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Volume 19
Issue 18
10.3390/en19184455
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Article

Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids

by
Junchi He
1,
Chenlei Li
2,
Shaofan Gu
1,
Shoujiang He
1,
Shouhua Pan
1,
Wenjing Xu
1,
Fei Ren
1,
Fan Xu
1,
Jintao Yu
3,
Xianglong Gu
3 and
Xiaozhen Zhao
3,4,*
1
State Grid Guanyun Power Supply Company, Lianyungang 222000, China
2
Jiangsu Electric Power Company, Nanjing 210024, China
3
State Key Laboratory of Smart Power Distribution Equipment and System, Hebei University of Technology, Tianjin 300401, China
4
Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300401, China
*
Author to whom correspondence should be addressed.
Energies 2026, 19(18), 4455; https://doi.org/10.3390/en19184455 (registering DOI)
Submission received: 23 August 2026 / Revised: 12 September 2026 / Accepted: 15 September 2026 / Published: 20 September 2026
(This article belongs to the Special Issue Advances in Diagnostic Analysis, Strategic Management, and Proactive Maintenance of Electrical Equipment—2nd Edition)
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Abstract

The methodological innovation of this study is a phase-domain separation-and-recombination framework that maps harmonic voltage to prospective flux, maps controlled quasi-DC winding current to magnetic operating-point displacement, and then resolves their nonlinear interaction through a shared-yoke three-limb model. A reduced nonlinear model informed by the measured major loops of a 50 kVA, 10 kV/400 V, Yyn0 transformer is evaluated over breaker-command angle and residual-flux sweeps. The operating matrix contains a sinusoidal baseline, a 0.15 p.u. negative-sequence second harmonic, a 0.08 p.u. negative-sequence fifth harmonic, their simultaneous application, and single-phase or asymmetric DC-current commands. Peak current, cycle-envelope decay, current total harmonic distortion, negative-sequence ratio, and a fourth-order three-phase current norm distinguish instantaneous from sustained stress. At the 60° command angle, the baseline, harmonic, DC-biased, and combined peaks are 21.30, 32.19, 35.15, and 41.67 A, respectively. Harmonic phase and sequence shift the knee-crossing instant and the dominant limb, whereas differential DC injection compresses one-directional saturation margin. The interaction contrast is interpreted as a model-output non-additivity statistic rather than an independent physical coupling constant. The conclusions are limited to the modeled distorted-source and differential-bias conditions; absolute prediction requires transformer-specific transient validation.
Keywords: transformer energization; magnetizing inrush current; harmonic voltage; DC bias; residual flux; coupling index transformer energization; magnetizing inrush current; harmonic voltage; DC bias; residual flux; coupling index

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MDPI and ACS Style

He, J.; Li, C.; Gu, S.; He, S.; Pan, S.; Xu, W.; Ren, F.; Xu, F.; Yu, J.; Gu, X.; et al. Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids. Energies 2026, 19, 4455. https://doi.org/10.3390/en19184455

AMA Style

He J, Li C, Gu S, He S, Pan S, Xu W, Ren F, Xu F, Yu J, Gu X, et al. Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids. Energies. 2026; 19(18):4455. https://doi.org/10.3390/en19184455

Chicago/Turabian Style

He, Junchi, Chenlei Li, Shaofan Gu, Shoujiang He, Shouhua Pan, Wenjing Xu, Fei Ren, Fan Xu, Jintao Yu, Xianglong Gu, and et al. 2026. "Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids" Energies 19, no. 18: 4455. https://doi.org/10.3390/en19184455

APA Style

He, J., Li, C., Gu, S., He, S., Pan, S., Xu, W., Ren, F., Xu, F., Yu, J., Gu, X., & Zhao, X. (2026). Influence of Harmonic and DC-Bias Coupling on Transformer Energization Inrush Current in Complex Power Grids. Energies, 19(18), 4455. https://doi.org/10.3390/en19184455

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