State estimation is essential for a smarter monitoring and control of distribution power networks, but need to rely largely on current magnitude measurements, which causes non-uniqueness of the solution. Constraining the problem based on prior knowledge of the sign of the injections, as previously proposed, requires more complex estimators, does not always ensure uniqueness and prevents anomaly detection in the case of wrong prior assumptions. By including also prior knowledge of the magnitudes of the injections, coming from statistical load modelling, we show how it is possible to resort to conventional state estimators while achieving an increased reliability of the solution as well as the ability to detect/correct wrong prior models, using classical bad data analysis.
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