title: Distributed Control for Charging Multiple Electric Vehicles with Overload Limitation
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Electric vehicle, charging scheduling, renewable energy, smart grid, Lyapunov optmization.

Introduction
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Nowadays pollution engendered by massively burning fossil fuel is serious. Hence more attention is paid on electric vehicles (EVs), to replace the traditional vehicles. The report by International Energy Agency (IEA) [@Trigg] shows that the number of global EV sales in 2012 reached 113,000, double of sales in 2011, and predicts that the expected number of EV on the road by 2020 will be up to 20 million. Therefore, massive plug-in electric vehicles (PEVs)/EVs will appear on the road in the near future, leading to huge amount of charging demands. This new kind of demand will surely be a challenge for the power grid, according to the survey conducted by Su *et al.* [@SuEichi]. The safety of distribution network to support the huge demand from PEVs/EVs is essential in regulating the demand from vehicles. Parts of EVs’ influences on the power grid have been studied in [@WuMohsenian-Rad]. Good simulation frameworks in [@Darabi] also show the interactions between plug-in hybrid electric vehicles (PHEVs) and the power grid.

Meanwhile, it is possible to integrate more renewable 