What is Measurement Uncertainty?

When we do high precision measurements we have to make sure that we are getting the measurement results as accurate as possible.
First of all, the measurement instrument needs to be calibrated. Calibration is typically done in an external laboratory or in an ISO17025 accredited laboratory in your power company.
We make an example:
Your laboratory has calibrated a portable reference standard RS350. The report shows that the error of this instrument is in all ranges within ± 0.05%.

The error calculation was done with the formula:


The term "accuracy" tells us, how close the measurement is to the real value. In the above case with our RS350 we have an accuracy of ± 0.05%, also stated as accuracy class 0.05.

How wonderful, but:

What is the real value? The calibrator measurement is compared with the measurement with a better accuracy class. To calibrate a class 0.05 instrument you would use a class 0.02 instrument, e.g. a reference standard CL3115 or CL3112.
These reference standards are calibrated in external test houses or at National Metrological Institutes.
How can the National Metrological Institutes know that their measurements are accurate?
In fact, they don't know exactly.
Don't be scared, we are talking now about a few ppm (parts per million) deviation. To make sure that the measurements are worldwide within a acceptable and trustable range the national metrological institutes are participating in a ring comparison to evaluate how far the measurements of the same unit under test are away between the different countries.
Based on the average results each national institute gets it's own measurement uncertainty.
When reference standards are calibrated vs. the national reference, this measurement uncertainty needs to be taken into consideration together with additional measurement uncertainties.

This uncertainties can be systematic or random. A good example for a systematic uncertainty is the display resolution.
Let's say, your instrument has a resolution with two decimals and you read a power of 1.05 kW. This doesn't mean that your power is 1.05 kW, it means your power is within 1.045 kW and 1.054 kW. So in worst case your systematic uncertainty coming from display reading is 0.5% (Use the above formula to calculate.)
Yes, you are a smart metering specialist. You will always select the best range and the best resolution. So you switch to reading in watt. Now you see that you have 1048.54 W.
The real value will be between 1048.535 W and 1048.544 W. The systematic uncertainty is now 0.0005%.
You can play this endless, there will always be an uncertainty. But it's getting smaller and smaller. Best praxis for energy metering is to keep the overall measurement uncertainty below 1/5 of the unit under test.

Beside of display resolution you have to deal with several other uncertainty factors, like microprocessor speed for error calculation, temperature variation, terminal resistance, wrong cable cross section, human error in operation.

Having a precision measurement instrument with a given accuracy class does not mandatory mean that your test results are right.
More information you can find in the GUM (Guides to the expression of uncertainty in measurement).

What about meter test benches?

Also a test bench has a measurement uncertainty. This uncertainty comes from reference standard resolution, error calculators, power resolution and accessories which are not covered by the reference standard, e.g. ICTs (isolated current transformers) and MSVTs (multi secondary voltage transformers).
As we are energy meter manufacturer we have to focus on measurement uncertainties as part of our quality control. The typical measurement uncertainty for a single-phase test bench is 0.02% (reference conditions and power factor 1).

What about energy meters?

Energy meters should be calibrated with enough margin to cover measurement uncertainties. In CLOU production we have set the PASS threshold on 40% of the accuracy class. Means a meter class 1 will have a maximum error of ±0.4% upon delivery. This assures that the meters will pass a test at any test laboratory worldwide as long as it has a valid accreditation.

Note that this post is extremely simplified. Be always aware that there are factors which can make your test results less accurate. Try to minimize this factors or limit your acceptance criteria. Our meter test software EMS5 can help you.
Thank you for reading.

Editor's note: This article was originally published in February 2020 and has been updated for comprehensiveness.

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