Zhang earns NSF CAREER award to develop novel power system optimization techniques

With more than 7,700 power plants, 3,300 utilities, and 2.7 million miles of transmission lines, the U.S. power grid is an extraordinarily complex system that constantly balances the supply and demand of electricity nationwide.

Operating this critical energy system is becoming more challenging as conventional fossil fuel power plants are retired, new wind and solar power is integrated into the grid, and the demand for electricity increases with rising electric vehicle sales.

“What makes the problem particularly challenging is that it entails making safety-critical decisions on a large-scale system over a short span of time,” said ECE Assistant Professor Richard Yi Zhang. “An electric grid operator must continuously balance supply and demand over a huge number of participants, but any mistake can cascade into devastating consequences.”

Federal agencies and policymakers have determined that grid modernization efforts will require new software to manage these recent developments.

“Over the years, optimization algorithms of increasing sophistication have been applied, but they have mostly been general-purpose techniques, which are too broad and all-encompassing to meet the specific needs of the power system,” Zhang said.

In the spring of 2021, Zhang received a $500,000 NSF CAREER award grant for young faculty to develop structure-exploiting optimization techniques that specifically address the mathematical structure of the electric power system.

“We seek to improve performance by sacrificing generality,” he said, “The goal of my CAREER project is to distill existing engineering intuition into rigorous mathematical constructs in order to develop an approach for the power system that not only works well but is guaranteed to work well.”

Zhang’s efforts are focusing on two mathematical structures that hold great potential. First, the U.S. power grid can be abstractly modeled as mathematical graphs on vertices and edges. When viewed in this manner, the grid has a structure that surprisingly resembles a tree.

“Tree-like graphs are interesting because many of the hardest graph optimization problems become easily solvable if the underlying graph is known to be tree-like,” said Zhang.  

In a second area of inquiry, Zhang is exploring the nonconvex relationship between power and voltage. Traditionally, researchers in optimization have always held nonconvexity to be a bad thing, as it presents a danger for algorithms to get stuck and fail. Within the context of electric grids, however, this failure seems to never occur.

“We believe that the power-voltage relationship presents a nonconvexity that is benign,” said Zhang. “Our goal is to use this nonconvexity to our advantage.”