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AMPS: Collaborative Research: A Convex Geometry and Homotopy Approach for Power-Flow Equations

AMPS：协作研究：潮流方程的凸几何和同伦方法

基本信息

批准号：
1923099
负责人：
Tianran Chen
金额：
$ 10.53万
依托单位：
Auburn University at Montgomery
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-15 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1923099&HistoricalAwards=false
关键词：
AMPS Collaborative Research Convex Geometry

项目摘要

Power networks are critical infrastructures for generating, transferring, and consuming electric energy, and they are of fundamental importance to every aspect of modern life. Improving the efficiency, stability, and resilience of power networks is therefore of great interest to our society. A single power network can operate on many different modes --- some lead to efficient operations while others lead to catastrophic failures. Understanding all such operation modes and the possible transition among them for large and complex power networks remains a difficult mathematical question that could have important real-world consequences. This project aims to develop new methodology and computational tools for solving this problem by utilizing recent discoveries in mathematics. The project will provide training to graduate and undergraduate students, and open source software to the larger community. At the heart of power network analysis lies the mathematical problem of solving power-flow equations: systems of nonlinear equations that describe the intricate balancing conditions of electric power in a power network. The solutions to power-flow equations describe the set of theoretically possible operating modes for a power network, which are of crucial importance in the rigorous analysis of power networks, especially in the problem of assessing network stability. Despite many decades of active research, the complete analysis of power-flow solutions is still a difficult and often computationally impractical task. By leveraging new tools developed in convex geometry, tropical geometry, and homotopy methods, this project aims to develop a flexible divide-and-conquer approach for completely solving power-flow equations and to create practical software implementations. The resulting theoretical framework and software packages would allow researchers to conduct a complete analysis of the full set of power-flow solutions and thus understand the stability and resilience of power networks. Moreover, this project provides opportunities for broadening our understanding of the role of convex polytopes in the study of emergent phenomena in complex networks that may be of value in a much broader context.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.

电网是生产、输送和消费电能的重要基础设施，对现代生活的方方面面都具有根本性的意义。因此，提高电网的效率、稳定性和弹性是我们社会的重大利益所在。一个单一的电力网络可以在许多不同的模式下运行-一些模式导致高效运行，而另一些模式则导致灾难性的故障。对于大型和复杂的电网，理解所有这些运行模式以及它们之间可能的转换仍然是一个困难的数学问题，可能会产生重要的现实后果。这个项目旨在开发新的方法和计算工具来利用数学上的最新发现来解决这个问题。该项目将为研究生和本科生提供培训，并向更大的社区提供开源软件。电力网络分析的核心是求解潮流方程的数学问题：描述电网中复杂的电力平衡条件的非线性方程组。潮流方程的解描述了电力网络理论上可能的运行模式的集合，这些模式在电力网络的严格分析中是至关重要的，特别是在评估网络稳定性的问题中。尽管经过几十年的积极研究，对潮流解的完整分析仍然是一项困难的任务，而且在计算上往往是不切实际的。通过利用凸几何、热带几何和同伦方法中开发的新工具，该项目旨在开发一种灵活的分而治之的方法来完全求解功率流方程，并创建实用的软件实现。由此产生的理论框架和软件包将使研究人员能够对一整套潮流解决方案进行完整的分析，从而了解电力网络的稳定性和弹性。此外，这个项目提供了机会来扩大我们对凸多面体在研究复杂网络中的紧急现象中的作用的理解，这在更广泛的背景下可能是有价值的。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。