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# what is true I^2*t Algorithm ?

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I am curious what the real algorithm is for integrated current limit.

According to documentation it is a running sum of the difference between square of commanded current and square of continuous current limit, and when this sum exceeds a value set by the user, it trips.

This implies that if commanded current is always lower than the continuous current limit, then the new value in the sum is always negative, and eventually the value will saturate as a large negative number.

Therefore, it will take longer to trip from this condition then it should based on the physics. For example, if the average current is 99% of the continuous limit, eventually the register will saturate negative, yet the motor at this point is close to it's thermal limit (as continuous current limit is typically defined as the current required to raise the temperature to its continuous limit), and won't take long to overheat if the current goes to 101% of limit.

I am guessing that the real algo is more complicated, or am I missing something? The actual algo has a big impact on how to set the values for max benefit.

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The integrated sum never goes below zero. That's the only complication you missed.
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So, mathematically speaking, the algorithm is in essence:

Sum = Sum + greater of (0 or I^2-continuous limit^2)

so that only when the current is greater than the continuous limit is it integrated?

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I guess I wasn't clear enough. I'll put it in mathematical terms as well:

Sum[n] = Sum[n-1] + (I^2 - Icont^2) * DeltaT

If Sum[n] < 0 then Sum[n] = 0

If Sum[n] > Limit then Fault

You can observe the running sum in the Watch window to see how it works. Define:

M158->D:\$DA,0,24 ; Motor 1 integrated current

This is in the same units as the I158 limit.

Thank you.
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