A linear programming-based matheuristic for reliable customer–feeder mapping in smart grids

Electric power distribution companies are highly concerned about their lack of knowledge about the distribution network maps used to give service to their customers. When dealing with three-phase networks, phase mapping is important to efficiently manage the power supply. However, even line mapping (which does not necessarily identify phases, just lines, or the feeders on top of them) is important for them as it allows companies to monitor other issues, such as non-registered customers, wrongly assigned meters, power transport and others. On-site verification of the network nodes is considered too complex and too costly. Since modern networks are able to record load data from feeders and customers’ meters at regular and frequent time intervals, companies prefer data-driven approaches to grid mapping. This paper introduces a mathematical heuristic (matheuristic) approach for reliably identifying meters connected to low-voltage feeders in smart grids, based on the optimization of a mixed 0-1 problem. Real-world applications often involve variables with limited presence in the problem, because their coefficients (meter loads) are small or mostly zero, compromising solution reliability. To address this, we propose a three-stage procedure leveraging linear relaxation and coefficient analysis (e.g., power consumption) to detect and mitigate sources of error. We have carried out a computational experiment using two real data sets: one consisting of partially simulated data from an unknown grid, and another in which the grid map is fully known. The proposed methodology has demonstrated notable improvements in both accuracy and efficiency. It has achieved correct meter identification rates ranging from 96% to 100%, while significantly reducing the computational effort required to solve the model. On average, computation time has been reduced by 40%–60%. In the most extreme case, this reduction has been particularly remarkable, dropping computation time from 5634 s to approximately 48 s.