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Hidden symmetries, cluster synchronization may be keys to better power grids, brain function

June 19, 2014 - By Kim Delker

In most parts of the world, we take for granted that when we turn on a light switch, the light flicks on in an instant. Or when we have multiple large appliances running at the same time in our homes, the electricity flow remains plentiful and stable so that we don’t have to worry about turning on a television or vacuuming.

However, the minute something goes wrong — such as a blackout or a power surge — consumers are frustrated and baffled, and power experts are often left scratching their heads as to what went wrong. And in many parts of the world, electrical instability is a near daily concern.

But new research examining the connection between what is known as network symmetry and cluster synchronization could some day lead to a solution to make power grids more stable. It could also have implications for treating neural network disorders of the brain, such as Parkinson's disease.

Francesco Sorrentino, an assistant professor in the University of New Mexico Department of Mechanical Engineering, is the co-author of a paper, "Cluster Synchronization and Isolated Desynchronization in Complex Networks with Symmetries," that appears in the current edition of Nature Communications. Sorrentino collaborated with researchers from the U.S. Naval Research Laboratory and the University of Maryland on the work.

Sorrentino and the research team examined synchronization, which is important in not just power distribution, but in telecommunications and biological networks. Many networks have been observed to produce patterns of synchronized clusters, but predicting these clusters, and understanding the conditions under which they persist, has been difficult.

An interesting phenomenon, which initially puzzled the team of researchers, was the observation of what they called isolated desynchronization — that is, a cluster can become unstable when other clusters remain synchronized.

But, using an electro-optic network, the team has been able to perform a theoretical and experimental demonstration of the existence and stability of cluster synchronized solutions that are related to the "hidden" symmetries of the network. And the experiment displayed isolated desynchronization as well. Sorrentino said these are the key findings from their study.

"It is quite surprising that such solutions may emerge and that they can be stable," he said. "It is also surprising that large number of hidden symmetries are present in several networks we analyzed."

The team found from their analysis of many real-life networks, including the network of power generators of Nepal and the Mesa del Sol electric grid in Albuquerque, that symmetries could be commonplace, and so the possibility of isolated desynchronization exists.

Sorrentino describes symmetry as the state when two network nodes can be swapped without this altering the topological structure of the network. A cluster is a set of nodes that don’t necessarily have to be connected to each other that synchronize. For instance, in power grid terms, a cluster could be a set of power generators that are synchronized with each other but not to the rest of the network.

In power systems, synchronization is desired, as loss of synchrony — either with the formation of subclusters or individual nodes becoming desynchronized — is a dangerous event for the grid and can cause blackouts or uneven power distribution.

Synchronized electrical grids are ideal because, "we want current coming out of the electrical plugs to be synchronous," Sorrentino said.

However, in biomedical applications, such as the case with epilepsy or Parkinson's disease, synchronization isn't always ideal, as having the different parts of the brain desynchronized could prevent the entire brain from becoming affected.

An additional significant finding is that while engineers may do everything they can to preserve synchronicity in the grid, they might not be able to tell exactly what went wrong when there are problems.

Sorrentino points out that the research is shedding light on areas and connections that have not been investigated heavily.

"It's like we’re exploring the ‘dark side of the moon,' " Sorrentino said.

So is a solution to unstable power grids in the near future? Sorrentino's work is currently in the theoretical stage, but putting that theory into real-life practice is a future goal.

"We work a lot with equations and models, and what we do is quite abstract, though quite cool," he said. "But still the connection with real technical systems needs to be reinforced."

Sorrentino's research is focused on applying the theory of dynamical systems to model, analyze, and control the dynamics of complex distributed energy systems, such as power networks and smart grids. A recent study he co-authored, "Inhibition Causes Ceaseless Dynamics in Networks of Excitable Nodes," published this spring in Physical Review Letters, shed some light on the activity of the brain’s neurological systems. The research found that due to the presence of inhibitory connections, the baseline activity of the brain is ceaseless. These inhibitory connections form about 20 percent of the synapses in the brain cortex and are known to have important effects on several functions of the brain. However, the research points out that an additional effect may be that of ensuring that brain activity self-sustains itself even in the absence of external stimuli.