Coulomb
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Yes, the "charger" tells the car to reduce its current draw. The on-board charger responds by reducing its output voltage very slightly, so that less power flows into the battery.On a related note, how is the current limited? The only way I can think that the charger can do it on its own is to drop the voltage a lot, but that can't really be it. Does the charger tell the car to back off?
For AC charging, the maximum charge current is communicated to the vehicle over the control pilot. This is one of the thin pins in the type 2 (or type 1 J1772) connector. The EVSE (AC "charger" outputs a 1kHz ±12V square wave over this wire, and the duty cycle (percentage of the time it's high compared to the whole cycle) is adjusted from some 5% to I think over 90%, representing 6A to 80A for the current limit.
The original intent of this signal was I think to prevent overloading of cables, but it's also useful for current sharing, and even for roughly matching EV charge power to excess solar power. The current sharing is usually at one cabinet that has two plugs, but it can also be implemented on a whole site basis with a bit more complexity.
DC rapid chargers often current share as well, both at a cabinet level (or two cabinets in the case of Tesla V2 superchargers), or of course whole site throttling, as a site with say 12 dispensers capable of 250kW each could total three megawatts. Often the site transformer will be limited to 2-4 megawatts, and often the site might have other loads that can't be throttled (e.g. at a shopping centre or workplace).
The current limit for DC chargers is negotiated digitally and dynamically between the vehicle and the charger. This also involves the control pilot signal, still with the 1kHz square wave, but now with a special duty cycle, and using Power Line Communication on top of this. At least that's my guess, perhaps they remove the 1kHz square wave once digital communications have started; the two transitions every millisecond would be very disruptive to the comms.