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The anomalous data identification procedures existing today in power system state estimation become problematic-if not totally unefficient-under stringent conditions, such as multiple and interacting bad data. The identification method presented in this paper attempts to alleviate these difficulties. It consists in :(i) computing measurement error estimates and using them as the random variables of concern;(ii) making decisions on the basis of a hypothesis testing which takes into account their statistical properties. Two identification techniques are then derived and further investigated and assessed by means of a realistic illustrative example. Conceptually novel, the identification methodology is thus shown to lead to practical procedures which are efficient, reliable and workable under all theoretically feasible conditions.