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What is the largest gage?

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What is the largest gauge wire that can be hooked up to a HPWC?

The largest ground wire that you can use is #4, but code only requires #8 for a 100 Amp circuit. All of this is for copper.

If you are going to use a 100 Amp breaker, then for residential, you are required to use at least #3 AWG wires for the power connections. For a business install, code requires #2 AWG wire. I don't know the maximum size that you can use, but I did an install with #2 at my house. The electrician had to wrestle with the big wires in the HPWC, but ended up with a clean install. I used the #2 to save a little on Voltage drop. That was somewhat extravagant, I'm not sure why you would go any bigger on the wire.

Good Luck!

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Update: Just opened the HPWC up and looked inside. The connector for the power wires into the HPWC is rated for #2 to #14 AWG wire. #2 is as big as you can go.
 
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Pretty much what Cottonwood says.

The installation manual specifies certain gauges of wire as well. While helping my installer/electrician, I recall that he'd noted the heaviness of the wire versus the slots the HPWC allowed. It was a tight fit.
 
If you've got some fatties delivering the goods you can always pigtail down to a gauge that will fit the HPWC. Use a separate box (with cover plate) if necessary. But this implies that you did the same on the input end as well (if it didn't fit in the breaker).
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The HPWC manual says for 100A to use a maximum of 3 gauge which can be hard to find. My electrician used 2 gauge though it was a tight fit. I'm amazed at how small the HPWC is. It's a fraction the size of the shut-off panel next to it required by my city.
 
#2 is the maximum for the lugs in the HPWC. It barely fits. #3 fits more easily, and is a little more flexible, but is harder to find and more expensive than #2 generally.

I just finished installing an HPWC in my second home. It was pretty easy because I put a 200 Amp sub-panel in the garage when I installed the HPC for the Roadster years ago. That panel is surface mount, and I don't mind surface mount conduit in my garage so most of the install was very simple and straight forward.. A pair of #2's and a #8 for ground feed just fine through the 1" conduit that Tesla recommends. Because the HPWC is MUCH tighter than the breaker panel, I started making connections there and then finished the connections in the 100 Amp breaker inside the Siemens CB Panel.

I completely agree with Lloyd's comment, "#2 is the maximum for the lugs in the HPWC. It barely fits." In fact, here is my analogy. Connecting the #2 wires in the HPWC is like wrestling an anaconda in your front coat closet, while connecting the same wire in the Siemens breaker panel, is like guiding a large, gentle horse into its stall.

I know that Tesla prides itself on sleek, industrial design, but they went too far in the HPWC. A little more space, and cable lugs one size larger, would have saved a lot of installer headaches across North America...