Mental exercise - think about how these properties apply to all complex, interdependent systems and entities: economies, companies, nation-states, etc.
article link: http://www.nationaljournal.com/tech/...-sand-20140408 ------ study link: http://scitation.aip.org/content/aip...1063/1.4868393
In other words, the grid may be not be the "right" size—big enough to distribute power efficiently, but small enough to prevent widespread blackouts, such as the 2003 blackout that cut power to 50 million people in the U.S. and Canada for two days. So, breaking up the system into smaller grids could reduce the likelihood of power outages, according to a new study in the journal Chaos, published by the American Institute of Physics.
"We found that for the best trade-off between providing backup power and blackout risk, the optimal size was 500 to 700 nodes," Newman said. The bigger the grid gets, the greater the risk of failures.
"Sandpiles are stable until you get to a certain height. Then you add one more grain and the whole thing starts to avalanche," Newman said. "This is because the pile's grains are already close to the critical angle where they will start rolling down the pile. All it takes is one grain to trigger a cascade."
The simulation results also show that medium size blackouts occur significantly more frequently in the multiple 100 node networks. In the large connected size networks, the large blackouts, although less frequent, increase greatly in relative frequency as a result of increasing the number of nodes. The emergence of the power tail for the large networks is characteristic of a system displaying critical behavior and is the main drawback of these large complex systems. This is why the advantage of a wider range of power dispatch options can turn into the large disadvantage of the increased risk of very large blackouts due to the increased probability of large cascading failures.
When we compare the risk function for the case of multiple 100 networks to that for large networks, we find the risk for the multiple 100-node networks has a large peak, due to high frequency of the blackouts, at medium values of load shed, while in contrast, the large networks show a slowly decreasing tail for very large values of load shed. Therefore, the cost of the large events may dominate the overall risk as the size of the system increases. This dominance depends on how fast the cost of the events increases with its size and how fast its probability decreases.
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