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Optimism born of hard limits

Leveraging worst-case scenarios, he strengthens complex networks.

Complex, dynamic networks are found in our cells, in the power grid, and in our financial markets. Nader Motee, assistant professor of mechanical engineering and mechanics, wants to make them more efficient and robust by developing a unified theory of networks that helps engineers build better systems.

The field of network theory burgeoned after World War II, but until about a dozen years ago most models simulated a simple “black box” with an input and an output.

Real-world networks are much more complex, says Motee, who directs Lehigh’s Distributed Control and Dynamical Systems (DCDS) Laboratory. “Networks of systems” now model the interconnections and interactions of many black boxes.

The nation’s power grid contains thousands of generating stations that use coal, gas, nuclear and hydropower to produce and distribute energy to millions of customers. While high-voltage transmission lines shift power across the nation, a vast web of smaller electric lines and transformers deliver consistent current. There are checks in place to reroute power around failed lines and keep power on.

The grid is feeling stress from soaring power consumption, Motee says. In regional monitoring centers, computers gather feedback from sensors around the grid and provide readouts to engineers who reroute power, often by hand. The volume and complexity of the data means it can require several minutes to resolve an issue.

But it can take just a few seconds for power lines to heat up and melt when they have to compensate for a failure by carrying a failed line’s load as well as their own, Motee says. A single short circuit or failed line can cause “cascading failures” that black out huge areas.

And as wind, solar and other renewable power sources come on line, complexity increases. Weather conditions can play havoc with wind and solar from minute to minute. And homes with turbines or solar panels don’t just consume electricity—sometimes they sell their excess back to the grid. The added variables make it harder and more time-consuming to adjust the grid.

The solution, says Motee, is more strategic monitoring and control. “If we can partition the network into sub-networks, say 50 across the eastern U.S., and have these bunches of nodes talk to other bunches,” he says, controllers can get the right information faster and avoid extraneous data.

The DCDS team mathematically models a network’s behavior so that worst-case scenarios can be run over and over, until the team is sure its result will work. Ph.D. candidate Milad Siami has proved that power loss in electrical transmission systems has nothing to do with the configuration of the network, but is a function of the properties of individual transmission lines.

Motee has a Young Investigator grant from the U.S. Air Force Office of Scientific Research to study another type of network—unmanned aerial vehicles, or “drones,” that fly in formation. This problem highlights the classic tradeoff between performance and stability.

“We have better coordination if every unit can talk to every other, but there is a cost,” Motee says. More communication requires more power, which means more batteries, greater weight and limited range for the drones. And increased radio traffic makes the drones easier for an enemy to detect and intercept.

“The challenge is to find the right level of sparsity, so that enough of the right information is exchanged only with the peers that need it, without incurring the cost of unnecessary communications,” he says.

Nature is often a model for Motee’s work. To get at the vexing question of “hard limits” in complex networks, he is analyzing the glycolysis pathway that produces the adenosine triphosphate (ATP) energy packets cells use for fuel.

The pathway withdraws ATP from the cell’s bank of energy packets in order to create more. There has to be enough ATP to initiate the process and make energy available to the rest of the cell; if not, “the cell will crash and die,” Motee says.

The electrical grid is subject to the same hard limits. If currents flowing through connected segments get too far out of phase, that part of the grid will crash, no matter how the network is designed or how much redundancy is in place.

In a project funded by the U.S. Office of Naval Research, Motee hopes to prove that cascading failures are the result of this hard limit. “Our team is developing a theory that shows that when there are hard limits, no matter what type of feedback strategies we use to control the networks, there will be critical tradeoffs among performance, robustness and fragility,” he says. His goal is to understand the impacts of hard limits in various types of networks and to discover principles that help engineers design “hard limit-free networks.”

His work has at least one occupational hazard, Motee says.

“My wife says I’m always thinking of the worst case scenario. It’s my job to design a network that works in the worst case, because then it will always work in ordinary situations.”