As a chemical engineer with a particular focus on energy systems and energy engineering, the power grid in the United States lends itself well for a study of network dynamics and cascading behavior. In a paper titled “Topology and Cascading Line Outages in Power Grids,” Professor David L. Pepyne studies the relationship between topology and power outage cascades in power grids.  Dr. Pepyne’s study makes use of the small-world network model by Watts & Strogatz that was discussed in class.

In the paper, Dr. Pepyne analyzes the effect of clusters in the power grid network on cascading power outages and tries to develop a model for predicting cascading behavior in the power grid. Dr. Pepyne places particular emphasis on power lines, as they are most susceptible to failure because of their exposure to the elements.  When a power line (edge on graph) is removed, the redistribution of power can cause power stations (nodes) to become overloaded leading to additional outages. Depending on the connectivity of the network and the position of the node in the network, this can lead to a cascade. The major blackout on the east coast in 2003 was an example of a cascading power outage as power stations failed consecutively as the load at each “node” became so high that the node tripped.

For simplicity, Dr. Pepyne used DC power flow equations to model power flow throughout the network, even though AC power flow is a more complete (but difficult) model. Using these equations, Dr. Pepyne modeled power flow through the network and threshold capacities that governed outages due to overload. Dr. Pepyne then modeled the network of power lines by drawing an undirected graph and connecting the appropriate nodes with edges. To test the model, one edge is randomly severed, causing a redistribution of power to other nodes in the graph. Each node has a threshold capacity, and if the redistributed power value exceeds that threshold, the node goes offline. However, despite more nodes going offline, the total power of the network remains constant, so the power is redistributed to other nodes. This potentially causes even more nodes to go over their threshold capacity, causing them to trip. Depending on the structure of the graph and the distribution of power, a cascade can form as node after node overloads and becomes disabled. In reality, because power grids are sparsely connected, a small number of simultaneous outages can result in much of the grid breaking up due to a cascade.

While the paper does not explicitly mention this concept, the distribution of power is analogous to PageRank. Under the assumption that the power network is constant (although, in reality, it is not) PageRank is never created or destroyed; it is simply moved around from one node to another. Dr. Pepyne’s model utilizes this property of PageRank, but extends it by allowing nodes to go offline when their distributed “PageRank” exceeds the threshold value, causing further redistribution of power. As a result, depending on the structure of the network, a cascade can be created as nodes go from on to off as their power value exceeds their threshold value. The key concept is that different nodes have different threshold values, depending on their capacities.

Dr. Pepyne refers to Watts & Strogatz’s small-world model and mentions that networks such as power grids tend to have high clustering and low path length. In fact, the clustering coefficient was often high enough such that a cascade did not typically begin when a power line (an edge on the graph) was removed and the power was redistributed to other nodes. As a result, Dr. Pepyne concluded that grids that contain many disordered connections between nodes tend to be better suited to avoiding cascades than those that do not. However, if a cascade does occur, grids that are more disordered tend to fall victim to cascades after fewer line outages than those that are more ordered. Therefore, a tradeoff exists between network robustness and network fragility, and future models can be used to determine the extent to which each should be considered.

The article in question can be found at http://www.springerlink.com/content/v828005316341ql3/fulltext.pdf. However, in order for Cornell students to obtain access to the full article, they must go through library.cornell.edu and search for “Topology and Cascading Line Outages in Power Grids” under the “articles” search tab.

Citation:

Pepyne, David L. “Topology and cascading line outages in power grids.” Journal of Systems Science and Systems Engineering 16 (2007): 202-21. Springerlink. June 2007. Accessed: 26 Apr. 2009 <http://www.springerlink.com/content/v828005316341ql3/>.