  Grid topology and line parameters are essential for grid operation and
planning, which may be missing or inaccurate in distribution grids. Existing
data-driven approaches for recovering such information usually suffer from
ignoring 1) input measurement errors and 2) possible state changes among
historical measurements. While using the errors-in-variables (EIV) model and
letting the parameter and topology estimation interact with each other (PaToPa)
can address input and output measurement error modeling, it only works when all
measurements are from a single system state. To solve the two challenges
simultaneously, we propose the PaToPaEM framework for joint line parameter and
topology estimation with historical measurements from different unknown states.
We improve the static framework that only works when measurements are from one
single state, by further treating state changes in historical measurements as
an unobserved latent variable. We then systematically analyze the new
mathematical modeling, decouple the optimization problem, and incorporate the
expectation-maximization (EM) algorithm to recover different hidden states in
measurements. Combining these, PaToPaEM framework enables joint topology and
line parameter estimation using noisy measurements from multiple system states.
It lays a solid foundation for data-driven system identification in
distribution grids. Superior numerical results validate the practicability of
the PaToPaEM framework.

Systems and Control