Fast calculation of Thévenin equivalents for real-time steady state voltage stability estimation

This paper aims to present a novel approach to quickly update Thévenin equivalents of multinodal systems, which can be used to calculate long-term Voltage Stability Margins (VSMs) for real-time applications considering n-k contingencies in the grid. To accomplish this, a derivation of the Thévenin equivalent parameters of a multiport system based on the impedance matrix (Zbus) is proposed. A new methodology to quickly update the Zbus of the system when n - k contingencies occur is explained using the matrix inversion lemma (MIL) and Kron reductions. The speed of this approach is due to the avoidance of inversion of matrices that is required when Thévenin equivalents are calculated using information of the admittance matrix of the network (Y bus). Instead of this, only matrix multiplications between Zbus element and other vectors are necessary to obtain Thévenin equivalents. This approach proposes a solution for some of the current issues associated with the implementation of long-term VSMs in real-time systems.