**5. Experimental Validation**

In this section, we present the results of an experimental validation carried out on the selected DUT, i.e., the ZERA WM3000I. This is intended as an experimental validation of the proposed calibration method as well as of its main uncertainty contributions in controlled laboratory testing conditions, as typical of metrological institute activities. In the following tables, the reported uncertainty takes into account both the calibration setup contribution and the statistical dispersion of the measurements of the device under test. For the sake of readability, a ceiling to the last significant digit has been applied.

For this analysis, we set the nominal frequency, current range and transformer ratio equal to 50 Hz, 5 A and 1:1. Otherwise differently stated, the signals at *N*- and *X*-channel consist of single-tone sinusoids, whose frequency, amplitude and initial phase are set equal to 50 Hz, 5 A, and 0 rad, respectively. In the following tests, such parameter values are suitably modified in order to reproduce different configurations of excitation, ratio and phase error, and thus span the entire operating range of the measuring bridge.

To this end, a total of 27 different configurations are taken into account. Each test has a duration of 5 min, including 1 min of settling time to allow for the proper stabilization of the current output of the transconductance amplifier. For each of the monitored quantities, 11 consecutive measurements are taken and their average and standard deviation values are employed to determine the corresponding measurement errors and uncertainties (In the presence of outliers, single measurements could be neglected. In this sense, the outlier detection criterion is based on the assumption that the measurements are normally distributed. Given a set of 11 measurements, if a single measurements differs from the average value by more than three standard deviations, its value is discarded from the computation of measurement errors and uncertainties). In more detail, the reported uncertainties for the excitation and ratio error, and for the phase displacement are obtained by merging the contributions of the calibration setup with the Type A uncertainty of the measuring bridge results.

For the sake of comparison, Table 2 reports the WM3000I specifications in terms of accuracy for the current measurement on the *N*-channel, the ratio error and the phase displacement. As previously observed, the excitation error in non-conventional mode descends directly from the accuracy of the measured *IN* amplitude, as the *IX* amplitude depends only on quantization and numerical errors whose impact on the overall uncertainty can be considered as negligible.


**Table 2.** Specifications of the measuring bridge under test.

In this context, Table 3 reports the measurement results in the presence of ratio and phase errors. For this analysis, the ratio error is varied within ±5% and the phase displacement is set in such a way to consider small offsets (e.g., ±10 ), large offsets (e.g., ±5400 ), and nearly phase opposition conditions (e.g., 10, 794 ) (Such variations have been obtained by modifying the content of the SV data packets, as the digital channel is characterized by lower uncertainty contributions. Nevertheless, similar results could be obtained by keeping unaltered the SV data packets and suitably modifying the current source flowing through the standard transformer).

The two phenomena are investigated both independently and simultaneously. In this way, it is possible to evaluate whether the measuring bridge is affected by any of the error source or by their combination.

As the excitation is kept equal to 100%, it is worth noticing as the measuring bridge exhibits an excitation error perfectly in line with its specifications and the uncertainty does not exceed 200 ppm. Similar considerations apply for ratio error and phase displacement. In this case, it is interesting to notice how Δ*ε* and Δ*ϕ* do not exhibit any dependence on the test setting.

**Table 3.** Characterization of the measuring bridge performance in the presence of ratio errors and phase displacements (coverage factor *k* = 2).


In Table 4, we report the measuring bridge errors and uncertainties in the presence of different excitation levels. For this analysis, we modified the *N*-channel current in such a way that the measuring bridge senses an excitation between 1 and 200%. Once more, the excitation error and the corresponding uncertainty are in line with the previous considerations. As regards ratio error and phase displacement, it is worth noticing how both measurements and uncertainties present a rapid increase as the excitation falls below 5%. Nevertheless, it is reasonable to expect that, in the presence of lower current levels, the accuracy of the internal sensors as well as the SNR decrease and the corresponding computations are affected by larger errors and uncertainties. Similar considerations hold also for the digital counterpart. The SV data format has a fixed range and number of bits: as a consequence, when transmitting low-amplitude signals, there is an inefficient exploitation of the 32 bits and the resulting estimates are likely to be affected by higher relative uncertainty.


**Table 4.** Characterization of the measuring bridge performance in the presence of different excitation levels (coverage factor *k* = 2).

The specific device under test provides a useful extra feature, i.e., a representation of the current flowing in the *N*-and *X*-channel as rotating vectors characterized in terms of RMS amplitude, phase, and frequency. The estimation accuracy of the first two parameters has been already investigated in the previous tables, but the frequency (particularly, the one of the *N*-channel) requires a separate investigation. To this end, we characterized the frequency measurements in the presence of different excitation levels and phase displacements. For the sake of consistency, the variation ranges of *E* and *ϕ* correspond to the ones applied in Tables 3 and 4.

In this context, Table 5 reports the measurement results and the associated uncertainty. It is worth noticing how the frequency error Δ*f* is quite stable around −0.54 mHz with a worst-case uncertainty of 0.06 mHz (when the excitation is set to its minimum value, i.e., 1%). In this case, the instrument specifications do not provide a performance target. Nevertheless, the obtained measurement accuracy is sufficient for the typical application of a measuring bridge for instrument transformers.


**Table 5.** Characterization of the measuring bridge frequency estimation accuracy in the presence of different excitation levels and phase displacements (coverage factor *k* = 2).
