Exploiting the Weighted Graph Laplacian for Power Systems: High-Degree Contingency, Machine Learning, Data Assimilation, and Parallel-in-Time Integration

利用电力系统的加权图拉普拉斯：高度偶然性、机器学习、数据同化和并行时间集成

• 批准号: 2229378
• 负责人: Barry Lee
• 金额: $ 27.62万
• 依托单位: Southern Methodist University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-11-01 至 2025-10-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2229378&HistoricalAwards=false
• 关键词: Exploiting; Weighted; Graph; Laplacian; Power

Modernizing the power grid continues to be a major national and international challenge. The urgency of this modernization has been accentuated by the devastating effects of climate change on the power infrastructure and the societal consequences that can occur when only minor, let alone major, damages are made to this infrastructure. Mathematics and statistics will play a special role in this modernization since the power system is modeled by complex systems of mathematical equations. This project will develop new fast and accurate computational techniques for solving the core mathematical equations modeling the grid. The crux of these new techniques will be based on the grid's network structure, which exposes the flow of electricity in the power grid. A common and significant problem in these techniques is determining the most relevant generators, loads, and substations in the grid. Knowing these components will allow power grid engineers to determine which parts of the grid are most vulnerable to disruptions coming from natural disasters and cyber attacks, and hence, help design a more resilient grid. The project will provide training opportunities to graduate students. This project aims to develop fast and accurate algorithms for analyzing large-scale, real-world power systems. A common feature of these algorithms is exploiting the system's associated weighted graph Laplacian to expose the diffusion of electricity in the network. The fundamental component of this research is determining the dependency and relevancy of the network buses, which is accomplished through state-of-the-art algebraic multigrid techniques for weighted graph Laplacians and approximate diffusion distance measures. The dependency and relevancy will be used to develop (1) fast and accurate screening techniques for high-degree contingency analysis; (2) multi-scale graph neural networks (GNNs) for regression in power grid analysis; and (3) optimal parallel-in-time integrators for dynamical power systems. Moreover, to avoid the vanishing gradient problem in the stochastic gradient method and to permit the natural incorporation of uncertainties in the GNN setting, an ensemble Kalman filter method will be used to train the GNN weights. More robust models, robust with respect to uncertainties, will be constructed by appropriately combining the surrogates obtained from the multi-scale GNNs with traditional power system models.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.

电网现代化仍然是一项重大的国家和国际挑战。气候变化对电力基础设施的破坏性影响，以及对这一基础设施造成轻微破坏（更不用说重大破坏）时可能产生的社会后果，都突出了这种现代化的紧迫性。数学和统计学将在这一现代化中发挥特殊作用，因为电力系统是由复杂的数学方程系统建模的。这个项目将开发新的快速和准确的计算技术，用于解决模拟网格的核心数学方程。这些新技术的关键将是基于电网的网络结构，它暴露了电网中的电流。这些技术中的一个常见且重要的问题是确定电网中最相关的发电机、负载和变电站。了解这些组件将使电网工程师能够确定电网的哪些部分最容易受到自然灾害和网络攻击的影响，从而帮助设计更具弹性的电网。该项目将为研究生提供培训机会。该项目旨在开发快速准确的算法，用于分析大规模，真实世界的电力系统。这些算法的一个共同特征是利用系统的相关加权图拉普拉斯算子来揭示网络中的电力扩散。这项研究的基本组成部分是确定网络总线的依赖性和相关性，这是通过最先进的代数多重网格技术的加权图拉普拉斯算子和近似扩散距离的措施。依赖性和相关性将用于开发（1）快速准确的筛选技术，用于高度应急分析;（2）多尺度图神经网络（GNNs），用于电网分析中的回归;以及（3）动态电力系统的最佳并行时间积分器。此外，为了避免随机梯度法中的消失梯度问题，并允许在GNN设置中自然地并入不确定性，将使用集合卡尔曼滤波器方法来训练GNN权重。通过将从多尺度GNN中获得的替代模型与传统电力系统模型适当结合，将构建更稳健的模型，对不确定性具有稳健性。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审查标准进行评估，被认为值得支持。