inverse time relay

dspguide.com has a nice chapter on running average (and other filters).

Bye Jack

If this is what it sounds like (I've never heard of it before) you shouldn't need a precise running average, but instead can use a simple digital filter, equivalent to an RC circuit. The algorithm is something like

new_x = old_x * rc_constant + instantaneous_current

updated at some regular interval from a clock interrupt or the like.

Trip the relay if new_x goes above a certain threshold. Choose the rc_constant (a number slightly less than 1) so that the exponential decay time gives the interval that you want.

Your "rc_constant" variable isn't really analogous to an RC time constant

-- it's the pole of the difference equation in the z domain, but unless you know what that means the information isn't of much use.

Something that'll work much better is

new_x = old_x + some_gain * (instantaneous_current - old_x);

As long as some_gain is less than about 1/10, the real, honest-to-gosh time constant of this will be close to

tc = sampling_interval / some_gain

-- closer the lower that some_gain is.

If you use exactly the difference equation I give, then 'new_x' will be equal to the average current -- the equation that Paul gives will have a gain that depends on the 'rc_constant', which means that as you change 'rc_constant' you'll need to change the threshold.

Un bel giorno EnigmaPaul digitò:

It also depends on what you are protecting. If it is something that breaks for Joule effect, the best way would be to convert your I(t) curve into a I²t(t) curve, then integrate the I² value over time and trip when it reaches its limit, i.e. if calculated_I²t(t) > I²t(t) for any value of t, then trip.

There are also several sub-optimal algorithms. The easiest one is to consider the entire overcurrent event as if it had a constant value equal to the last value: you start a timer when the current goes past the "minimum" trip value, then you check if last_I(t) > I(t) for any value of t.