Online Monitoring Method for Transformer Winding Deformation Based on Three-Dimensional Lissajous Curves
Xinyu Yue1, Zhenhua Li1,2,*, Zhenxing Li1, Tao Zhang1, Yanchun Xu1, Xiaozhen Zhao3
1 College of Electrical Engineering and New Energy, China Three Gorges University, Yichang, China
2 Hubei Provincial Engineering Research Center of Intelligent Energy Technology, China Three Gorges University, Yichang, China
3 State Key Laboratory of Intelligent Power Distribution Equipment and System, Hebei University of Technology, Tianjin, China
* Corresponding Author: Zhenhua Li. Email: 
Energy Engineering https://doi.org/10.32604/ee.2026.077395
Received 08 December 2025; Accepted 26 February 2026; Published online 18 March 2026
Abstract
Winding deformation is a predominant cause of transformer failures and critically compromises the safe, reliable, and economic operation of power systems. To overcome the inadequacy of the conventional three-dimensional (3D) Lissajous curve method in discriminating among various types of winding faults, this paper proposes an online monitoring method for transformer winding deformation based on 3D Lissajous curves. In the proposed method, the primary current
di1(t)/dt, the derivative of the primary current
di1(t)/dt, and the voltage difference between the primary and secondary sides
Δu(t) are adopted as the coordinate axes to construct 3D Lissajous curves. Through simulation modeling, the variation patterns of the curve shape characteristics are qualitatively analyzed under both sinusoidal and non-sinusoidal (including harmonic) excitation conditions. Furthermore, by integrating covariance matrix analysis with adaptive particle swarm optimization (APSO), characteristic parameters corresponding to different fault types are extracted and subsequently input into a support vector machine (SVM) for fault classification and identification. Simulation results demonstrate that the proposed method achieves a fault classification accuracy of 98.15% and exhibits high classification stability under diverse operating conditions. This study presents a novel technical approach for online monitoring and fault-type discrimination of transformer winding deformation.
Keywords
Power transformer; winding deformation; online detection; characteristic graph method
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