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Distribution systems of the future smart grid require enhancements to thereliability of distribution system state estimation (DSSE) in the face of lowmeasurement redundancy, unsynchronized measurements, and dynamic load profiles.Micro phasor measurement units ($\mu$PMUs) facilitate co-synchronizedmeasurements with high granularity, albeit at an often prohibitively expensiveinstallation cost. Supervisory control and data acquisition (SCADA)measurements can supplement $\mu$PMU data, although they are received at aslower sampling rate. Further complicating matters is the uncertaintyassociated with load dynamics and unsynchronized measurements-not only are theSCADA and $\mu$PMU measurements not synchronized with each other, but the SCADAmeasurements themselves are received at different time intervals with respectto one another. This paper proposes a non-linear state estimation frameworkwhich models dynamic load uncertainty error by updating the variances of theunsynchronized measurements, leading to a time-varying system of weights in theweighted least squares state estimator. Case studies are performed on the33-Bus Distribution System in MATPOWER, using Ornstein-Uhlenbeck stochasticprocesses to simulate dynamic load conditions.

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and $\mu$PMU Measurements