Inversion of symmetric matrices using unsymmetrical fault analysis

Matrix inversion is a fundamental operation in matrix algebra which is widely used in many electrical engineering applications. Although there are many inversion algorithms prevalent, a new method based on unsymmetrical fault analysis is presented here. The proposed approach highlights a wonderful analogy between mathematics and electrical circuits. It focuses on finding inverse of an invertible symmetric matrix purely based on techniques developed for line to line fault analysis. First, the elements of the given matrix are used to form a bus admittance matrix. Then, a line-to-line fault is assumed to simulate a real-life scenario and power system fault analysis is used to calculate the corresponding fault current. From the thus obtained results, the inverse of the matrix is computed. Simulation is used to validate the results which demonstrate that the method can be used to perform matrix inversion of symmetric matrices using the developed concepts of power system fault analysis.