两所大学的多个现有课程中。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。这些算子的特征值和特征函数具有丰富的信息，对电网的稳定监测具有重要意义。这项工作建立了一个框架，将电力系统状态子集的测量与潜在的粗糙电力系统模型结合起来，使用机器学习的核方法自适应地计算特征值和特征函数。然后利用特征函数估计电力系统动力学吸引区域，传播初始条件和模型参数中的不确定性。特别注意的是该方法的可扩展性，以可行地评估电力系统的稳定性，在（几乎）实时。所提出的方法从根本上不同于依赖局部线性化的技术，后者不能捕捉电力系统动态的复杂非线性行为。这些方法深深植根于动力系统理论，并提供了一种自然的机制，在统一的框架内利用模型信息和传感器的测量。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.