Space, Physics, and Math

Catastrophic cascades

What can we do to prevent the electrical grid from toppling like dominoes?

January 27, 2011

Early in the morning of September 28, 2003, as Italians gathered in the streets for Rome’s annual White Night Festival, Italy went black. A single felled tree had knocked out a power transmission line from Switzerland to Italy, initiating a cascade of electrical failures that cut power to 56 million people, stranding hundreds in underground trains and leaving revelers out in the rain without transportation.

The power grid in the United States is similar to Italy’s: a complex web of generators and transmission lines, intricately interconnected yet independently controlled — and prone to failure in unpredictable ways. Past failures, like the blackout that hit the Northeast just before Italy’s 2003 outage, combined with the continuing threat of terrorist attacks on the grid, are making defense of the power grid a priority for engineers and officials.

In order to protect our electrical grid against cascading failures, government officials and engineers need to know where the system is most vulnerable, and for that they need an accurate model.

While individual elements in the power system are relatively easy to model, “the real challenge comes in predicting coupled behavior on a national scale,” said electrical engineer Christopher DeMarco of the University of Wisconsin. Because no comprehensive model of the nationwide grid exists, researchers have had to cobble together their best predictions using the tools available. And those tools don’t always agree with each other, as a paper by University of Vermont engineer Paul Hines and his colleagues demonstrates.

The study, published in the journal Chaos in September, pits two methods of modeling the grid against each other. The first, topological modeling, determines vulnerability by analyzing only the grid’s structure: the geometric layout of circuit junctions, known as nodes. The second, power-flow or dynamic modeling, finds vulnerable points by predicting the electrical flow through those nodes using the laws of physics, specifically Kirchhoff’s circuit laws.

Topological models have made some riveting predictions, according to Hines. A paper by Chinese engineering graduate student Wang Jianwei published in Safety Science last year identified low-flow nodes in the United States as vulnerable points that could initiate cascading failure. The finding is counterintuitive: The failure of nodes with more power flowing through them would seem more likely to produce greater effects. The paper caught the attention of government higher-ups because Wang, whose work was purely academic, described the nodes as hypothetical attack sites.

But Wang’s topological approach, and therefore his results, may be deeply flawed. The problem with topological modeling is that it doesn’t address the most fundamental part of the electrical grid — the physical flow of power — said Pennsylvania State University engineer Seth Blumsack, who is one of the authors of the new Chaos paper. Blumsack’s group found that each model resulted in very different estimates of blackout size when applied to a small portion of the grid. “It is a lot harder to bring down the system than these topological models would suggest,” Blumsack said.

Topological models do have their uses. Boston University physicist Gerald Paul, who used topology to model the 2003 blackout in Italy, said it excels in measuring network robustness, or how well the grid stands up to losing nodes overall. But power engineers generally agree that a complete model of the grid must include an understanding of electrical flow, which means using a power-flow model.

Power-flow models can only be successful, though, if researchers have the real-life data to inform them. Reka Albert, a physicist and biologist at Pennsylvania State University who was not involved in the research, said that this often isn’t the case. “If the information necessary for power-flow modeling were broadly available, people would adopt it,” Albert said.

As with many issues of national security, funding is a major consideration for the future of grid protection. “There are scarce security dollars,” Blumsack said. “How do you want to spend them?” The University of Wisconsin’s DeMarco said that historically we’ve protected individual components of the grid: the big generators and transformers that he called the Achilles’ heel of the electrical grid. Hines said that his modeling results indicate that protecting substations with the most power flowing through them is the most cost-effective strategy.

But it may be that the best line of defense for the electrical grid is more research into the best line of defense. “We would learn a lot from a concerted effort to accurately and usefully model the electricity infrastructure,” said Hines. The Department of Energy seems to recognize the need to deliver the best predictive models, though it might not be giving them enough financial backing. In its 2011 budget request, the Office of Electricity Delivery and Energy Reliability asked for $10 million for “Advanced Modeling Grid Research.” The research will focus on improving modeling as the smart grid, which digitally regulates power flow, is implemented. Hines said that isn’t nearly enough funding.

As the smart grid improves our energy efficiency, DeMarco said, it will also create new vulnerabilities, which the next generation of models will need to anticipate. The new technology has the potential to make the grid more efficient by allowing more individualized control over power distribution, said DeMarco, “but that creates vulnerabilities that we haven’t had in the past.” Modeling research will have to progress and manage its current inconsistencies in order to safely and efficiently capitalize on the smart grid.

About the Author

Katie Palmer

Katie Palmer graduated from Williams College with a B.A. in chemistry and a concentration in neuroscience, though her classmates knew her best as “that cellist.” Guided by interests in cognitive science and neuroscience, she has probed rat brains for hints of anxiety traits and attempted to reconcile consciousness with the reality of the nervous system. Katie hopes to follow these topics and more in the process of bringing science to the public. You can follow her on her personal webpage or on Twitter.



Every house should have a bicycle with a dynamo on the back wheel.

Don says:

It seems kind of strange that we base our whole civilization on the power grid and that we don’t have a working model of it. Almost everything would grind to a halt without electricity.
One of the major reasons cited for a nationwide grid is efficiency. I say that we should also look at robustness. Someone shorting out a substation in WA shouldn’t be able to knock out electrical distribution down in AZ. The grid needs to be broken up into sectors for robustness.
Also, we need to take the grid completely off of the internet to decrease vulnerability to attack.
Furthermore it’s important to have more localized electrical generation with more buildings being completely energy independent.

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