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Once the Model 3 comes online in larger numbers I fear the chargers will be overwhelmed.
Fear not. TL;DR version: All is yet quite well.
It will take at least a couple of years to get 250,000 Model 3s produced. Approximately half of those are for non-US markets (e.g, the rest of the world). Of the remainder, approximately 40% will end up in California.
250K * 50% * 40% = 50,000 cars. By, say, early 2020. Statewide.
Keep in mind:
1. CA is the #7 economy in the world (give or take a spot). Lots of innovation and still some instances of progressive governing going on.
2. The CA-only portion of the VW Dieselgate scandal is $800M. It was $1.2B, and somehow $400M disappeared - colour me shocked. Anyway, to further set context, $800M is approximately 3000 supercharger sites. There aren't even 500 SC locations in North America yet. And while not a dime of Dieselgate money will go toward a SC location, that $800M is specifically earmarked for chargers and the maintenance thereof and it will buy tens of thousands of them statewide.
3. The state's 2 largest utilities have committed to 12,500 L2 and L3 chargers statewide.
4. Large-scale installations are afoot - see JPL's 50 L2s, and Costco's commitment to 12-16 L2s (Lomita) at least for new construction.
5. Proven models (see Aerovironment's $19.95/month unlimited Chademo plan) have been successful elsewhere (see Oregon Coast), and it's just a matter of time before some firm solves the puzzle in CA. Canada's deployment of at least 1 EV charger per gas station up north in some fairly remote areas (e.g., 125 miles north of Edmonton) is impressive.
6. At $0.20/kW, few Model 3 owners who have home charging will use SCs instead of home charging - especially when they figure out the practical urban limitations upon range that can easily account for 30% less range and therefore 30% more cost for which to budget. As a result, those who don't have home charging will be quite vocal in getting it either at home or at the office or where they shop, work out, or eat. We already see this proliferation in the Beach Cities at grocery stores, gyms, restaurants and bars, along with office buildings.
7. Businesses will become more aware of HPWCs being a differentiator, not to mention SCs urban and otherwise - once they have them, their business shows up in the Nav - and that's worth money.
Limitations:
1. From an overall perspective, most of the non-Tesla fast chargers are singlets and that's just not practical for scale.
2. Neither CCS nor Chademo have emerged as the standard for fast charging yet. Rumor has it that CCS has the edge, and that's what the Chevy Bolt includes, but the Nissan Leaf has Chademo. Bleh.
Summary:
CA supercharging sites are in no danger of getting overrun by Model 3s anytime soon. Tesla has the capability to stay ahead of demand for a while yet.
The pain will be felt by Bolt and Leaf owners as their ranges increase. I already saw a brand new Bolt owner try to plug in at SpaceX and it was somewhere between comical and painful. Fortunately, the kindly but firm security guard who 86d the offending fellow did note that there were J-1772s quite nearby, and patiently directed him thereto.