Inverse matrix modification lemma and Thévenin theorem for compensated network solutions

Abstract

The close relationship between the inverse matrix modification lemma (IMML) and the Thévenin theorem is investigated. Making reference to the modified network solution by compensation, the IMML formula is demonstrated using the Thévenin theorem (or its dual Norton theorem) and superposition. Such equivalence allows either approach to be applied to network modification cases with the same computation burden. However, the Thévenin–Norton approach leads to a reduced number of operations compared to IMML in those contingency cases involving solid connections (bus join). Examples of the compensation procedure based on the Thévenin–Norton approach are given with reference to IEEE and to actual large-scale power networks.