An overhead power line insulator is provided including a device for detecting and measuring a leakage current and for transmitting data, the device being arranged in such a manner as to perform: measuring a leakage current of an insulator during a first measurement period and during a second measurement period in a measurement circuit; comparing two values of the current that are obtained during respective ones of the two measurement periods; and stopping the measurement circuit for a certain sleep period of time if the second value of the current is less than or equal to the first value of the current, and then starting the measurement circuit again after the certain sleep period of time.