PostgreSQL window function: Add value in CASE running sum gets below threshold

For context:

I am playing with a filling level sensor, a water tank and a watering pump and have the following problem:

1. I have an initial filling value for my tank.

2. Each time step, I am subtracting a certain amount (the outflow) from this init value via a window function, in order to get a time series with the filling level.

3. Should that running sum get below a lower threshold, it gets "refilled" to an upper threshold for the refill.

4. From there, I want to keep subtracting until it hits the lower value again, then refill, etc.

5. I would like to sum up the refill amount over the series

Something like the following:

Image may be NSFW.
Clik here to view.

Assuming I start from 10, and refill from 5 as lower limit to 8 as upper limit. The table should look something like this, with running sum being the amount of water in the tank, refill_amount as the amount that was needed to refill, and/or refill_running_sum to get a final, total amount for refilling:

 time_step | running_sum | refill_amount | refill_running_sum   | ----------+-------------+---------------+----------------------|            1          10             0                 0               2           9             0                 0               3           8             0                 0               4           7             0                 0               5           6             0                 0               6  -  -  -  5  -   -   -  3  -   -   -   -  3  -  --refill      7           8             0                 3               8           7             0                 3               9           6             0                 3               10 -  -  -  5  -   -   -  3  -   -   -   -  6  -  --refill           11          8             0                 6              12          7             0                 6               13          6             0                 6               14 -  -  -  5  -   -   -  3  -   -   -   -  9  -  --refill           15          8             0                 9         

I got as far as the SQL below dbfiddle here:

Using a CASE statement, I get to refill the amount once and get the first amount of water to refill. But I would need a CTE with a case for every single refill.

Apologies as I know I'm missing SQL vocabulary here to properly approach this. Yet thank you for any pointers!

    /* Generate some mockup series with init+threshold limits */     WITH vals AS (         SELECT             generate_series(1,30,1) AS time_step            ,10 AS init_val            ,8 AS upper_limit_refill            ,5 AS lower_limit_refill            ,random() AS random_val    ),     /* Create the window function subtracting a mockup val */    example_series AS (         SELECT             *               ,init_val-sum(random_val) OVER(ORDER BY time_step ASC) AS running_amount        FROM vals    )    SELECT         time_step        ,running_amount        /* I manage to get the amount needed to refill ONCE, but I'd need a new CTE and CASE for each refill like this*/        ,CASE             WHEN running_amount < lower_limit_refill             THEN upper_limit_refill +  running_amount -sum(random_val) OVER(ORDER BY time_step ASC  ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING)             ELSE 0         END AS refill_once        ,CASE             WHEN running_amount < lower_limit_refill             THEN upper_limit_refill - running_amount            ELSE 0         END AS refill_to_limit_amount    FROM example_series