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Specific on and off charging

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Not from the car, no. Tesla doesn't seem to understand, or care, about a short window of off-peak charging.
I used Ev.energy app until few months ago... but seem don't work anymore (at least for me). If smart charging is on, the charging will not start. Contacted the support without any solution.
So, for now set to start from the car/app at 00.30 and adjust the % limit (in my case 40% of charge for 4h)
 
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You can do it in the app!
  1. On the Charge Stats page, scroll down and hit settings
  2. Choose Home (as you can now set rates and tarrifs for Home, Work and Other)
  3. Fill in the details about tarrif name etc. When you get to the page that has Seasons/Time of use, select just time of use
  4. In here, you can set the peak hours and the cost
  5. Now back in the main app menu, check schedule and enable off-peak charge
You car should only charge off peak when at home. You can override it by hitting charge now in the app or in the car.
 
My method is just set the start time of your off peak in the car or app… you never have to touch it again.

Each time you want to charge just bear in mind how much percentage you can add in the off peak slot. About 40% for a 3 LR or 56% for an older SR+. Only need to alter your set percentage (using the app) if you see it won’t fit in the time available.

The advantage of this method is that you can always get as much charge as as you essentially need for the next day… because it will just run over into peak on those few occasions when you need more. With a fixed start and stop time you can only get 28kW for 4 hrs and that won’t always be enough. We have flaky mains out in the sticks and if the rate drops there is the danger I could fail to reach my set percentage if I had a fixed stop/start.
 
Which app? Don’t see that in the Tesla app.
Yep, Tesla app.

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You can do it in the app!
  1. On the Charge Stats page, scroll down and hit settings
  2. Choose Home (as you can now set rates and tarrifs for Home, Work and Other)
  3. Fill in the details about tarrif name etc. When you get to the page that has Seasons/Time of use, select just time of use
  4. In here, you can set the peak hours and the cost
  5. Now back in the main app menu, check schedule and enable off-peak charge
You car should only charge off peak when at home. You can override it by hitting charge now in the app or in the car.
I'm pretty sure the Scheduled departure Off Peak charging is not related to the settings in the Charge Stats. When you enable Off Peak it asks you when your off peak period ends, and then will start whenever it needs in order to reach your desired SoC by that time, it has no concept of a start time.

The only way to keep charging to a narrow window like Octopus Go are

1. Manually choosing the target charge each night
2. A third party app like TeslaFi etc. to send a stop charging command
3. All new EV chargers now are required to provide start and stop periods

I'm using 3. with a first get EO Mini and it works well, the only downside it that the charger won't provide power at other times e.g. preconditioning unless I go into the app and tell it.