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In recent years, the buffer layer ablation failures of high voltage cables are frequently reported by the power systems. Previous studies have dominantly regarded the buffer layer as the continuous homogeneous medium, whereas neglects its microstructures. In this paper, the current distribution within the random fiber networks of buffer layer are investigated. Experiment results of our self-designed platform revealed an uneven current distribution in buffer layer at the moment of bearing current. This phenomenon is named as the intrinsic current concentration where the current density concentrates at certain sites inner the buffer layer. And the degree of current concentration will be suppressed by compressing the sample. Then, a 2D simulation model of the random fiber networks was constructed based on the Mikado model. The simulation results also presented an uneven current distribution in the networks whose every fiber can be viewed as a micro-resistor. Two types of dimensionless current concentration factors were defined to describe the degree of current concentration, finding their values decreasing with the rise of fiber density. Meanwhile, it is equivalent of compressing the buffer layer and increasing the fiber density of model. We believe that the intrinsic current concentration phenomenon is mainly related with the inhomogeneity of geometry structure of buffer layer. The ablation traces and fracture fibers observed by the X-ray micro-computed tomography test supported this point. In addition, the non-ideal surface of sample can also induce this phenomenon. The intrinsic current concentration can aggravate the degree of originally existed macroscopic current concentration in cables, thus causing the ablation failure. Our work may unveil a deeper understanding on the cable ablation failure and the electrical response of the similar fibrous materials.