AMPS: Advanced Mathematical Algorithms for Model Reduction and Stochastic Modeling for the Emerging Power Grid

AMPS：用于新兴电网模型简化和随机建模的高级数学算法

• 批准号: 1734727
• 负责人: Barry Lee
• 金额: $ 24万
• 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: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1734727&HistoricalAwards=false
• 关键词: AMPS; Advanced; Mathematical; Algorithms; Model

This project will develop tools to analyze and help design robust and resilient modern power grid systems. The emergent power grid is very different from the traditional grid, which is based on technology dating back to the early 20'th century. With new technologies and regulatory policies, new challenges are arising in the design of stable power systems that can reliably deliver electric power. To tackle these challenges, mathematical and computational tools are needed to analyze these power grids with the new features. The goal of this project is to develop these mathematical and computational tools. Specifically, this project will examine model reduction, uncertainty/stochasticity, and stability, which are some of the new features that must be incorporated in the models of the modern grid. Stability will be the connecting theme in these topics since stability is required to ensure a resilient grid with reduced risks. The PI will examine (1) how synchrony in the oscillations of the grid can be used to determine coherent sets of generators and loads for accurate model reduction; (2) what are the relevant structures that must be reserved to produce accurate reduced models; (3) how to develop multilevel solvers for decentralized systems; (4) how stochasticity affects the synchrony, coherency, model reduction, and stability of the grid; and (5) how observed data can be assimilated into the stochastic models. The stochasticity will be incorporated using stochastic differential-algebraic equations. This stochasticity will be introduced using the Orstein-Uhlenbeck process that best describes the stochasticity in the components of the system.

该项目将开发工具来分析和帮助设计强大且有弹性的现代电网系统。新兴电网与传统电网有很大不同，传统电网的技术可追溯到 20 世纪初。随着新技术和监管政策的出现，设计能够可靠地输送电力的稳定电力系统面临着新的挑战。为了应对这些挑战，需要数学和计算工具来分析这些具有新功能的电网。该项目的目标是开发这些数学和计算工具。 具体来说，该项目将研究模型简化、不确定性/随机性和稳定性，这些是现代电网模型中必须纳入的一些新功能。稳定性将成为这些主题的连接主题，因为需要稳定性来确保具有弹性的电网并降低风险。 PI 将检查 (1) 如何使用电网振荡的同步性来确定发电机和负载的相干组，以实现精确的模型简化； （2）为了产生准确的简化模型必须保留哪些相关结构； （3）如何为去中心化系统开发多级求解器； (4)随机性如何影响网格的同步性、一致性、模型简化和稳定性； (5)如何将观察到的数据同化到随机模型中。将使用随机微分代数方程纳入随机性。这种随机性将使用 Orstein-Uhlenbeck 过程来引入，该过程最好地描述了系统组件中的随机性。

项目成果

Multigrid for model reduction of power grid networks

• DOI: 10.1002/nla.2201
• 发表时间: 2018-07
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: Barry Lee

Bringing physics into the coarse‐grid selection: Approximate diffusion distance/effective resistance measures for network analysis and algebraic multigrid for graph Laplacians and systems of elliptic partial differential equations

将物理学引入粗网格选择：用于网络分析的近似扩散距离/有效阻力测量以及用于图拉普拉斯算子和椭圆偏微分方程组的代数多重网格

• DOI: 10.1002/nla.2539
• 发表时间: 2023
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: Lee, Barry

Algebraic multigrid for the nonlinear powerflow equations

• DOI: 10.1002/nla.2347
• 发表时间: 2020-11
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: Barry Lee;Enrique Pereira Batista

Algebraic multigrid for systems of elliptic boundary‐value problems

椭圆边界值问题系统的代数多重网格

• DOI: 10.1002/nla.2303
• 发表时间: 2021
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: Lee, Barry