Enhanced Kopplin models for incipient faults in underground power cables

Abstract

The incipient faults (IFs) in underground power cables (UPCs) are primarily caused by insulation failure in power cables, defects in splices, and water penetration. IF modeling is crucial for generating data under various conditions to ensure the performance and accuracy of algorithms in IF detection. This paper aims to establish and develop a robust yet practical model for IFs, utilizing real data. Practical records obtained from a laboratory are utilized in the process of identifying the models. Although many papers have been presented on arc modeling in other applications, none have been dedicated to modeling the IF in UPCs, except for two papers published by the authors of this paper. However, this paper presents the third model based on the time-varying property of the IF. This paper focuses on developing effective models based on Kopplin equations. Therefore, two modified Kopplin models are presented for modeling the IFs, and both proposed models demonstrate exemplary performance in modeling this fault. In the proposed models, the concept of time-varying coefficients is employed to illustrate the time-varying properties of IFs. Also, the new approach in this study, which utilizes the Levenberg-Marquardt algorithm, updates the model coefficients for each cycle. Finally, for robustness, the proposed models were evaluated using two error indices, which yielded low error indices. Since the model coefficients change in every cycle, to demonstrate their stochastic behavior, probability distribution functions (PDFs) were employed. Consequently, for every set of models’ coefficients, several PDFs are tested, and the PDF with the best match to real data is selected.