Power Flow Solution in Unbalanced 3-Wire MV and 4-Wire LV Networks Using Symmetrical and Eigen-basis Coordinates

The large penetration of distributed generations impacts both the secondary low-voltage (LV) and the primary medium-voltage (MV) segments of the distribution network. Optimizing power flow calculations for the integrated MV/LV networks is crucial for the real-time management of modern distribution networks. Traditional methods in symmetrical coordinates are primarily limited to the three-wire model of three-phase networks, often leading to inaccuracies in power flow calculations when applied to three-phase four-wire LV segments. This paper introduces a novel power flow method for integrated three-wire MV and four-wire LV networks. Using eigenvector decomposition to diagonalize the admittance matrix of four-wire LV lines, the proposed method improves the computational efficiency of power flow calculations and accurately calculates the neutral-to-ground voltage. The results of the case studies show over 50\% reduction in the number of non-zero elements in the LU factors of the bus admittance matrix, and speed-up factors of 2.78 on the IEEE 123-node test system and 3.63 on the IEEE 8500-node test system in execution times for Volt/Var control (VVC), compared to the phase coordinates model.