Back in 2011, President Obama set the ambitious goal of having 1 million electric vehicles on US roads by 2015. Whether automakers will hit this target is the subject of much debate. But the possibility of the widespread adoption of electric vehicles raises an interesting problem.

It’s easy to imagine the number of electric cars increasing but it’s much harder to see the electricity generating capacity increasing the same rate at the same time. Generating capacity will eventually catch up with this extra demand. But in the meantime, how can all these cars be charged?

Today, Yingjie Zhou at Sichuan University in China and a few pals show that it is possible to solve this problem using the same kind of algorithms that control resources in communications networks. But they also say there is a trade off–car owners will have to provide accurate information about their driving habits. Is that too much to ask?

The basic problem is that most electric vehicles will require overnight charging so that they are ready when the owners need their cars for the morning commute. Any given grid will have a certain amount of excess capacity which it can devote to this problem. But if the number of cars is large, it cannot charge them all.

So the idea that Yingjie and co explore is to find a fair way to charge as many as possible with minimum disruption.

One approach is the first-come-first-serve method that charges the vehicles in the order in which they are plugged into the grid.

Another is a round robin method that cycles through all the vehicles requesting charge, giving say five minutes to each in every round. That ensures that all the vehicles receive the same amount of charge.

But Yingjie and co use real power data and commuting data to simulate these charging systems and say neither works well. “Even when the power network has three times as much excess power as the vehicles require, some vehicles will be delayed by more than 100 minutes beyond their required departure time,” they say.

That’s a significant problem. Imagine leaving your house for your morning commute but finding that your car will not have enough juice for the journey from another 90 minutes.

But all is not lost. Yingjie and co say they’ve found a better method but that it requires users to supply certain amount of information about their car and their plans. Specifically, Yingjie and co have simulated a system that measures the power levels in vehicle batteries and also uses the expected departure time and commuting distances of the car owners to work out how best to charge them all.

This information dramatically improves the efficiency of the charging system. It allows the team to design an algorithm that provides enough charge for a given commute while minimising the delays experienced by any user.

“The proposed scheme needs only 5 per cent more than the power demanded to ensure all the vehicles departing with delay in a few minutes,” say Yingjie and co.

That’s certainly an improvement.

But there is a potential problem. It’s not entirely clear that users would be honest about their requirements, perhaps saying they will leave earlier than planned and that they have a longer commute, to ensure a full charge. In fact, it’s hard to imagine that people would not attempt to game such a system.

And therein lies a fundamental problem for humanity– how to distribute a limited resource fairly.

There are, of course, myriad other schemes that mathematicians can explore, involving incentives as well as penalties for various types of behaviour.

But the bottom line here is that however desirable electric vehicles may be, their widespread adoption is likely to produce considerable inconvenience for some unless problems like this can be ironed out in advance.

Ref: arxiv.org/abs/1402.2489: Distributing Power to Electric Vehicles on a Smart Grid