Time-varying probabilistic models for incipient fault in underground cables

The incipient faults in underground cables are mainly caused by cable insulation failure, defects in splices, and water penetration. Incipient fault modeling is essential to ensure the algorithms' performance and accuracy in detecting incipient faults or generating data under various conditions. This article aims to create and develop a robust yet practical model for incipient faults by considering actual recorded data. Experimental records derived from a laboratory setup are used in the models' identification procedure. Considering that there is no arc model for the incipient fault in underground cables, this article concentrates on driving effective models based on Schwarz equations for incipient fault using actual recorded data. Three modified Schwarz models for modeling the voltage and current of incipient faults in cables are presented. In the proposed models, the idea of time-varying parameters is used to show the time-varying properties of incipient faults. The models' parameters are updated using the least squares method for each cycle of power frequency. The best order of each model is determined using two error indices. Since the model parameters change in every cycle, probability distribution functions (PDFs) were used to show the stochastic behavior of the parameters. As a result, several PDFs are examined for every set of the model's parameters, and the one that best fits the actual data is selected.