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Level 2 Charger to Tesla Y Charging?

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Sorry if this was already answered. New to be tesla owner

I have Level 2 charger for my Prius Prime in the garage. What should i get as an adapter for Tesla?
Your new Tesla Model Y will come with the Tesla SAE J1772 charging adapter (look in the rear hatch lower storage bin area.) You do not need to buy any additional adapter to use your existing Level 2 EVSE to charge your Tesla Model Y. (If you want to purchase an additional/spare J1772 adapter these are available from Tesla.com online store for $50.)
 
I also found that there is a 240V outlet in the garage. Is there any advantage of using Level 2 charger over 240 Outlet?
Maybe, depending on the size of the circuit behind that 240V outlet and the plug-in charger you use. In the best case, it is a 50A circuit. If so, then you could install a plug-in charger there and charge at 40A, which would be a lot better than your existing 30A charger. Tesla portable chargers (plug-in) top out at 32A, so that is not a material improvement over your current charger.
 
I also found that there is a 240V outlet in the garage. Is there any advantage of using Level 2 charger over 240 Outlet?
The short answer: Hardwired is better than a socket.

Speaking as a EE, the basic deal is that Moving Parts and Connectors are to be avoided unless they're designed to do that.

Well, the only moving part in the L2 Charger you've got is a contactor (read: Honking Big Relay). Those are designed to handle lots of power. Besides, the way the protocols generally work, the contactor is activated/deactivated when the power being delivered is zero. And, even if it wasn't, well, power contactors are built to handle it.

The problem with 240 VAC sockets, at least in the U.S., is that they're generally designed to be inserted/de-inserted a handful of times in their lifetimes. Hence, the el-cheapo, known-to-fail ones that one finds over at Home Depot. Yeah, they'll carry the rated current sans problems for, say, an electric oven. But put a portable welder on one of the Home Depot (or a Tesla Mobile Connector, same basic idea) with one plugging it in and out all the time and in a year's time or two it'll fail. Hence the existence of much more expensive sockets that cost 3x the Home Depot ones. And, if one disassembles one, there's a lot fancier, bigger metal surfaces and such in there that make them worth the money. Having said all that - even the fancy ones won't last as long as the contactor in a hardwired L2 wall connector.

The J1772 and Tesla connectors have great, big honking contact surfaces and are designed to handle lots of insertions and removals. If I'm not mistaken, the Tesla connectors appear to be silver plated; you can't find better conductivity than that.

Next thing: 30A. That (hopefully) means that the L2 charger you've got is wired to (at least) a 40A breaker.

Back up. Here's how it works, at least for heavy loads like a Tesla. What you're supposed to have: A breaker rated for XX amps, wire rated for XX amps, a socket (if there is one) rated for XX amps, and the load, which can be no larger than 80% of XX amps. There are settings in the L2 charger that, through a protocol, tell the car what L2 charger's maximum current is, and that maximum current is set through switches or some kind of GUI.

Example: In my garage I have a Gen 2 Tesla Wall Connector (equivalent to your L2 Charger) that is wired to a 60A breaker, using wire rated for 60A for the distance it has to run, and the mechanical rotary switches on the circuit board were set to reflect the first two items, as stated in the TWC manual. Maximum current drawn by the car is 48A which, you'll note, is 80% of 60A.

Now, as it happens, I could have had the electrician put in a 50A breaker and 50A wire. If I had done that, I would have set the switches in the TWC to reflect that fact - and the car, being informed through the protocol, would draw no more than 40A (80% of 50A).

In fact, since the TWC in the garage is a Gen 2, it can actually be told through the switches that there's a 100A breaker and 100A wires out there and, given the right kind of Tesla (an older Model S), it and the car would happily send 80A to the car. However, with the M3 and MY in the garage, even in this case (assuming that I would have done such a thing), 48A is all one is going to get - the lowest limit wins, and the M3/MY max charging rates is 48A. (Gen 3 TWC's don't support 100A :).)

So: Go Ye To Ye Breaker Panel And Check Out The Breaker. If it's 40A, then you'll get 30A from your L2 charger. If it's 30A, the max you should see once you get the Tesla will be 24A. (If you see 30A and you've got a 30A breaker, then you have Trouble. That's a National Electric Code thingy that says that max steady state load is 80% of the breaker rating, and they're not kidding.)

Finally, charge rate. There's losses (there's always losses), but for back-of-the-envelope calculations, one uses the Model Y's efficiency number, 270 W-hr/mile.

So, two possibilities: You've got 240 VAC at 24A (assuming a 30A breaker at the panel) or you've got 240 VAC at 30A (going by the L2 charger manual).

P = V*I, so you've got either 240VAC*24A = 5.76kW or you've got 240VAC*30A = 7.2 kW

So, rate of charge P/Efficiency, so, at 5.76kW, we have Miles_per_Hour_of_Charge = 5.76 kW/(0.27 kW-hr) = 21.3
At 7.2 kW, you got 7.2/0.27 = 26.7 Miles of Charge Per Hour.

So, say you've got a MY with a 320 mile range. It's down to, say, 80 miles. One generally charges to, at most, 90% of full charge, 288 miles. So one needs to put 208 miles on it.

At 5.76 kW, that'll take 208/21.3 = 9.76 hours. At 7.2 kW, that'll take 208/26.7 = 7.8 hours.

Either way, this counts as Overnight. Plug it in when one gets home, it'll be ready in the morning.

One last thing. Yeah, everybody calls that thing on the wall a, "charger". Um. No, it's not. The actual battery charger is in the car. Whether it's a Tesla or Other. With your Level 2 Wall Connector (because that's what it is), all that thing does is (a) tells the car what kind of voltage/current it can supply and (b) connects 240 VAC via a relay to the car, when commanded. A charger.. like, say, one of those 12V battery chargers one can buy at an auto parts store, actively monitors the voltage and current going into a 12V lead-acid battery, doesn't overcharge the thing, and has all the smarts. The Wall Connectors simply supplies 240 VAC (or 120 VAC, if it's a Level 1); it's the car, with a little information from the connector about what's available, that decides how much current to draw and what to do with it.