Capacity of Charging Stations Using an Erlang-B Model

Cottonwood over on TMC applied the Erlang-B model to Tesla SuperChargers which I found very interesting. Make sure you read his subsequent post as well where he estimates which stations need to have more SuperChargers added.

If you're not familiar with the Erlang-B model, it is used in the telephony world to predict how many customers will encounter a busy circuit given an average call length and maximum number of concurrent calls.

In the EV world, a "call" is a charging session.

What I found interesting is how low the utilization or efficiency rate of a single station is if you want to avoid unnecessary blocking and how much more efficient the group of stations becomes as you add more stations. This has always been my gut feeling, but I didn't know there was an actual formula for it.


This is just another data-point that really highlights how Tesla gets it. By installing stations at fewer locations but installing more of them (and they typically install 6-8 plugs), they maximize the efficiency of their SuperChargers and minimize potential delays customers might experience plugging in. Also, the fact that two plugs share a single SuperCharger stack also nicely fits in with the ~50% efficiency factor.

I don't know about the rest of you, but one worry I always have when going on a trip that requires QC is that I'm going to find someone else using the spot (or worse finding the station out of order). But if there were more than one QC per location, even if both were in use, your wait time would likely be significantly reduced.

I've only QCd about 10 times. But two of those times I had to wait to use the station.

If you assume a blocking rate of 20%, here's what the capacity/efficiency looks like:
Adding a second plug quadruples your capacity and more than doubles your efficiency. It's a no-brainer. You are much better off installing 2 20-25 kW QC stations over a single 45-50 kW station even with the reduction in charge rate. Why don't Nissan or any of the major charging networks understand this? I think Blink may have been the only other company to realize this as at least they have dual-plug stations (even if they only charge sequentially) and always seemed to install at least 2 if not 3-4 L2 stations at a location.

Interesting, thanks. I'll pass this on to my DOT contacts, as they're investigating install sites.

One drawback to having fewer sites is they're only useful if you're going that way, no matter how efficient they are.

A broader spread of single QCs gives you more options, if they're usable. Multiple plugs at each would be my preference too, but then there's the cost.

I think it could be improved in two ways.

Network managers could analyze the usage data, adding units and plugs at locations that show back to back sessions.

Or, if ever QCs become as ubiquitous as gas stations, the shear volume of them would alleviate the problem. That, and longer range cars, would be ideal.

It's only a matter of time, and the ball's rolling fast enough now that we won't be stuck in the Stone Age too much longer.

Connecticut seems to be doing this as they install QC's at their highway service plazas. So far, each plaza has received/will receive 2 CHAdeMO units. However, the downside is that they're only installing the stations at one of the two plazas, so for I-95 in Darien they're on the Southbound side of the highway only, and for the Merritt Parkway in Greenwich they're going to be on the Northbound side only. Part of me would rather see one station in each direction to save myself the time and trouble of getting off the highway and backtracking just to get a charge, but I definitely see the benefits of having 2+ QCs in one spot. The ultimate solution is going to be to install stations in both directions, of course...

DNAinaGoodWay said:

One drawback to having fewer sites is they're only useful if you're going that way, no matter how efficient they are.

A broader spread of single QCs gives you more options, if they're usable. Multiple plugs at each would be my preference too, but then there's the cost.

Click to expand...

Yeah, obviously the Erlang-B model doesn't perfectly fit charging infrastructure usage. For example, sites that are close enough together such that either may be used could probably be considered a single location, as in NYLEAF's example in CT.

But even in NYLEAF's example, I still think that having two stations close to each other is better than a single station on either side of the freeway as it gives you immediate visibility on the availability of each station.

Imagine if both are busy - are you going to drive back and forth until one opens up?

Or imagine that the stations are a few miles apart - you may decide to venture on to the other station if the first is busy, but then what if the second station is busy, too?

Yes, cost is an issue, but with Nissan's less expensive hardware the biggest cost is still trenching and hookup. With multiple stations in a single spot, you get economies of scale that you simply can't get otherwise.

In urban areas especially, L2 stations should also be considered, especially with 30A charging becoming common (Chargepoint dual head CT4000s are great here). If a site is busy you may be stuck 30 minutes waiting for a QC to open up with a total wait time of 40-45 minutes, but with 30A charging that may get you enough to your next destination as you can pick up 20 mi charge in that same amount of time.