3D-Visualization of Power System Data Using Triangulation and Subdivision Techniques

3-D surface visualizations of various power system operating quantities has always been challenging in terms of correctly capturing the changes of an arbitrary geographical shape power system. Triangulation methods offer promise for meaningful 3-D surface visualizations of such systems. In this paper we propose a scheme for such visualizations based on subdivision of triangle meshes. Input consists of various power system quantities such as voltage magnitude, voltage phase, reactive power flow, real power flow, electric current, etc. The data may be available from simulations or from real time streaming data from a model that is two-dimensional (geographic). We first perform a Delaunay triangulation on the set of 2D sites and generate a triangle mesh. This triangle mesh is used to represent a coarse 3D surface. The height of this surface at a site is equal to the power system quantity at that site. This surface is refined using the butterfly subdivision scheme with an additional constraint that the heights of the interpolated vertices lie within the bounds of the original vertices from which they were interpolated. After each level of subdivision, we perform a modified Laplacian smoothing to compensate for the discontinuity introduced due to this bounding. The method is suitable for effective visualization of large geographic data. Example visualizations and performance indices are provided in the paper.