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Braess’ Paradox and power grids

In class today we talked briefly about Braess’s Paradox. If you need a reminder (or if you were zoning out), it’s the concept that adding extra paths to a directed network (like a network showing the possible roads from starting point A to destination B) might actually decrease the overall performance of the network. This means that adding a new metro line or bus route to an existing network, depending on the arrangement of the nodes in the network and the costs of the paths, might actually make travel time slower.

This counterintuitive conclusion is applicable to areas other than transportation. It has actually been revealed (in a study by the Max Planck Institute) that it can affect the transmission of electricity through power grids. Electricity networks have a certain grid frequency, and generators of large power plants are regulated in a way that they tune to this frequency. In turn, the grid imposes its frequency on all the consumers of the electricity, like hair dryers and washing machines and refrigerators, so all the elements are synchronized. The power grid and its constituent parts generally self-synchronize, but this balance can be disrupted when a new source of electricity is added to the grid. If a new line is built to link two machines, care must be taken to ensure that their oscillations (which will synchronize with each other, so that they reach minimum and maximum voltage at the same time) are compatible with the machines on the old line. If there is a conflict between the shortcut and the old line, this new phase relationship has the potential to desynchronize the entire network (causing short circuits and emergency shutdowns).

So just like the considerations made when adding a new road between two cities, care should be taken to ensure two electrical nodes can be linked without risk. In general, though, you shouldn’t worry about adding solar panels to the roof of your house or the new wind farm that’s supplying electricity to your neighborhood. The study also found that a decentralized network with many smaller suppliers of electricity (as shown in the graphic below) has many useful collective effects, such as its ability to compensate for the damage of a single line in the network (unlike in networks clustered around a single main power plant). And, best of all, these networks are quite resilient. Consumers and power plants in these decentralized networks will self-synchronize, and may be less vulnerable to outages than present-day grids.

densegrid

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