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

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.