Electric cars have finally crossed the line from being futuristic possibilities, through hybrids that exploit some of the benefits of electric power but still burn petroleum, to fully electric vehicles. Tesla and Nissan are the big trendsetters, but now pretty much all the carmakers are on board.
Charging an electric car presents some special problems, mainly stemming from the fact that moving the mass of a car (and passengers) requires quite a bit of energy. Gasoline (and its relatives) have tremendously high energy density. The breakthrough that's made electric cars finally feasible is the lithium ion battery, which is both smaller and lighter than it's predecessors. But it still takes much longer to charge a battery than it does to fill a tank with gasoline.
Broadly speaking, there are three types of charger that have evolved, which go by the name "Level 1", "Level 2" and "Level 3". The first two are not really chargers, but EVSEs "Electric Vehicle Service Equipment". They just pass the power unchanged, with the addition of some safety equipment. The charger is on the car. A level 1 EVSE uses one phase, line voltage power. In the US, this means 120V, 15 or 12A. The SAE definition is that a level 1 EVSE is single phase and not capable of charging at faster than 1920W. A level 2 EVSE is 2 phase, 208 to 240V and may go at up to 80 amps, but very few of them actually do that. This is a theoretical peak of 19200W, but very few go higher than 7800. "Level 3" is not defined, but in practice, it's anything that goes higher than 19200W.
The standard EVSE system is SAE J1772, which defines a 5 conductor connector, which has two power conductors, a ground, a "pilot" and a "proximity" conductor. The latter are used for safety signaling. The "pilot" carries a 12V 1KHz square wave which is used to detect continuity, and the "proximity" signals to the car that it's plugged in, and blocks the vehicle from being driven until it's disconnected. Power is just passed through on the three power and ground conductors, but a relay opens the circuit unless pilot and proximity are deemed valid. The idea is to make it impossible to charge a car with a kludged up power cord, just the sort of thing that might start fires, and to reinforce it, they tell you not to use extension cords when you buy the car. Virtually all electric and plug-in hybrid cars support J1772, although a few, such as Tesla S, require an adapter. (Tesla exploits their incompatibility to use the same conductors for their "supercharger" level 3 scheme.)
The electric code also requires that lines being heavily loaded for more than half an hour only carry 80% of their design capacity. This is also to prevent fire--heat builds up gradually, and your charger is likely running while you're sleeping. This is the reason that a charger wired for 15 amps is only allowed to draw 12, 50 amps only allowed 40, and so forth.
Level 3 chargers typically use special power arrangements to draw more than 80 amps. Generally they are called DC chargers but that oversimplifies what they're doing. They require smart electronics and high power connectors--generally beyond the capacity of home chargers The three main protocols are the still evolving J1772 level 3, the CHAdeMO, and the Tesla Supercharger. The first two require a very special connector, while the Tesla uses the same connector as level 1 and 2. (this is the main reason Tesla went its own way rather than allowing J1772 to plug in directly). BMW and Nissan tried to negotiate a license to use the system during summer 2014, but BMW recently announced that it's building its own network of level 3 chargers using the J1772 "combo" connector, which is a kludge involving a J1772 and a separate, higher capacity connector in the same plug.
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