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Power grid and cascades

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7742575

In the study published in IET Journals entitle “Cascading failure model in power grids using the complex network theory”, Fan Wenli et al. uncover the way in which our electric power grid is affected by and vulnerable to a cascading model diffusion within its complex network. To understand this we must first be able to visualize our power grid as a graph composed of multiple nodes and links with a the traffic dynamic between them. Nodes in this case represent a specific voltage of electricity within systems like transformers, transmitters, and circuit breakers– in fact voltage depends where you are in the grid (which transformers and substations the electricity has passed) – and links represent the power lines. Nodes are interconnected meaning they have multiple power lines connecting to other nodes. More importantly the grid is composed of different clusters – clusters are more vulnerable components because, as shown by the model diffusion described in chapter 19, the nodes within clusters are more likely to adopt new behaviors inside of densely connected communities. Additionally, based off of the cascade model described in chapter 19, we can understand how major blackouts can happen, which is what is described in Wenli et al’s study. We can visualize this by the figure below, which is proposed in their study: this shows a simplified model of the grid and exposes how one failure in a single node (such as the overheating of a system – which can make nodes switch behaviors : either by emitting less electricity, more electricity, or shut down completely) can eventually cascade to all other nodes and create a massive blackout.

 

Wenli et al. look at a specific case study in which a node overheats  (they use the term load to describe the amount of electricity and overheating). One node load malfunctions to the point where the neighboring node with a degree of only two outgoing links also malfunctions. They imply the idea of thresholds – in this case it happens at q=0.5. Eventually, the power grid can get an immense amount of loads and cascade into a full on blackout – as it happened in 2003. “Actually, the hidden failures will be induced along with the overload cascade of nodes, which further triggers node load redistribution and may cause a new round of node overload phenomenon. Accordingly, the node overload failure and hidden failure interacting with and promoting each other intensify widening the blackout scales.”

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