An analysis of Supercharging strategies

[KarenRei]

Out of curiosity, I wrote a program to model potential Tesla supercharging strategies, relative to the current "first come, first serve" - particularly with respect to how they might differ as charger powers and numbers of stalls changes. It's set for a "near future" scenario where 65% of vehicles at SCs are Model 3s, 20% are Model S and 15% are Model X (with a further breakdown of battery types and charge rate limitations therein). Vehicles arrive at various charge states - usually low - and charge to some higher charge state - usually over half, but usually not to 100%. Just basically tried to keep it realistic. I had it maintain a level of "business" such that around 1 in 10 vehicles would have to wait for a stall. Arrival rates follow a gaussian distribution. A total of 400000 vehicles were run through the system for each config.

I had charger powers and per-stall power grow with the number of stalls. For each combination:

2 stalls, 145kW total power, 117kW stall power:

• First come, first served: Time=(Avg=34.0m, Stdev=20.4m), kW=(Avg=85.3, Stdev=25.6)
• Last come, first served: Time=(Avg=35.2m, Stdev=23.2m), kW=(Avg=85.4, Stdev=26.5)
• Lowest max charge power, first served: Time=(Avg=35.5m, Stdev=22.8m), kW=(Avg=84.6, Stdev=26.5)
• Highest max charge power, first served: Time=(Avg=34.0m, Stdev=20.6m), kW=(Avg=85.4, Stdev=24.8)
• Fewest kWh remaining to charge, first served: Time=(Avg=35.0m, Stdev=21.4m), kW=(Avg=83.8, Stdev=26.0)
• Most kWh remaining to charge, first served: Time=(Avg=34.4m, Stdev=22.2m), kW=(Avg=86.1, Stdev=24.7)

4 stalls, 220kW total power, 154kW stall power:

• First come, first served: Time=(Avg=35.9m, Stdev=23.2m), kW=(Avg=86.5, Stdev=36.2)
• Last come, first served: Time=(Avg=37.9m, Stdev=28.6m), kW=(Avg=88.8, Stdev=38.7)
• Lowest max charge power, first served: Time=(Avg=38.1m, Stdev=27.7m), kW=(Avg=87.7, Stdev=39.4)
• Highest max charge power, first served: Time=(Avg=35.7m, Stdev=24.1m), kW=(Avg=87.4, Stdev=34.5)
• Fewest kWh remaining to charge, first served: Time=(Avg=37.2m, Stdev=24.2m), kW=(Avg=84.8, Stdev=36.7)
• Most kWh remaining to charge, first served: Time=(Avg=36.6m, Stdev=27.8m), kW=(Avg=89.8, Stdev=36.2)

6 stalls, 280kW total power, 182kW stall power:

• First come, first served: Time=(Avg=39.0m, Stdev=25.3m), kW=(Avg=81.2, Stdev=37.2)
• Last come, first served: Time=(Avg=40.3m, Stdev=32.2m), kW=(Avg=87.8, Stdev=41.6)
• Lowest max charge power, first served: Time=(Avg=40.4m, Stdev=30.7m), kW=(Avg=86.8, Stdev=42.4)
• Highest max charge power, first served: Time=(Avg=38.8m, Stdev=27.4m), kW=(Avg=83.1, Stdev=35.3)
• Fewest kWh remaining to charge, first served: Time=(Avg=39.6m, Stdev=25.9m), kW=(Avg=81.4, Stdev=38.0)
• Most kWh remaining to charge, first served: Time=(Avg=39.6m, Stdev=32.8m), kW=(Avg=88.1, Stdev=39.3)

8 stalls, 333kW total power, 204kW stall power:

• First come, first served: Time=(Avg=41.6m, Stdev=26.6m), kW=(Avg=76.8, Stdev=37.3)
• Last come, first served: Time=(Avg=42.7m, Stdev=35.3m), kW=(Avg=86.2, Stdev=43.6)
• Lowest max charge power, first served: Time=(Avg=42.7m, Stdev=33.3m), kW=(Avg=85.2, Stdev=44.5)
• Highest max charge power, first served: Time=(Avg=41.5m, Stdev=30.2m), kW=(Avg=79.8, Stdev=35.7)
• Fewest kWh remaining to charge, first served: Time=(Avg=42.2m, Stdev=27.3m), kW=(Avg=77.5, Stdev=38.7)
• Most kWh remaining to charge, first served: Time=(Avg=42.3m, Stdev=37.1m), kW=(Avg=86.7, Stdev=41.5)

Summary:
Perhaps it shouldn't be surprising, but Tesla's strategy of "first come, first served", appears to be the best. It provides for both short charging times and a low standard deviation (aka, it's generally "fair"). Its success generally holds out to the other scenarios tested (although there could exist other scenarios where it might not fare as well). A close contender is "highest max charge power, first served". The option "Fewest kWh remaining to charge, first served" is better performing than average (except in the 2-stall case), but not spectacular. Other options are generally unappealing.

Code is attached below in case anyone wants to play with it. I wrote it in English so it would be understandable

 

[ewoodrick]

Interesting math, a few things

If you have 10% of the cars having to wait for charging, then how would the other scenarios work? My thoughts would be that you would generally need 5+ cars waiting for a model such as "lowest charge first" to make any difference. After all, if there is no wait time (90% of the time) then the other algorithms don't really come into play.

You have a breakdown for Model 3 vs the other cars. I'm assuming that this is somewhat a guess from estimated sales? I don't think that it includes that most Model 3s don't have free charging, so they are less likely to use Superchargers.

And somewhat along the same lines, I think that there are some very different Supercharger profiles. A Supercharger at a delivery center has a very different utilization than one along an Interstate. And some California Superchargers have very different profiles than those in other cities. A lot of California Superchargers are used as "daily" chargers by folks without home charging.

But I think that Tesla's intent is to make this a non-issue, by providing enough capacity to handle the non-home charging requirements.

 

[KarenRei]

Interesting math, a few things

If you have 10% of the cars having to wait for charging, then how would the other scenarios work? My thoughts would be that you would generally need 5+ cars waiting for a model such as "lowest charge first" to make any difference. After all, if there is no wait time (90% of the time) then the other algorithms don't really come into play.

You have a breakdown for Model 3 vs the other cars. I'm assuming that this is somewhat a guess from estimated sales? I don't think that it includes that most Model 3s don't have free charging, so they are less likely to use Superchargers.

And somewhat along the same lines, I think that there are some very different Supercharger profiles. A Supercharger at a delivery center has a very different utilization than one along an Interstate. And some California Superchargers have very different profiles than those in other cities. A lot of California Superchargers are used as "daily" chargers by folks without home charging.

But I think that Tesla's intent is to make this a non-issue, by providing enough capacity to handle the non-home charging requirements.

By all means fiddle with the config to try other wait time / vehicle mix / etc settings! And yes, all mixes of vehicle are guestimates, and to a lesser extent some of the charging curves are as well (although they're based on the real data I could come across with some quick searching). Charging curves are a simplistic model - a plateau (of variable length) followed by a linear decline to a couple kW at 100%. The peaks are commonly set at higher powers than can be currently achieved, on vehicles that are presumed capable of handling higher charge rates if superchargers offered more power per stall (since part of the whole point was to test how different approaches would perform in various potential future supercharger configurations)

I expect that - particularly with the ongoing Model 3 surge - that soon most superchargers will have roughly the same usage profile, with Tesla building more stations wherever lines are appearing (or may soon appear). Currently underutilized superchargers will become increasingly utilized the more Teslas there are on the road.

 

[Brando]

If I remember correctly, the UW=University of Washington, did a study to determine the best strategy for web-server response times (and to maximize throughput). First In - First Out won the day.