CAREER: Structure-Exploiting Optimization for Power Systems and Applications to Large-Scale Networks

这个NSF CAREER项目将研究用于电力系统优化的结构开发优化技术。该项目通过识别和利用数学结构，寻求在最先进的基础上进行根本性的、变革性的改进，使电力系统优化从根本上区别于通用优化。虽然电力系统优化在最坏的情况下是难以处理的，但特定于结构的技术的优势在于，它可以优先针对现实世界中出现的那些更容易处理的实例。该项目的智力优点包括：(i)在固定的计算时间内提供高质量解决方案的可证明保证；通过（ii）直接和显式地利用电网树状图特性的低复杂度算法；(3)理解和利用电压和功率之间的二次非线性的类凸行为。该项目的更广泛影响包括：(i)解决对软件的迫切需求，能够满足电力系统的安全关键、大规模和时间敏感需求；（ii）将技术转移到具有大规模网络结构的其他社会应用，例如交通运输、网络统计、机器学习和人工智能；（iii）伊利诺伊大学的研究和教育整合，包括吸引和激励K-12学生和教育工作者的外展努力。电力系统优化尤其具有挑战性的是，它需要在短时间内对大型系统做出安全关键决策。通用优化技术通常过于宽泛和包罗万象，无法满足系统的特定需求。在开发结构开发技术方面，本项目将重点关注两个在现有和相关文献中显示出特殊前景的数学结构。首先是电网的树状图结构，它可以很容易地解决许多最难的组合优化问题。我们的研究旨在解决电力系统的优化是否可以很容易地在树状图上求解。其次是功率和电压之间的二次非线性，尽管不是凸的，但表现出类似凸的行为。该项目将寻求保证这种类凸行为，并探索其对大规模优化的影响。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。

This NSF CAREER project will investigate structure-exploiting optimization techniques for power system optimization. The project seeks radical, transformative improvements upon the state-of-the-art by identifying and exploiting the mathematical structures that make power system optimization fundamentally distinct from general purpose optimization. While power system optimization is intractable in the worst case, the advantage of a structure-specific technique is that it can preferentially target those more tractable instances that appear in the real world. The intellectual merits of the project include: (i) provable guarantees on a high-quality solution within a fixed amount of computing time; via (ii) low-complexity algorithms that directly and explicitly make use of tree-like graph property of electric grids; and (iii) understanding and exploiting the convex-like behavior in the quadratic nonlinearity between voltage and power. The broader impacts of the project include: (i) addressing the urgent need for software capable of meeting the safety-critical, large-scale, and time-sensitive needs of power systems; (ii) technology transfer to other societal applications with a large-scale network structure, such as transportation, network statistics, machine learning, and artificial intelligence; and (iii) integration of research and education at the University of Illinois, including outreach efforts to attract and inspire K-12 students and educators. What makes power system optimization particularly challenging is that it entails making safety-critical decisions on a large-scale system over a short span of time. General-purpose optimization techniques are often too broad and all-encompassing to meet the specific needs of the system. In developing structure-exploiting techniques, this project will focus on two mathematical structures that have shown exceptional promise in the existing and related literature. The first is the tree-like graph structure of the electric grid, which allows many of the hardest combinatorial optimization to be easily solved. Our study will aim to resolve whether power system optimization can be easily solved on a tree-like graph. The second is the quadratic nonlinearity between power and voltage, which exhibits a convex-like behavior despite not being convex. The project will seek to guarantee this convex-like behavior, and to explore its implications for large-scale optimization.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.