Parameters of 3D Fractal Dimension for a Population of Long Spark Discharges

Coordination insulation of transmission lines requires evaluation of voltage breakdown between live-to-live and live-to-earthed parts of the line conductors and the tower structure. Modeling work supports the design process, requiring experimental data for validation of the models to prove their relevance and accuracy. A fractal model has been proposed to embrace the statistical nature of the voltage breakdown in air. In this article, we offer a method of providing parameters of electrical discharges that can be implemented in the process of fractal model validation. We propose a 3D fractal dimension calculation applied to a population of a set of electrical discharges of a given type. We report using this approach for long spark discharges generated with 3.4 MV lightning impulse and 2.3 MV switching impulse in controlled laboratory conditions for Sphere-Sphere and Sphere-Plane electrode systems. The reported results show the ability of the proposed approach to perform classification of the types of discharges, making it suitable for validation of simulation models, which was not feasible with the so far reported 2D calculations performed for individual discharges.