Real-Time Control and Reconfiguration in Eigen-basis Coordinates for Multi-phase Unbalanced Distribution Networks

Abstract

The increasing penetration of distributed energy resources (DERs) has extended the scope of distribution network management from the medium-voltage (MV) level into the low-voltage (LV) level. This transition introduces new challenges for Distribution Management Systems (DMS) to satisfy real-time operational requirements. The combination of unsymmetrical line configurations and unbalanced load conditions in LV networks necessitates detailed multiphase modeling. These characteristics prevent the direct adaptation of computationally efficient algorithms traditionally used in transmission system management, which rely on balanced positive-sequence representations of the network. This thesis introduces the modeling of LV networks in eigen-basis coordinates to enable efficient implementation of DMS functions. The assessment and optimization functions formulated in eigen-basis coordinates include power flow calculation, Volt/Var Control (VVC), and Optimal Network Reconfiguration (ONR). The proposed model employs eigenvector decomposition to diagonalize the admittance matrix of four-wire LV lines, improving computational efficiency and accurately computing the neutral-to-ground voltage. Case studies demonstrate a reduction of over 50\% in the number of non-zero elements in the LU factors of the bus admittance matrix and speed-up factors of 2.79 on the IEEE-123 bus feeder and 3.62 on the IEEE-8500 node feeder in VVC execution times, compared to the phase-coordinate model. A framework is proposed for applying low-rank update methods to model network topology changes using the eigen-basis coordinate representation of distribution networks. The proposed framework is integrated into a heuristic ONR algorithm and tested on the non-synthetic European low-voltage (NSELV) network and the IEEE 123-bus feeder. Results demonstrate significant reductions in computational requirements compared with practical methods currently used in industry: the compensation method requires only one-third of the power flow runs needed by the multiphase power injection method to simulate a switch exchange, and the partial refactorization method achieves speed-up factors of up to 100× compared to full refactorization.