A Tensor Approach to the Mesh Resistance Matrix

This paper presents a tensor approach to obtain the mesh resistance matrix of a power system. The traditional approach to the mesh matrices naturally relates to graph theory, where the fundamental loops of a representative graph are found from a spanning tree. While valid, mesh identification is time consuming, involves unnecessary programming overhead, yields dense mesh matrices, and requires developing good search heuristics. The proposed approach uses a connection tensor to form a sparse mesh resistance matrix without resorting to graph theory. It allows for the interconnection of only those meshes circulating around the terminals of each power apparatus, which is more effective than searching for the meshes of an entire power system. Detailed steps to form the tensor and supporting examples illustrate the procedure presented in several scenarios. It is also shown that the mesh resistance matrix is sparse and that the computational effort to form the tensor is negligible.