Integral value is incorrect when max_sub_interval less than sensor update interval

[gagara]

The problem

I have sensor which is updated every 15 sec (instant value of the power produced by solar inverter)
If I create left Riemann integral helper with max_sub_interval=20sec then everything works fine. Calculated integral value is correct (I can confirm this by comparing with the value calculated by solar inverter itself)
But if I use max_sub_interval=10sec then calculated integral is incorrect. Usually it is x2 greater.
It feels like it is calculated twice in this case. i.e. time based calculation happens every 10 sec (because sensor is updated every 15sec) and then usual calculation happens in 5sec when updated value for sensor arrives.
If it is expected behavior then probably doc should explicitly say that max_sub_interval should not be less that update interval of the sensor?

What version of Home Assistant Core has the issue?

2025.2.4

What was the last working version of Home Assistant Core?

No response

What type of installation are you running?

Home Assistant OS

Integration causing the issue

No response

Link to integration documentation on our website

No response

Diagnostics information

No response

Example YAML snippet

Anything in the logs that might be useful for us?

Additional information

No response

[home-assistant]

Hey there @dgomes, mind taking a look at this issue as it has been labeled with an integration (integration) you are listed as a code owner for? Thanks!

Code owner commands

Code owners of integration can trigger bot actions by commenting:

• @home-assistant close Closes the issue.
• @home-assistant rename Awesome new title Renames the issue.
• @home-assistant reopen Reopen the issue.
• @home-assistant unassign integration Removes the current integration label and assignees on the issue, add the integration domain after the command.
• @home-assistant add-label needs-more-information Add a label (needs-more-information, problem in dependency, problem in custom component) to the issue.
• @home-assistant remove-label needs-more-information Remove a label (needs-more-information, problem in dependency, problem in custom component) on the issue.

_{^{(message by CodeOwnersMention)}}

---

integration documentation
integration source
_{^{(message by IssueLinks)}}

[dgomes]

Please share your configuration

Could you provide detailed graphs of your test cases ? 20sec vs 10sec

[gagara]

Yes. Sure. Here is graph of integral helpers:

Here is the source sensor which is used by integrals (updated every 15 sec):

Config for 10s integral:

Config for 20s integral:

[dgomes]

The max_sub_interval was introduced for use cases in which source sensor doesn't update often and the source sensor is predictable (things such as resistive loads, e.g. lamps) and therefore this integration makes "assumptions" (which I believe are bad, and expressed myself against this option)

When you use max_sub_inteval of 20sec and your sensor update every 15sec, basically means this function never kicks in (it is not used)

When you go below 15sec, then you start seeing this behaviour.

Last word: with a sensor that updates so frequently, you will get better results with trapezoidal, as this is what it was designed for.