Is it really possible to measure “robustness?” If initial results from a recent simulation are any indication, it may not be as far-fetched as some may think, and it could have significant implications for electrical power grids.

A team of researchers recently completed simulations for a computational tool that uses network science to quantitatively measure power grid systems. The results have been promising thus far, and the team next hopes to apply its model in a real-life grid in China with a focus on minimizing blackouts.

What makes this particularly impressive is that power grids are nearly impossible to analyze at-large due to their scale and constantly fluctuating nature to meet energy load demands. There are nearly 20,000 individual generators in the U.S. alone operating in complex networks – and using different types of fuel – to serve millions of residential and commercial consumers. On top of that, they are equipped to dynamically redistribute power flow when a component breaks down, sometimes succeeding and other times leading to cascading failures and black-outs depending on load capacities. All these factors make it very difficult to establish a uniform measurement system to assess a grid’s robustness, or its ability to tolerate faults.

Simulation of cascading failure triggered by breakdown of transmission line (77, 82) of IEEE 118 bus. Squares are generators. Red nodes are unserved nodes.


At the same time, measuring a grid’s robustness has become more critical than ever as cyber-attacks increasingly threaten national security, and officials around the world seek ways to minimize damage in case energy supply is cut off.

Dr. Chi “Michael” Tse believes concepts from the still-emerging field of network science can provide answers to measuring – and therefore improving – a power system’s robustness.

Network science is the study of the connectivity of complex networks using links (edges) and nodes (vertices). The science has been around for centuries, but gained popularity in the 1990s for its study of social structures, including phenomena such as six degrees of separation and small-world theory. Network science has been studied in context of the power grid before, but a) it’s only been applied to local clusters and b) it hasn’t properly accounted for physical laws in the electrical world – such as Ohms and Kirchoff’s laws – creating insufficient shortcuts and discrepancies.

We’re entering a golden era for applications of network science

In the new research, Tse and his team took useful network science concepts and reformulated them to account for electrical laws. They did so by defining new parameters they believe are relevant to large-scale power networks, including:

  • Percentage of unserved nodes (PUN). Unserved nodes are those deprived of power in a blackout. A component that creates a large network PUN upon failure can seriously damage the network, whereas a component whose failure leads to a small PUN will not have significant influence.
  • Percentage of noncritical links (PNL). This is a threshold parameter to indicate the ability of an entire network to tolerate faults in relation to PUNs. Large PNL is key to a robust system.
  • Distance to generator (DG). Small DG indicates better accessibility to power sources, and a more spread-out or decentralized percentage of generators. Small DG isn’t necessarily better, as it can also lead to higher dependency and sensitivity should one node fail.


The model provides a platform on which engineers can simulate the impact of change, and compare structures before they’re even developed to favor the most robust one. Additionally, the model can be extended to other types of electrical components, such as solar panels in renewable energy systems.

“Our paper is the first to address robustness assessment for an entire network and in actual terms that can be deployed,” said Tse. “We’ve received a lot of international interest from researchers starting to use our model, and I believe it will become significant in the next few years. More broadly, I believe we’re entering a golden era for applications of network science in general, including and going far beyond the power grid.”

Find more articles about “network robustness” in IEEE Xplore.