  Distributed energy resources are better for the environment but may cause
transformer overload in distribution grids, calling for recovering
meter-transformer mapping to provide situational awareness, i.e., the
transformer loading. The challenge lies in recovering meter-transformer (M.T.)
mapping for two common scenarios, e.g., large distances between a meter and its
parent transformer or high similarity of a meter's consumption pattern to a
non-parent transformer's meters. Past methods either assume a variety of data
as in the transmission grid or ignore the two common scenarios mentioned above.
Therefore, we propose to utilize the above observation via spectral embedding
by using the property that inter-transformer meter consumptions are not the
same and that the noise in data is limited so that all the k smallest
eigenvalues of the voltage-based Laplacian matrix are smaller than the next
smallest eigenvalue of the ideal Laplacian matrix. We also provide a guarantee
based on this understanding. Furthermore, we partially relax the assumption by
utilizing location information to aid voltage information for areas
geographically far away but with similar voltages. Numerical simulations on the
IEEE test systems and real feeders from our partner utility show that the
proposed method correctly identifies M.T. mapping.
