What's the best way to charge millions of electric vehicles at once?

[Jim__]

From phys.org:

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(Phys.org)—About 350,000 plug-in electric vehicles (EVs) have been sold in the US from 2008—when they first entered the market—to mid-2015. Although EVs still represent a small fraction of the country's 250 million total vehicles, the continual increase in sales suggests that EVs will become even more popular over the next few decades. This raises the question of how millions of EVs may be charged at once on a grid that was not originally intended to supply such large amounts of power.

The main problem, as researchers Rui Carvalho and coauthors from the UK and Slovakia explain in a recent paper published in the New Journal of Physics, is congestion—not road traffic congestion, but charging traffic congestion. In their paper, they show that when the number of EVs being plugged into the network reaches a critical point, the system undergoes a phase transition from a "freeflow" state (where all vehicles can be fully charged within the expected time period, say 4 hours) to a congested state. In the congested state, some vehicles have to wait for increasingly long times to fully charge, resulting in queues of vehicles rapidly building up that will then face even longer charging times.

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In their paper, the researchers compared two charging strategies ("max-flow" and "proportional fairness&quot with the aim to guide network designers in deciding which algorithms to implement in the real world. Both algorithms investigated here rely on recent advances that combine tools from optimization and critical phenomena. As vehicles randomly plug in to the network, the network must continually solve the congestion control problem and allocate each vehicle an instantaneous power using the algorithm. The researchers compared the outcomes of both algorithms using simulations that are only possible due to techniques developed since 2012.

As the researchers explained, a good algorithm will have two features: it charges more vehicles at once, and it does so fairly, meaning all vehicles' charging times are roughly equal. As an example of unfairness, the "max-flow" algorithm charges vehicles closer to the main power source faster than those further away, which the researchers expect will not be socially acceptable. Fairness can be quantified by the Gini coefficient, which is traditionally used to measure income inequality. For comparison, the researchers note that Sweden has a Gini of 0.26, the US has a Gini of 0.41, and the Seychelles has the highest Gini of 0.66. The researchers explain that these values might provide a useful benchmark for identifying socially acceptable values for EV charging algorithms.

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