Statistical and topological characterization of PD defects

The dynamic evolution of partial discharges (PDs) is nonlinear and chaotic in nature. This means that although a PD has a definite governing principle which dictates its evolution, it may behave in an apparently random manner due the existence of nonlinearity. Analyzing the PD process entails considering a PD as a dynamical system. As the PD process evolves, it marks a trajectory in the state-space which is attracted to a specific region. This region of the the state-space is called the attractor. Distinct PD defects have distinct dynamics of evolution which result in a unique structure for PD attractors. In this paper, two methods of characterizing PD attractors are discussed. The first method relates to the statistical or the metric characterization of the PD attractor which attempts to describe the structure of the attractor in metric terms. The topological characterization aims at evaluating the topological invariants of the system, which describe the geometry of the attractor.