Dong Liu, Sander Timmerman, Yu Xiang et al.
Most existing phase balancing and topology reconfiguration problems are formulated as mixed-integer optimization problems that depend on network topologies~\cite{10098964,11017695,10571996}. However, these topologies are often inaccurate and outdated for distribution system operators~(DSOs) due to missing recordings, topology maintenance and reconfiguration, such as congestion management ~\cite{vanin2024phase}. Thus, the topology of the low-voltage distribution network (LVDN) needs to be checked and corrected when it is outdated. The increasing uncertainty of distributed energy resources (DERs), including household photovoltaic (PV), heating pumps, etc., impacts the frequency of topology reconfiguration and challenges the correction of the low-voltage distribution network topology~\cite{10026490, 10347462, 10475702}. Moreover, the available smart meter (SM) datasets are often limited due to privacy concerns and random communication channel failure, challenging the topology correction~\cite{9696306, costa2022identification, dande2025consumer}. Synthetic European networks and benchmark models presented in~\cite{birchfield2016grid,2020Non} are benchmarks for research but insufficient to represent the diversity of European LVDNs for practical use by DSOs (e.g., state estimation). Thus, practical topology identification and correction approaches are required for real-time topology updating for active management of LVDNs.