Analysis of Errors in Active Power and Energy Measurements Under Random Harmonic Distortion Conditions

Abstract

As harmonic distortion of voltage and current is reality in the power system, the need for accurate measurement of electrical power and energy goes beyond the instruments’ specifications and calibration procedures regarding pure sine wave signals. Several international standards and recommendations provide test signals for examination of electricity meters under non-sinusoidal conditions, however, not all of the test signal parameters’ possible states are faithfully represented in those documents. Because the high order harmonics may possess random amplitudes and phase shifts in relation to components at fundamental frequency, it is important that the meter’s performance is verified with random waveforms as well. The non-linear dependence between the measured power/energy and the phase shifts, both between fundamental and harmonic components, provides additional complexity of such an analysis. Simple test signals, which are in accordance with the standards’ demands and propositions, are used for determination of the measurement error in case of different harmonic distortion parameter change. In order for a general error function for any measurement device to be determined, mathematical modelling, regarding the results from multiple tests, is performed. The mathematical model presents a strong dependence between a single component’s phase shifts and a meter’s error and it provides a systematization of all signal parameters’ influence on the measurement accuracy.

Active Power Measurement Uncertainty Budget Modelling in Case of Harmonically Distorted Voltages and Currents

“…Next, an analysis of the uncertainty intensity in active power measurement will be performed, regarding 2 different approaches. For the concrete performance, voltage and current signals with 230 V and 5 A RMS values and random harmonic distortion [3] are generated from CALMET C300 [14]. The single harmonics' share and phase shifts in relation to fundamentals are illustrated in Table 1.…”

“…The performance of power and electricity meters, in case of harmonically distorted signals, has been regarded in many scientific contributions [1][2][3][4][5][6]. Measurement errors have been analyzed in relation to different input influence quantities, such as:…”

“…• the disturbances duration [4], etc. Analysis have been conducted by using both test waveforms proposed in standards [7][8][9][10], as well as randomly distorted voltages and currents [1,3].…”

Refinement of the mathematical model of electrical energy measurement uncertainty in reduced load mode

“…In particular, in [4] a significant influence of the parameters of measuring transformers on the metering unit operation accuracy was determined, especially when the power factor of load changes. It was also experimentally found that the accuracy of electricity metering is reduced due to the non-sinusoidal nature of load [5], especially in the case of LED lighting [6]. A priori uncertainty estimates may significantly exceed actual values.…”

Reactive Power and Energy Instrument’s Performance in Non-Sinusoidal Conditions Regarding Different Power Theories

“…In the domain of active electricity meter testing, several international standards [4]- [6], a recommendation [2], and plenty of scientific works [7]- [14] exist, and therefore different examination protocols are established. In the EN 50470-3 standard [6], signals that possess the 5th order harmonics, beside fundamental voltages and currents, are proposed as test conditions for calibration of active electricity meters in non-sinusoidal environment.…”