A 3-D numerical simulation of partial discharge acoustic wave propagation in a model transformer

In this paper, the authors present a three-dimensional numerical simulation of partial discharge (PD) acoustic wave propagation that has been developed to provide time-domain signal representation in a model transformer. The numerical modeling of acoustic PD data is used to support interpretations of laboratory experimental data and to enhance the understanding of acoustic wave propagation in a structure like the power transformer, and hence PD source location in the same. It is intended that an extension of the work presented here, to account for real transformer geometry and also to visualize the propagation of acoustic wave fronts, will later be compared with field results. The three-dimensional wave equation, given by c²∇²P=∂²P/∂t², where c is the acoustic velocity and P the pressure wave field, defines an initial value problem and describes time evolution. The goal of the numerical code is to track that time evolution with some desired accuracy taking into consideration the boundary conditions that govern the evolution in time of points on the boundary of the spatial region of interest. This is particularly important for the satisfactory modeling of a complex structure like power transformer. In solving the above equation using the finite-difference method, of particular interest are the conditions of numerical stability. In this paper, the authors apply the stability analysis method originally developed by Von Neumann. The simulation results are in agreement with the results obtained from the laboratory experiments.