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<p>This study presents an advanced framework for harmonic analysis in three-phase systems based on differential geometry principles. The proposed method employs the Frenet frame to geometrically represent voltage and current waveforms as spatial curves, establishing a consistent foundation for power computation under unbalanced and dynamically changing conditions. Compared to conventional approaches such as Clarke and Park transforms, this framework demonstrates improved accuracy in handling asymmetrical operating scenarios. The methodology is validated through extensive simulation using ERPI-DOE test signals, confirming its robustness and computational efficiency. The outcomes highlight the potential of the proposed approach to enhance power quality assessment and strengthen control strategies in modern power converter systems.</p>

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Differential geometry-based harmonic analysis of three-phase systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月17日

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  • Nitin Sundriyal,
  • Padmanabh Thakur,
  • Ashutosh Dixit,
  • Sandeep Gupta,
  • Mukesh Kumar

摘要

This study presents an advanced framework for harmonic analysis in three-phase systems based on differential geometry principles. The proposed method employs the Frenet frame to geometrically represent voltage and current waveforms as spatial curves, establishing a consistent foundation for power computation under unbalanced and dynamically changing conditions. Compared to conventional approaches such as Clarke and Park transforms, this framework demonstrates improved accuracy in handling asymmetrical operating scenarios. The methodology is validated through extensive simulation using ERPI-DOE test signals, confirming its robustness and computational efficiency. The outcomes highlight the potential of the proposed approach to enhance power quality assessment and strengthen control strategies in modern power converter systems.