Experts have decried congressional and academic reliance on a mathematical model for understanding complex systems that suggests an attack on a small part of the U.S. power grid could disrupt the entire power system network.

“Some modelers have gotten so fascinated with these abstract networks that they’ve ignored the physics of how things actually work—like electricity infrastructure,” said Paul Hines, University of Vermont assistant professor at the College of Engineering and Mathematical Sciences. “And this can lead you grossly astray.”

Hines pointed specifically at a model described in a scientific study in the journal Safety Science (Dec. 2009) ; the paper was cited by a military analyst at a congressional hearing this March when he warned of how an attack on an unimportant part of the U.S. power grid might, like dominoes, bring the whole grid down. A similar paper was published in the journal Nature the following month that presented a model of how a cascade of failing interconnected networks led to a countrywide blackout in Italy in 2003.

According to Hines, the so-called topographical model in the Safety Science paper came to the “highly counter-intuitive conclusion” that the smallest, lowest-flow parts of the electrical system—a minor substation in a neighborhood, for example—were likely to be the most effective spots for a targeted attack to bring down the U.S. grid.

A study published by Hines and Penn State’s Seth Blumsack in the journal Chaos this September found just the opposite. Drawing on real-world data from the eastern U.S. power grid and accounting for the two most important laws of physics governing the flow of electricity, they show that “the most vulnerable locations are the ones that have most flow through them,” such as highly connected transformers and major power-generating stations. “If the government takes these topological models seriously,” Hines said, “and changes their investment strategy to put walls around the substations that have the least amount of flow—it would be a massive waste of resources.”

As Hines explained, many topological models are basically graphs of connected links and nodes that represent the flows and paths within a system. When a node changes or fails, its nearest connected neighbor will often change or fail next. “This abstraction has provided profound insights into many complex systems, like river networks, supply chains, and highway traffic. But electricity is strange and the US electric grid even stranger.”

Hines pointed to the August 2003 blackout, which started in Ohio and then spread to New York City. Cleveland went down, and soon Toronto was affected. “The blackout was able to jump over long distances” because, “when a transmission line fails—instantly, at nearly the speed of light, everything changes. Everything that is connected will change just a little bit, but in ways that are hard to predict.” This is compounded by the fact that the U.S. electric grid is more an “intractable patchwork of history than a rational design,” he said.

Using real-world data from a 2005 North American Electric Reliability Corp. test case, Hines and Blumsack compared how vulnerable parts of the grid appeared in the differing models. The topological measures—so-called “characteristic path lengths” and “connectivity loss” between nodes—came up with dramatically different and less-accurate results than a model that calculated blackout size driven by the two rules that most influence actual electric transmissions: Ohm’s and Kirchhoff’s laws.

The study, funded by the National Science Foundation, shows that the electric grid “is probably more secure than many people realize—because it is so unpredictable.”

“Our system is quite robust to small things failing—which is very good,” Hines said. “Even hurricanes have trouble taking out power systems. Hurricanes do cause power system failures, but they don’t often take out the whole system.”

“It takes an incredible amount of information,” he concluded, “to really figure out how to make the grid fail.”

–Sonal Patel is POWER’s senior writer