Power grids depend on precise power measurements for various operational, economic, and security decisions. Wrong measurement data can lead to wrong or delayed decisions, ultimately wasting resources. This paper examines the detection of wrong data in active power measurements for distribution grids using Bayesian networks. Both supervised and unsupervised approaches are explored, where the supervised approach learns a Naive Bayes-type classifier from labeled active power measurements data, while the unsupervised method utilizes unlabeled data in conjunction with a surprise index (data conflict measure) to identify unusual data. An experimental analysis is conducted using a real-world dataset from a medium-voltage grid, where multiple types of anomalies are injected into the time series of active power data. The supervised model demonstrates high detection rates and short delays, while the performance of the unsupervised approach is promising.