Impact of External Distortion Sources on Harmonic Voltage Profiles of Consumers
DOI:
https://doi.org/10.25729/esr.2026.01.0004Keywords:
Distortion, harmonics, power quality, short-circuit power, linear load, nonlinear loadAbstract
The study assesses how nonlinear electrical loads of external consumers connected at the point of common coupling impact the electrical installation of a small-scale enterprise. The nonlinear electrical load of the traction substation is considered as an external nonlinear load while the electrical installation of the enterprise represents a low-capacity consumer. The developed analytical expressions enable the assessment of external distortion impacts, considering the network short-circuit power at various points, along with the nonlinear and linear load of the low-capacity consumer represented by induction motors. The study reveals that the linear load of the consumer under study has a significant shunting effect, reducing voltage harmonics from the nonlinear electrical load of external consumers. The findings also indicate that the voltage harmonic distortion factor scales with the nonlinear load power of the traction substation, which can be determined using the derived analytical expressions. The introduced criterion enables a preliminary evaluation of the harmonic level, characterized by the ratio of the short-circuit power at the transformer secondary to the transformer capacity. The analytical calculation results showed strong agreement with the MATLAB/Simulink simulations.
References
H. A. Alashaary, G. N. Al Shaba’an, W. F. Abu Shehab, S. A. Ali, “Estimation of harmonic impedance and resonance in power systems,” Int. J. Electr. Comput. Eng., vol. 15, no. 1, pp. 67–75, 2025. DOI: 10.11591/ijece.v15i1.pp67-75.
A. N. Nazarychev, T. E. Minakova, M. V. Popov, “Results of research into interharmonics of traction electric drive systems for mining transport machines,” Gornaya Promyshlennost, vol. 1S, pp. 68–72, 2025. DOI: 10.30686/1609-9192-2025-1S-68-72. (In Russian)
L. I. Kovernikova, B. N. Hung, “Estimation of active power loss due to supraharmonics in a 22 kV transmission line,” Energy Syst. Res., vol. 7, no. 3, pp. 14–21, 2024. DOI: 10.25729/esr.2024.03.0002.
A. A. Belsky, V. V. Starshaia, J. E. Shklyarsky, “Enhanced energy efficiency of oil production using photovoltaic installation,” Int. J. Eng., vol. 38, no. 1, pp. 194–204, 2025. DOI: 10.5829/ije.2025.38.01a.18. (In Russian)
M. Jiménez Carrizosa, N. Stankovic, J.-C. Vannier, Y. Shklyarskiy, A. Bardanov, “Multi-terminal DC grid overall control with modular multilevel converters,” J. Min. Inst., vol. 243, pp. 357–370, 2020. DOI: 10.31897/pmi.2020.3.357.
Y. Yerbayev, I. Artyukhov, A. Zemtsov, D. Artyukhov, S. Molot, D. Japarova, V. Zakharov, “Negative impact mitigation on the power system of a fans group with frequency-variable drive,” Energies, vol. 15, no. 23, Art. no. 8858, 2022. DOI: 10.3390/en15238858.
S. Yanchenko, A. Kulikov, S. Tsyruk, “Modeling harmonic amplification effects of modern household devices,” Electr. Power Syst. Res., vol. 163, pp. 28–37, 2018. DOI: 10.1016/j.epsr.2018.05.021.
Yu. L. Zhukovskii, P. K. Suslikov, “Identification and classification of electrical loads in mining enterprises based on signal decomposition methods,” J. Min. Inst., vol. 275, pp. 5–17, 2025.
H. Hua, H. Gao, L. Gao, H. Guo, “A novel method for calculating harmonic contribution based on difference recurrence estimation,” IET Gener. Transm. Distrib., vol. 18, no. 3, pp. 596–608, 2024. DOI: 10.1049/gtd2.13097.
Z. Jin, H. Zhang, V. Terzija, “An embedded estimator for online harmonic monitoring in power-electronic grids,” IEEE Trans. Smart Grid, vol. 13, no. 6, pp. 4677–4689, 2022. DOI: 10.1109/TSG.2022.3186341.
M. H. Jopri, M. A. Ghani, A. Abdullah, T. Sutikno, M. Manap, J. Too, “Naïve Bayes and linear discriminate analysis based diagnostic analytic of harmonic source identification,” Indones. J. Electr. Eng. Comput. Sci., vol. 20, no. 3, pp. 1626–1633, 2020. DOI: 10.11591/ijeecs.v20.i3.pp1626-1633.
V. Y. Bazhin, Y. V. Ustinova, S. N. Fedorov, M. E. K. Shalabi, “Improvement of energy efficiency of ore-thermal furnaces in smelting of alumosilicic raw materials,” J. Min. Inst., vol. 261, pp. 384–391, 2023.
N. Korolev, “Analytical diagnostic and control system of energy and mechanical efficiency of electric drives,” Energies, vol. 18, no. 9, Art. no. 2266, 2025. DOI: 10.3390/en18092266.
Y. Li, Y. Sun, K.-J. Li, K. Sun, Z. Liu, Q. Xu, “Harmonic modeling of the series-connected multipulse rectifiers under unbalanced conditions,” IEEE Trans. Ind. Electron., vol. 70, no. 7, pp. 6494–6505, 2023. DOI: 10.1109/TIE.2022.3203747.
D. Fallows, S. Nuzzo, A. Costabeber, M. Galea, “Harmonic reduction methods for electrical generation: a review,” IET Gener. Transm. Distrib., vol. 12, no. 13, pp. 3107–3113, 2018. DOI: 10.1049/iet-gtd.2018.0008.
P. Lingom, E. Agamloh, A. von Jouanne, A. Yokochi, J. Song-Manguelle, R. Unruh, “Comparison of phase-shifted and phase-disposition PWM schemes in an asymmetrical cascaded H-bridge converter,” in 2024 IEEE Energy Conversion Congress and Exposition (ECCE), Phoenix, AZ, USA, 20–24 October 2024, pp. 3494–3499. DOI: 10.1109/ECCE55643.2024.10860878.
H. A. Mohamed, “Approach method to evaluate the total harmonic distortion for a system has multiple nonlinear loads,” Int. J. Eng. Res., vol. 4, no. 11, pp. 618–624, 2015. DOI: 10.17950/ijer/v4s11/1109.
I. Papic, et al., “A benchmark test system to evaluate methods of harmonic contribution determination,” IEEE Trans. Power Deliv., vol. 34, no. 1, pp. 23–31, 2019. DOI: 10.1109/TPWRD.2018.2817542.
T. V. Ancharova, M. A. Rashevskaya, E. D. Stebunova, “Power supply and electrical equipment of buildings and structures,” 2nd ed. Moscow, Russia: FORUM: INFRA-M, 2024, 415 p. Available: https://znanium.ru/catalog/product/2078400. Accessed on: Mar. 24, 2026. (In Russian)
V. A. Shpenst, A. A. Belsky, E. A. Orel, “Improving the efficiency of autonomous electrical complex with renewable energy sources by means of adaptive regulation of its operating modes,” J. Min. Inst., vol. 261, pp. 479–492, 2023.
L. I. Kovernikova, B. N. Hung, “Additional power losses under non-sinusoidal conditions in a 22 kV overhead power line,” Energy Syst. Res., vol. 7, no. 1, pp. 31–36, 2024. DOI: 10.25729/esr.2024.01.0003.
D. A. Ustinov, I. I. Rastvorova, A. E. Polivanov “Up-to-date methods of distributed generation optimization,” Gornyi Zhurnal, no. 9, pp. 1–8, 2025. DOI: 10.17580/gzh.2025.09.03. (In Russian)
Q. Shu, Y. Fan, F. Xu, C. Wang, J. He, “A harmonic impedance estimation method based on AR model and Burg algorithm,” Electr. Power Syst. Res., vol. 202, Art. no. 107568, 2022. DOI: 10.1016/j.epsr.2021.107568.
Q. Shu, T. Liu, F. Xu, “A new algorithm for calculating utility harmonic impedance,” Electr. Power Syst. Res., vol. 191, Art. no. 106893, 2021. DOI: 10.1016/j.epsr.2020.106893.
I. Tokarev, Y. Shklyarskiy, T. Pudkova, A. Nazarychev, “Determining the dependence of the electricity storage system parameters on the electrical load curve leveling degree,” Elektrichestvo, no. 9, pp. 45–51, 2024. DOI: 10.24160/0013-5380-2024-9-45-51. (In Russian)
F. Xu, C. Wang, K. Guo, Q. Shu, Z. Ma, H. Zheng, “Harmonic sources’ location and emission estimation in underdetermined measurement system,” IEEE Trans. Instrum. Meas., vol. 70, Art no. 9003511, 2021. DOI: 10.1109/TIM.2021.3077658.
S. Yin, Y. Sun, Q. Xu, K. Sun, Y. Li, L. Ding, Y. Liu. “Multi-harmonic sources identification and evaluation method based on cloud-edge-end collaboration,” Int. J. Electr. Power Energy Syst., vol. 156, Art. no. 109681, 2024. DOI: 10.1016/j.ijepes.2023.109681.
D. A. Ustinov, A. R. Aysar, “Using artificial neural network methods to increase the sensitivity of distance protection,” Int. J. Eng., vol. 37, no. 11, pp. 2192–2199, 2024. DOI: 10.5829/IJE.2024.37.11B.06.
D. Vujatovic, K. L. Koo, Z. Emin, “Methodology of calculating harmonic distortion from multiple traction loads,” Electr. Power Syst. Res., vol. 138, pp. 165–171, 2016. DOI: 10.1016/j.epsr.2016.02.014.
G. Zhang, Y. Sheng, “Estimating time-varying parameters in uncertain differential equations,” Appl. Math. Comput., vol. 425, Art. no. 127084, 2022. DOI: 10.1016/j.amc.2022.127084.
R. Zhou, X. Ma, R. Xu, X. Xiao, J. Zhao, “Novel method for estimating utility harmonic impedance for a direct-drive permanent magnet synchronous generator wind farm,” IEEE Access, vol. 10, pp. 25872–25882, 2022. DOI: 10.1109/ACCESS.2022.3141312.
Electromagnetic compatibility (EMC) – Part 3–6: Limits. – Assessment of emission limits for the connection of distorting installations to MV, HV and EHV power systems, IEC TR 61000-3-6, Ed. 2.0, 2008.
V. B. Yurievich, N. T. Hien, “Stochastic pulse-width modulation and modification of direct torque control based on a three-level neutral-point clamped inverter,” Energies, vol. 17, no. 23, Art. no. 6017, 2024. DOI: 10.3390/en17236017.
N. Koteleva, N. Korolev, “A diagnostic curve for online fault detection in AC drives,” Energies, vol. 17, no. 5, Art. no. 1234, 2024. DOI: 10.3390/en17051234.
I. V. Blagouchine, E. Moreau, “Analytic method for the computation of the total harmonic distortion by the Cauchy method of residues,” IEEE Trans. Commun., vol. 59, no. 9, pp. 2478–2491, 2011. DOI: 10.1109/TCOMM.2011.061511.100749.
K. Shao, M. Zhao, J. Zheng, G. Zeng, B. Li, B. Ma, Z. Wu, “A high-precision harmonic distortion measurement algorithm and its system design based on time-domain matrix operations,” J. Phys. Conf. Ser., vol. 2290, no. 1, Art. no. 012109, 2022. DOI: 10.1088/1742-6596/2290/1/012109.
Y. Zhukovsky, P. Suslikov, “Assessment of the potential effect of applying demand management technology at mining enterprises,” Sustain. Dev. Mt. Territ., vol. 16, no. 3, pp. 895–908, 2024. DOI: 10.21177/1998-4502-2024-16-3-895-908. (In Russian)
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Energy Systems Research

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
