Inaccuracy in arc power calculation through a product of voltage and current averages

Abstract

AbstractPower is an indirect measurand, determined by processing voltage and current analogue signals through calculations. Using arc welding as a case study, the objective of this work was to bring up subsidies for power calculation. Based on the definitions of correlation and covariance in statistics, a mathematical demonstration was developed to point out the difference between the product of two averages (e.g. P = $$\overline{U} x \overline{I}$$ U ¯ x I ¯ ) and the average of the products (e.g. P = ($$\overline{UxI}$$ UxI ¯ ). Complementarily, a brief on U and I waveform distortion sources were discussed, emphasising the difference between signal standard deviations and measurement errors. It was demonstrated that the product of two averages is not the same as the average of the products, unless in specific conditions (when the variables are fully correlated). It was concluded that the statistical correlation can easily flag the interrelation, but if assisted by covariance, these statistics quantify the inaccuracy between approaches. Finally, although the statistics' determination is easy to implement, it is proposed that power should always be calculated as the average of the instantaneous U and I products. It is also proposed that measurement error sources should be observed and mitigated, since they predictably interfere in power calculation accuracy.