Capacity of Superchargers Using an Erlang-B Model

[Cottonwood]

I'm not sure i understand why you think 10-12 stalls are better than 2 stations with 6 stalls maybe 30 or 40 miles apart. The later would appear to offer a lot more flexibility depending on where people come from and go to.

Can you explain the logic (or likely, the math)?

In terms of total charging capacity without significant queues (less than 2% chance), 1 Supercharger with 12 stalls has an average usage of 6.6 cars charging at once, but 2 Superchargers each with 6 stalls have an average usage of 2.25 at the same 2% queue chance. That means that 2 Superchargers with 6 stalls each, have an average capacity of 4.5 cars charging, while the single Supercharger with 12 stalls has a capacity of 6.6. That gives the single 12-stall Supercharger 47% better capacity than the two 6-stall Superchargers.

It's very similar to waiting for a bank teller. There are smaller total queues and the average wait time is less if there is one queue for two tellers than if each teller has its own queue. On top of that, I am sure that it is cheaper for Tesla to build 1 12-stall Supercharger than to build 2 6-stall Superchargers.

OTOH, convenience and flexibility are very important, but once there are enough spaced out for convenience and flexibility, the busy ones have to have enough stalls. That is why the Superchargers in Lusk and Gallup have 4 stalls while Gilroy and Centralia have 10 stalls. In hindsight, Tesla should have outfitted Hawthorne with 10 or 12 stalls, but the showcase, Space-X location just does not have much room left. Hopefully, the extra dot near Hawthorne on the "coming soon" map will be online soon and have a lot of stalls.

 

[David99]

Hawthorne and Fremont are always the two top used SC on Tesla's usage display. Both of them get about twice to three times as much usage as the others in the top ten list. I have been at Hawthorne many times. The problem there in the past few weeks has been broken stalls. 80% of the time I was there up to three stalls (of a total of 6) where coned off or just not working. When all stalls were available I never had to wait. The Supercharger usage monitor also shows that they are used more on weekends, less on weekdays. So I'm not sure how useful a theoretical model is to calculate capacity.

We should also keep in mind that if there are 6 cars at a SC with 6 stalls, we already have extra waiting time because of power being shared.

 

[rcc]

I was Hawthorne a couple of weeks ago charging on a weekday. Charged twice. Day 1 - no waiting. Day 2, had to wait behind 2 other cars but was able to start charging within 10 minutes. Both times 1 stall was out.

Not sure how much of the demand was from locals charging and how much was out of towners charging because destination charging in their part of LA was uncertain or unavailable. I know at least one other car besides myself fell into the latter category.

 

[Cottonwood]

Hawthorne and Fremont are always the two top used SC on Tesla's usage display. Both of them get about twice to three times as much usage as the others in the top ten list. I have been at Hawthorne many times. The problem there in the past few weeks has been broken stalls. 80% of the time I was there up to three stalls (of a total of 6) where coned off or just not working. When all stalls were available I never had to wait. The Supercharger usage monitor also shows that they are used more on weekends, less on weekdays. So I'm not sure how useful a theoretical model is to calculate capacity.

We should also keep in mind that if there are 6 cars at a SC with 6 stalls, we already have extra waiting time because of power being shared.

The Erlang model works based on an average service rate and random arrivals, independent of time of day or time of week. The average capacity vs queue probability applies whether it is 5 pm on Friday or 2 am on Sunday. What will distort the numbers is a non-random arrival rate, like a convoy of cars all arriving together.

More Supercharger Cabinets and Stalls will always help, it's just a matter of how much. Also, more power (120 kW, 135 kW, etc) makes the sharing less of an issue.

The real problem that I had at Hawthorne was figuring which stalls are paired. I could not find any labels. Last time I was there, I was the third car to arrive with six stalls working. My first choice of stalls was power limited and had to guess which of the other three empty stalls was not paired with another car. I took an educated guess, had a two out of three chance, got lucky, and moved to a stall with full power.

 

[David99]

The real problem that I had at Hawthorne was figuring which stalls are paired. I could not find any labels. Last time I was there, I was the third car to arrive with six stalls working. My first choice of stalls was power limited and had to guess which of the other three empty stalls was not paired with another car. I took an educated guess, had a two out of three chance, got lucky, and moved to a stall with full power.

I'm in the same boat. Once I moved my car 4 times to find the best charging speed. I believe two adjacent ones share one SC. No matter what stall, I never got more than 100 kW in Hawthorne. That in itself slows down the charging progress and contributes to higher congestion probability.

Another big factor is educating drivers. I had one Model S owner going the same way as I. I knew I needed 150 miles to get to the next SC so that's all I charged up to. The other driver didn't know and charged another 30 min to get to 250 miles. I think many charge much more than they would need just because they don't know how much they really need.

 

[rcc]

I'm in the same boat. Once I moved my car 4 times to find the best charging speed. I believe two adjacent ones share one SC. No matter what stall, I never got more than 100 kW in Hawthorne. That in itself slows down the charging progress and contributes to higher congestion probability.

Another big factor is educating drivers. I had one Model S owner going the same way as I. I knew I needed 150 miles to get to the next SC so that's all I charged up to. The other driver didn't know and charged another 30 min to get to 250 miles. I think many charge much more than they would need just because they don't know how much they really need.

The real problem with Hawthorne is the lousy destination charging in some areas of LA. If you're going to be someplace in LA for a couple of days and aren't sure you'll have access to charging, it makes sense to charge at Hawthorne until you're full then go to your destination.

Similar problem in San Diego. The always-accessible HPWC's at the San Diego Trade Place Tesla Service Station was a lifesaver.

 

[Benjamin Brooks]

With all of the talk of queues at some Superchargers, see Interesting night at the Supercharger, I decided to see if there was available information that could let us see how close some of the existing Superchargers are to having queuing problems from over use, and then see if that correlates with TMC user observations.

I hope that someone at Tesla is tracking busy hour utilization and comparing that to Erlang models to stay ahead of capacity problems. All they need to do is track stall utilization as a function of time of day, day of week, special days, etc. to see when the Supercharger sites are starting to reach capacity. In addition, tracking full utilization times with short times between one car disconnecting and another connecting are good indications of a queue forming.

We don't have this info, but a few of us have taken a picture of the Hawthorne Supercharger Dashboard that shows total MWh usage by site in the last 30 days. Below is a picture that I took on March 12.
View attachment 45086


If I make some assumptions, I can get an estimate of busy hour usage and compare that to usage that would create a 2% blocking rate, the rate where short queues will occasionally form, or at the threshold of queues being annoying.

A few assumption/estimates: I will assume that the average power draw per stall is 60 kW. Telecommunications engineers have long used the rule of thumb that busy hour usage is 1/5 of average daily usage or a day's usage is the equivalent of 5 busy hours. The period for the Dashboard picture is 30 days. Multiplying these together says that a fully utilized stall will draw 9 MWh in a 30 day period.
View attachment 47507

If we fold this into the table at the start of this thread, we can calculate the energy usage in 30 days for a Supercharger at a busy hour blocking rate of 2% for various number of stalls available:
View attachment 47508

Now, if I read the actual 30-Day energy use from the March 12 Dashboard Picture above, we can compare that to 2% threshold usage. The last column displays that as a percentage ratio. More than 100% says the Supercharger is operating beyond a 2% blocking capacity.
View attachment 47509

Remember that this is all based on some pretty broad assumptions, but perhaps it can provide some insight to what is going on. Here are some of my interpretations. I would love to hear other thoughts.

• Hawthorne - This site is way over a threshold capacity. It is so far over capacity, I would expect more complaints. My guess is that its urban usage is really spread over more than 5 busy hours a day. At any rate, Tesla needs more stalls at Hawthorne and more Superchargers in the area very soon!
• Fremont - We don't hear much about queues at Fremont. I think this is because a lot of the use is the factory for new cars, and that use is spread over 16 hours a day.
• Gilroy - Good thing they have 10 stalls there!
• Oosterhoot - Getting close to capacity. What are observations from locals?
• Vacaville/Harris - Will need capacity in the future. Maybe Roseville will take some pressure off of Vacaville.
• Tejon - Are queues starting to appear on occasion?
• Folsom/Barstow - We know about many reported queues at Barstow. How is Folsom?

I think your calculations & analysis are fairly accurate. I've had to wait / seen queues at Fremont, Folsom, Harris Ranch, and Tejon Ranch over the past couple months. Haven't seen/experienced queuing at Gilroy since they went to 10 stalls.