Leveraging Behavioral Correlation in Distribution System State Estimation for the Recognition of Critical System States

State estimation for distribution systems faces the challenge of dealing with limited real-time measurements and historical data. This work describes a Bayesian state estimation approach tailored for practical implementation in different data availability scenarios, especially when both real-time and historical data are scarce. The approach leverages statistical correlations of the state variables from a twofold origin: (1) from the physical coupling through the grid and (2) from similar behavioral patterns of customers. We show how these correlations can be parameterized, especially when no historical time series data are available, and that accounting for these correlations yields substantial accuracy gains for state estimation and for the recognition of critical system states, i.e., states with voltage or current limit violations. In a case study, the approach is tested in a realistic European-type, medium-voltage grid. The method accurately recognizes critical system states with an aggregated true positive rate of 98%. Compared to widely used approaches that do not consider these correlations, the number of undetected true critical cases can be reduced by a factor of up to 9. Particularly in the case where no historical smart meter time series data is available, the recognition accuracy of critical system states is nearly as high as with full smart meter coverage.