Characterizing the Harmonic Measurement Accuracy of Voltage Transformers: The Role of the Number of Test Waveforms

Assessing the accuracy of instrument transformers in measuring harmonics has paramount importance in the context of modern distribution grids. Nevertheless, the relevant standards do not provide a reference procedure. It is well-known that a mere frequency response measurement is not able to fully characterize their metrological behavior in the presence of nonlinearity. An attractive approach is based on theory of the best linear approximation that, for a given class of realistic test signals, estimates the optimal complex-valued ratio for reconstructing primary side harmonic phasors. Moreover. it quantifies the scattering of the resulting reconstruction error due to nonlinearity, expressed in terms of its standard deviation.The target of this paper is studying the impact of the number of excitation signals on the trustworthiness of the characterization. In this framework the estimated optimal complex-valued ratio and the standard deviations of the reconstruction error are modeled as random variables, whose probability distributions are related to the cardinality of the set of test waveforms. Expressions of their standard deviations are derived, so that the user may easily verify wether the characterization complies with a predetermined accuracy target, or if more waveforms have to be applied. The proposed approach is applied, through numerical simulations, to a realistic model of voltage transformer.