Data-Driven Validation and Correction of the Distortion Factor Estimated from Current Total Harmonic Distortion Using Industrial Field Measurements

Abstract

In this study, the validity of the theoretical distortion factor based on total harmonic distortion of current (THDI) under industrial field conditions was evaluated, and low-complexity, data-driven correction models were developed to reduce formula error. The dataset was compiled from three-phase field measurements at 12 industrial measurement points. The measurement-based distortion factor was calculated from the PF/dPF ratio, while the theoretical distortion factor was calculated from the THDI-based equation. Since the phases at the same measurement point were not considered independent, the models were evaluated using a 12-cycle out-of-sample cross-validation method. The theoretical formula produced a mean absolute error of 0.015662, a root mean square error of 0.019681, and a mean bias of −0.009357. Among the compared models, restricted second-order regression produced the lowest error values, providing improvements of 31.83% and 15.70% in MAE and RMSE, respectively. Ridge regression, on the other hand, reduced the MAE to 0.012263 and brought the mean bias close to zero. However, the data-driven models did not reduce the maximum absolute error. At the measurement-point level, the Wilcoxon signed-rank test indicated lower paired errors after Ridge correction (P=0.0342), whereas the 95% bootstrap confidence interval for the mean paired MAE difference included zero. Taken together, these findings provide positive but limited evidence regarding the error-reduction potential of the Ridge correction. The results show that the THDI-based formula provides an interpretable initial estimate but cannot, on its own, account for field conditions such as phase asymmetry, load level, power factor, and voltage distortion. The proposed correction approach should be considered not as a universal formula but as an empirical calibration approach specific to the available field data.

Keywords

• Distortion factor
• Total harmonic distortion of current
• Power factor
• Industrial field measurements
• Ridge regression
• Out-of-measurement-point cross-validation

Ethical Statement

Ethics committee approval was not required for this study because the research did not involve human participants, human biological materials, animals, or animal experiments. The study was based on the analysis of previously collected industrial electrical measurement data.

Thanks

The authors would like to thank Aydemir Kalebek and Kayhan Kalebek for their technical support and contributions during the course of this study.

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