Why the fault current equation does not include the transformer impedance and upstream 400V impedance?

In principle it should (BS 7671 talks about the impedance of 'the source' (411.4.4) which would include the windings and a proportion of the upstream impedances). It's often approximated to 'the transformer winding' on the assumption that the HV side of the national grid has in effect an almost infinite amount of power available to it, so the effective impedance is negligibly low and due to the step-down effect of the transformer the effect of impedances on the primary side is less Ohm for Ohm than on the secondary side.  BTW the 400V/230V designation is referring to the star arrangement of the secondary windings - 230V L-N but 400V between different lines - the primary voltage is usually far far higher - typically 11kV or 33kV in the UK - so the turns ratio is quite large.

If you had a small transformer (e.g. one for 110V tools) fed from the LV system, you'd certainly need to take account of the upstream impedances and %age impedance of the transformer to get anything like accurate results.

I suspect what you're seeing is a textbook example of what happens in schools - first teaching a simplified version and only later adding in a few complexities. (Like at primary school 'you can't take a larger number away from a smaller number'; but in secondary school saying, that's not quite right and introducing negative numbers).

   - Andy.

Seconded - the (hidden) assumption is that the transformer is a high power unit, capable of providing a short circuit current so high that it's extra impedance is small enough to be safely ignored.

That is probably true if it is a megawatt sized lump sitting on the ground, as the voltage drop at the transformer at normal full load will be a few percent ( full load currentt is 1MW/ 3 per phase = 330000watts at 230V - call it  1.4kA per phase) , so at your 3kA fault, your assumption that 115V is dropped in the phase, 115V in the CPC needs to be corrected to more like 100V in the CPC , 100V in the phase, and the transformer output droops from 230V to more like something between 200 to 210 volt or so, for the short time until the fault  clears.

In terms of touch voltage, the risk is more or less the same so the simpler estimation method is good, and by over-estimation, errs on the side of safety in any case.

Of course if the transformer was a 'pole-pig' 50kVA unit on a wooden pole at the end of a long HV line to a small place in the country, then the  transformer impedance would be 20 times higher and very noticeable, and the voltage droop on the primary 11kV supply line may also have a noticeable  effect and for a truly complete model all this really needs to be included.

Do you need a complete model, or just one that gives an estimate erring on the side of safety ?

Mike

Seconded - the (hidden) assumption is that the transformer is a high power unit, capable of providing a short circuit current so high that it's extra impedance is small enough to be safely ignored.

That is probably true if it is a megawatt sized lump sitting on the ground, as the voltage drop at the transformer at normal full load will be a few percent ( full load currentt is 1MW/ 3 per phase = 330000watts at 230V - call it  1.4kA per phase) , so at your 3kA fault, your assumption that 115V is dropped in the phase, 115V in the CPC needs to be corrected to more like 100V in the CPC , 100V in the phase, and the transformer output droops from 230V to more like something between 200 to 210 volt or so, for the short time until the fault  clears.

In terms of touch voltage, the risk is more or less the same so the simpler estimation method is good, and by over-estimation, errs on the side of safety in any case.

Of course if the transformer was a 'pole-pig' 50kVA unit on a wooden pole at the end of a long HV line to a small place in the country, then the  transformer impedance would be 20 times higher and very noticeable, and the voltage droop on the primary 11kV supply line may also have a noticeable  effect and for a truly complete model all this really needs to be included.

Do you need a complete model, or just one that gives an estimate erring on the side of safety ?

Mike