I have no knowledge of Tesla's algorithm. I have however written a few algorithms.
I don't know if this helps, but here is how I look at the discharge behavior. If you discharged the solar directly to the grid, you would get credit for 1kWh at off peak, or mid-peak rates. If instead, you put 1.1kWh into your Powerwall, you will get back 1.0kWh for later use or export.
- If the Powerwall discharge algorithm misses discharging 1.0 kWh at peak, it is one peak kWh of missed credit/income, that day, and the Powerwalls start the next day up 1 kWh. (Undershoot)
- If the discharge algorithm and your usage align, you end up at your reserve with no carry over. (Ideal case)
- If the discharge algorithm overshoots, and your demand draws a peak kWh that is later offset, the total loss is one NBC+any other noncreditable charges, I.e. small additional cost. (Minimal cost overshoot)
- If the discharge algorithm overshoots, and your demand draws a peak kWh that is not later offset, the total loss is 1 peak kWh. (Full overshoot cost)
#4 is only really "knowable" at the end of the net metering year.
In the first case, sooner or later, the algorithm will catch on to the fact that the battery is increasingly full, and ought to trend toward case #2. In the third and fourth cases, the algorithm ought to back off on the discharge for the next day(s). A well designed algorithm for the user, ought penalize #3 and #4 more heavily than #1. A well designed algorithm ought to have some sense of your historical usage patterns (daily, weekly, semifixed N day usage pattern, etc...), to average out past usage, and anticipate future usage. The operative word here being "ought". Normal variation in usage is always going to push/pull the algorithm into one bin or the other. How the algorithm designer weights things in the algorithm determines how much weight recent history and recent settings influence current behavior. The choice on weighting isn't simple, but I would bet that most owners have some sort of seven day pattern that is dominant, and that the pattern changes with seasons and weather.
A simple but greedy algorithm would just do the opposite of yesterday, and you would endlessly cycle around the right behavior. A good one would split the difference. A better one would look at yesterday, and compare where it was in the owner's daily cycle, and adjust accordingly. An even better one might look at microclimate history and forecasts for the owners location... in the end, the issue becomes weighting the relative factors.
From the outside, there is no way of knowing how simple or complicated Tesla's black box algorithm is, and therefore how long one should wait after changing settings for behavior to stabilize, or even if it would ever settle into stable behavior for any given user. (Imagine the usage swings for an AirBnB house...) To make things worse, Tesla is probably comparing the algorithm performance over many users, and changing it, while you are also changing things, with real potential to get way off target.
I think that if case #3 is problematic for you, then it is probably best addressed by daily adjustment of the discharge. An algorithm is never going to know that the person behind you in line at the store barfed all over you, and you suddenly are doing extra laundry, heating more water and using the dryer during peak times.
Personally, guessing that the algorithm has some "knowledge" of weeks, I would give the algorithm at least several weeks between changing the settings, and then I would change the settings only by small increments.
YMWV...
All the best,
BG