by Fred Steinhauser, OMICRON electronics GmbH, Austria
Calculators and computer programs process the numbers we feed them to their numerical capacity and deliver results with many decimal digits. But depending on the context, the results need some reasonable polishing to make sense. However, this post-processing of the results is all too often omitted.
On a sign promoting a PV power project, a figure for the annual CO2 savings was shown. It was in the order of 100 tons, but it was not properly expressed as such an estimate. The value was given as a 6-digit number in kilograms, with all the digits populated without trailing zeroes. This made it obvious that those who wrote this did not understand how much restricted they were when estimating the related figures. When looking for the CO2 savings per kWh produced from PVs, the figures vary between 0.5 and 0.8 kg/kWh. The numbers for the energy harvested per year from a given area of solar panels vary in a similar wide range. So, even giving just two non-zero leading digits in the result suggests an accuracy that may not apply. Whatever the calculator had spit out after poking in some chosen values for the mentioned input parameters was taken as the result without further consideration.
This leads to the concept of significant figures that account for the uncertainties within a measurement processes. This concept is at least well understood in the context of precision electronic multimeters, where the achievable uncertainty and the resolution are usually sensibly aligned, comprehensively described, and also (hopefully) well understood by the users.
In software displaying such results on a computer screen, this is often not implemented so consistently. A fixed number of digits after the decimal point is more common. But even when the measurement chain starts with a class 0.1 instrument transformer, the pieces must be carefully kept together to make the fourth digit of a measurement really significant. So, while a reading of 1.234 V makes pefect sense in this case, 123.456 V does not.
On the other hand, there are cases where the number of digits and their accuracy are the core of the matter. In 1748, Leonhard Euler published that he had calculated the number e to 23 decimal places, also stating that even the last digit was “consistent” (constentanea.)
He showed how he could calculate the formerly only vaguely known value up to a chosen precision. But this is a mathematical/numerical context, not practical engineering.
As one of the last ones who learned how to use a slide rule, I still foster nostalgic feelings for this, although I exclusively used electronic calculators ever since they became available. The slide rule demanded an involvement in the calculation process that unfortunately got lost since we have these electronic gadgets. When calculating with the slide rule, you had to be very careful to preserve 3 significant digits, and you always had to be aware of the order of magnitude of the results by yourself. Because, when the slide rule gave you, e.g. 832, you still had to know if this meant 0.832, 8.32, or 83.2. Brainlessly copying a figure was not an option, you were always forced to think and to make sure that the result makes sense.
Something we should still do today
Biography:
Fred Steinhauser studied Electrical Engineering at the Vienna University of Technology, where he obtained his diploma in 1986 and received a Dr. of Technical Sciences in 1991. He joined OMICRON and worked on several aspects of testing power system protection. Since 2000 he worked as a product manager with a focus on power utility communication. Since 2014 he is active within the Power Utility Communication business of OMICRON, focusing on Digital Substations and serving as an IEC 61850 expert. Fred is a member of WG10 in the TC57 of the IEC and contributes to IEC 61850. He is one of the main authors of the UCA Implementation Guideline for Sampled Values (9-2LE). Within TC95, he contributes to IEC 61850 related topics. As a member of CIGRÉ he is active within the scope of SC D2 and SC B5. He also contributed to the synchrophasor standard IEEE C37.118.
