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Article

A Method for Extracting Characteristic Parameters of Frequency Domain Dielectric Spectroscopy of Oil-Paper Insulation Using Modified Cole–Cole Model

by
Raheel Ahmed
1,
Liu Ji
2,*,
Zhang Mingze
3 and
Muhammad Zahid Hammad
4
1
School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China
2
State Key Laboratory Breeding Base of Dielectrics Engineering, Harbin University of Science and Technology, Harbin 150080, China
3
Key Laboratory of Engineering Dielectrics and Its Application Ministry of Education, Harbin University of Science and Technology, Harbin 150080, China
4
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150009, China
*
Author to whom correspondence should be addressed.
Electronics 2025, 14(13), 2656; https://doi.org/10.3390/electronics14132656
Submission received: 30 May 2025 / Revised: 23 June 2025 / Accepted: 23 June 2025 / Published: 30 June 2025
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Abstract

To quantitatively describe the frequency domain spectroscopy (FDS) characteristics of transformer oil-paper insulation under varying temperature, moisture, and aging conditions, a modified Cole–Cole model is introduced. This model decomposes the dielectric spectrum into polarization, DC conduction, and hopping conduction components, with parameters reflecting insulation characteristics. Methods for determining initial parameter values and optimizing the objective function are proposed. Using a three-electrode setup, FDS measurements were conducted on oil-paper insulation samples at different temperatures, and extracted parameters were analyzed for their variation patterns. Within the frequency range of 1.98 × 10−4 Hz to 1 × 103 Hz, the model achieves a goodness-of-fit (R2) exceeding 0.97 for both real and imaginary permittivity components, with the sum of squared errors reduced from 259 to 57.35 at 70 °C, outperforming the fundamental Cole–Cole and Ekanayake’s models. Temperature significantly affects the relaxation and DC conductivity components; both adhere to the Arrhenius equation, enabling precise condition assessment of transformer insulation.
Keywords: characteristic extraction; Cole–Cole model; complex relative permittivity; condition assessment; frequency domain spectroscopy; oil-paper insulation characteristic extraction; Cole–Cole model; complex relative permittivity; condition assessment; frequency domain spectroscopy; oil-paper insulation

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MDPI and ACS Style

Ahmed, R.; Ji, L.; Mingze, Z.; Hammad, M.Z. A Method for Extracting Characteristic Parameters of Frequency Domain Dielectric Spectroscopy of Oil-Paper Insulation Using Modified Cole–Cole Model. Electronics 2025, 14, 2656. https://doi.org/10.3390/electronics14132656

AMA Style

Ahmed R, Ji L, Mingze Z, Hammad MZ. A Method for Extracting Characteristic Parameters of Frequency Domain Dielectric Spectroscopy of Oil-Paper Insulation Using Modified Cole–Cole Model. Electronics. 2025; 14(13):2656. https://doi.org/10.3390/electronics14132656

Chicago/Turabian Style

Ahmed, Raheel, Liu Ji, Zhang Mingze, and Muhammad Zahid Hammad. 2025. "A Method for Extracting Characteristic Parameters of Frequency Domain Dielectric Spectroscopy of Oil-Paper Insulation Using Modified Cole–Cole Model" Electronics 14, no. 13: 2656. https://doi.org/10.3390/electronics14132656

APA Style

Ahmed, R., Ji, L., Mingze, Z., & Hammad, M. Z. (2025). A Method for Extracting Characteristic Parameters of Frequency Domain Dielectric Spectroscopy of Oil-Paper Insulation Using Modified Cole–Cole Model. Electronics, 14(13), 2656. https://doi.org/10.3390/electronics14132656

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