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Braess’s Paradox in Electrical Power Grids

Networks Blog Post 2:

We rely on electrical power grids to deliver us electricity all over the world. These grids are constantly changing as we add more types of energy sources such as renewables. In terms of electrical current, “electrical power grids operate in alternating current (AC) mode and all generators in the grid operate at the same frequency (50 Hz in Europe) and are synchronized across the network” (Cockbill). The frequency of the grid relates to the frequency at which the generator rotates: “if you draw energy out of the system it is taken from the rotating energy of this rotor, effectively slowing the generator down and causing grid frequency to drop” (Cockbill). Once this drop occurs, primary control systems to re-stabilize the frequency. The primary controls are not powerful enough to raise it back to 50 Hz, leaving the system vulnerable to future drops. Secondary control systems are needed to raise the frequency back to 50 Hz.


Braess’s paradox is phenomenon first discovered by Dietrich Braess in 1968 , “that adding resources to a transportation network can sometimes hurt performance at equilibrium” (Easley, Kleinberg 232). Researchers found that Braess’s paradox applies to power grids as well: “adding transmission capacity to a network can degrade the network’s performance” (Cockbill). Benjamin Schäfer and colleagues at the Technical University Dresden studied Braess’s paradox in electrical grids and starting with two connected nodes and adding more lines. They found that, “with no secondary control, adding a line causes a sudden blackout, a prototypical Braess’ paradox. But in the same network with secondary control, adding a line has no effect,” (Schäfer qtd. in Cockbill).


Schäfer and colleagues hope to do more research in the future as to why this is so and the effects of the amount of control in a system.


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