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Grid topology and line parameters are essential for grid operation andplanning, which may be missing or inaccurate in distribution grids. Existingdata-driven approaches for recovering such information usually suffer fromignoring 1) input measurement errors and 2) possible state changes amonghistorical measurements. While using the errors-in-variables (EIV) model andletting the parameter and topology estimation interact with each other (PaToPa)can address input and output measurement error modeling, it only works when allmeasurements are from a single system state. To solve the two challengessimultaneously, we propose the PaToPaEM framework for joint line parameter andtopology estimation with historical measurements from different unknown states.We improve the static framework that only works when measurements are from onesingle state, by further treating state changes in historical measurements asan unobserved latent variable. We then systematically analyze the newmathematical modeling, decouple the optimization problem, and incorporate theexpectation-maximization (EM) algorithm to recover different hidden states inmeasurements. Combining these, PaToPaEM framework enables joint topology andline parameter estimation using noisy measurements from multiple system states.It lays a solid foundation for data-driven system identification indistribution grids. Superior numerical results validate the practicability ofthe PaToPaEM framework.

PaToPaEM: A Data-Driven Parameter and Topology Joint Estimation Framework for Time Varying System in Distribution Grids