kA^2s

   "If the derived unit is A²s, then 1000 A²s = 1 kA²s."

This interpretation appears to be what the standard intended. For the 1300 A peak value, a let-through of 1600 A²s implies a duration of a few milliseconds, given that the current will be less than the peak during most of the time. This time is consistent with the clear intention that there is current-limiting protection.

And this interpretation also looks consistent with conventions for multiplied symbols, where RI² is the same as R(I²) but not (RI)².

 

However ... contentious claim coming up ... it's wrong!

It is, of course, just a convention how we write things. If the IEC wants to define that prefixes are used as above, it can do so. But I don't think the IEC or any other standards organization really would claim that they agree with that use. Two reasons:

1.   It's not consistent with some other cases, such as mm². If we followed the above interpretation, then 1 mm² would be 0.001 m², which is the area of a circle of about 36 mm diameter. There would be no need to worry about unevenly distributed loading on a 32 A ring-socket circuit with 2.5 mm² copper conductors, if using that sort of mm². But terminations would be difficult, as that's nearly the biggest conductor area found in single-core transmission cables: it's 2500 of the real mm².

2.  I find it unlikely that IEC/ISO/etc would choose to go against the normal rules of the SI system. The 'custodian' of SI units is BIPM, the Bureau International des Poids et Mesures. Its document "The International System of Units (SI)" has instructions and examples about prefixes, on page 143: "The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or sub-multiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.". It goes on to give examples, including ones similar in principle to the above point about mm².

So, having written kA, it is the whole kiloampere that is affected by an exponent such as the squaring. In the style of the quotation above, "the prefix 'kilo' is attached to the unit 'ampere' to form a new inseparable unit symbol 'kiloampere' that can be raised to the power of two and combined with the unit 'second' to form a compound unit symbol".

That is:    1 kA²s = 10⁶ A²s.

It's unlikely that the standard's misuse of a prefix will actually cause confusion, as a difference by a factor 1000 is hard not to notice. It's been there for decades, and there must be tens of millions of devices in use that didn't pass the tests prescribed by the standard, even if they passed the tests that were doubtless intended. I only noticed this issue when taking I²t values from several manufacturers' specifications, one of which used 'k' instead of a number. For the future, I'd advise using 10³ A²s, in order to be clear and correct.

   "If the derived unit is A²s, then 1000 A²s = 1 kA²s."

This interpretation appears to be what the standard intended. For the 1300 A peak value, a let-through of 1600 A²s implies a duration of a few milliseconds, given that the current will be less than the peak during most of the time. This time is consistent with the clear intention that there is current-limiting protection.

And this interpretation also looks consistent with conventions for multiplied symbols, where RI² is the same as R(I²) but not (RI)².

 

However ... contentious claim coming up ... it's wrong!

It is, of course, just a convention how we write things. If the IEC wants to define that prefixes are used as above, it can do so. But I don't think the IEC or any other standards organization really would claim that they agree with that use. Two reasons:

1.   It's not consistent with some other cases, such as mm². If we followed the above interpretation, then 1 mm² would be 0.001 m², which is the area of a circle of about 36 mm diameter. There would be no need to worry about unevenly distributed loading on a 32 A ring-socket circuit with 2.5 mm² copper conductors, if using that sort of mm². But terminations would be difficult, as that's nearly the biggest conductor area found in single-core transmission cables: it's 2500 of the real mm².

2.  I find it unlikely that IEC/ISO/etc would choose to go against the normal rules of the SI system. The 'custodian' of SI units is BIPM, the Bureau International des Poids et Mesures. Its document "The International System of Units (SI)" has instructions and examples about prefixes, on page 143: "The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or sub-multiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.". It goes on to give examples, including ones similar in principle to the above point about mm².

So, having written kA, it is the whole kiloampere that is affected by an exponent such as the squaring. In the style of the quotation above, "the prefix 'kilo' is attached to the unit 'ampere' to form a new inseparable unit symbol 'kiloampere' that can be raised to the power of two and combined with the unit 'second' to form a compound unit symbol".

That is:    1 kA²s = 10⁶ A²s.

It's unlikely that the standard's misuse of a prefix will actually cause confusion, as a difference by a factor 1000 is hard not to notice. It's been there for decades, and there must be tens of millions of devices in use that didn't pass the tests prescribed by the standard, even if they passed the tests that were doubtless intended. I only noticed this issue when taking I²t values from several manufacturers' specifications, one of which used 'k' instead of a number. For the future, I'd advise using 10³ A²s, in order to be clear and correct.